Essay Eight Part Two: Conflicting View Of Forces

Readers need to make note of the fact that this Essay does not represent my final view on any of the issues raised. It is merely 'work in progress'.

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This Essay is over 86,000 words long; a summary of its main ideas can be found here.

Quick Links

Anyone using these links must remember that they will be skipping past supporting argument and evidence set out in earlier sections:

(1) Forces And Contradictions

(a) Gravity Is Annoyingly Undialectical

(2) Is This An Apt Analogy?

(a) Are Forces Merely 'Dialectical Figures Of Speech'?

(b) Are 'Contradictions' Merely Mathematical Models?

(c) Are They Properties Of Totalities?

(3) What Exactly Do Forces 'Contradict'?

(a) Different Types Of Force Couples

(b) AA- And RR-Forces

(c) A First Attempt At Clarification

(d) AR-Forces

(4) A Contradictory Theory?

(a) Literal Forces In Opposition

(b) The Revenge Of The Non-Existent

(c) Prevention And Its Discontents

(d) A Balanced Account Of Prevention?

(e) S&M?

(f) Hole To Let

(g) Too Many Forces Spoil The Broth

(5) Real Material Contradictions -- Or Are They?

(a) Sinking In Concrete

(b) John Rees And Concrete Forces

(c) The Impertinent Explanation

(d) Conflict Resolution

(e) Where The Shoe Pinches

(f) Not What The System Ordered

(g) An Apparent Contradiction At Last!

(h) Opposite Tendencies I

(i) Opposite Tendencies II

(6) Last Rites

(a) Dialectics In ER

(b) Back To The Drawing-Board

(c) Dialectics And The Revival Of Teleology

(d) Coup De Grace

(e) For Dialectics, Truth Is The Hole, And It's Six Feet Deep

(7) True Contradictions?

(8) Well, What Are 'Dialectical Contradictions' Anyway?

(a) The Best Article I Have Read

(b) Yet Another Syntactic Mess

(c) Rosa's Pedantry?

(d) Hegel Screws Up Big Time

(e) Law Of Identity Mis-Identified

(f) More Dark Sayings From Hegel's Dungeon

(g) 'Difference' Made Unrecognisable

(h) The Fog Thickens

(i) Zeno Is No Help At All

(j) A Unity Of Opposites?

(k) The Magical Use Of 'Negation'

(l) Hegel's Hermetic House Of Horrors

(m) Acid Corrodes Hegel's 'Logic'

(n) Two Senses Of "Independent" Confused

(o) Threadbare

(p) What A Dialectical Dog's Dinner!

(9) Contradictions In Das Kapital?

(10) Notes

(11) References

Abbreviations Used At This Site

In Part Two of this Essay, I intend to substantiate a claim made in Part One, which was that it is not possible to equate 'contradictions' with 'opposing forces', either literally or figuratively.


Forces And Contradictions

DM-theorists frequently assert that "contradictions" (in nature or society) may be understood as the inter-relationship between "opposing forces". These forces condition one another, and, according to some, they operate either in equilibrium or in disequilibrium, depending on circumstances -- but, only as revealed by careful scientific analysis, tested in practice.1

Citations like those listed in Note 1 -- that make the same point -- can be multiplied almost indefinitely. To be sure, such passages are often accompanied by extensive qualifications, depending on context, but the overall message is reasonably clear.2

Nevertheless, my concern here is not so much with whether these passages are consistent with one another, or even whether any attempt has (ever) been made to substantiate the sweeping statements they contain with adequate evidence -- or any at all --, but with whether the idea that forces can model contradictions itself makes any sense.3


Gravity Is Annoyingly Undialectical

As we will see, the identification of forces with contradictions is highly dubious, at best.4 There are several obvious initial difficulties with the whole idea. For example, if the forces in a system are in 'conflict' -- and are hence 'contradictory' -- there would clearly have to be at least two forces present, operational and oppositional for that to be the case. But when we consider one of the most important and general types of motion found in the universe -- the orbital trajectory of bodies in a gravitational field -- we find that in classical Physics, at least, this sort of motion is governed by the operation of at most one force, which deflects the otherwise (assumed) rectilinear path of the body in question toward the centre of mass of the system. So, if classical Physics is correct, it is not easy to see how such forces could be viewed as 'contradictions'.5

Even post-classical Physics offers little comfort for DM-theorists; here such motion is either a function of the topology of Spacetime (gravitational 'force' having been edited out of the picture), or it is the result of a body being situated in a tensor, vector and/or scalar field, in as many dimensions of phase space as are deemed necessary.6

And this is not just true of gravity; as Max Jammer notes:

"[The eliminability of force] not confined to the force of gravitation. The question of whether forces of any kind do exist, or do not and are only conventions, ha[s] become the subject of heated debates....

"In quantum chromodynamics, gauge theories, and the so-called Standard Model the notion of 'force' is treated only as an exchange of momentum and therefore replaced by the ontologically less demanding concept of 'interaction' between particles, which manifests itself by the exchange of different particles that mediate this interaction...." [Jammer (1999), p.v.]6a

Even comrades Woods and Grant acknowledge this fact:

"Gravity is not a 'force,' but a relation between real objects. To a man falling off a high building, it seems that the ground is 'rushing towards him.' From the standpoint of relativity, that observation is not wrong. Only if we adopt the mechanistic and one-sided concept of 'force' do we view this process as the earth's gravity pulling the man downwards, instead of seeing that it is precisely the interaction of two bodies upon each other." [Woods and Grant (1995), p.156.]

However, and despite what these two say, a mere "relation" between two bodies would be incapable of making one or both of them move, unless there was a force there (or something else consequent on that relation  -- such as a time-based trajectory along a "world-line", perhaps?) to bring this about.

Unfortunately, this now means that most (if not all) of the bulk motion in the universe cannot be accounted for by DM (that is, if it is viewed as the result of 'contradictions', which are then interpreted as opposing forces). Plainly, if there is only one force present (or perhaps none at all), there could be no dialectical 'contradictions'. Hence, it would seem that DM can't explain much -- if any -- of the movement found in nature.

[DM = Dialectical Materialism.]

Admittedly, Engels made a weak attempt to solve the orbital 'problem' by inventing a repulsive force, which he implausibly identified with "heat"; this fanciful notion is discussed in Note 7.7


Is This An Apt Analogy?

Are Forces Merely 'Dialectical Figures Of Speech'?

In view of the above, it might be wise to interpret "opposing forces" as figurative 'contradictions' -- or, maybe, the other way round, interpreting 'contradictions' as figurative "forces". Either or both of these could then form part of an analogical or perhaps metaphorical (but non-literal) depiction of nature. Alternatively, forces could be described as 'contradictions' as a part of a sort of shorthand, which would then enable the modelling of different types of accelerated motion. Naturally, that approach would allow the word "force" to be edited out of the picture as a physical entity in its own right. Indeed, Engels seems to have had this in mind in the quotation below, where he argues that attraction and repulsion should not be regarded as forces, but as simple forms of motion. This retreat was perhaps recommended to him by his admission that the concept "force" was derived from ancient animistic/mystical views of nature, hence its use in DM could smack of anthropomorphism:8

"All motion is bound up with some change of place…. The whole of nature accessible to us forms a system, an interconnected totality of bodies…. [These] react one on another, and it is precisely this mutual reaction that constitutes motion…. When two bodies act on each other…they either attract each other or they repel each other…in short, the old polar opposites of attraction and repulsion…. It is expressly to be noted that attraction and repulsion are not regarded here as so-called 'forces', but as simple forms of motion.... [Engels (1954), pp.70-71. Bold emphasis added.]

"All natural processes are two-sided, they are based on the relation of at least two operative parts, action and reaction. The notion of force, however, owing to its origin from the action of the human organism on the external world…implies that only one part is active, the other part being passive…[and appearing] as a resistance." [Ibid., p.82. Bold emphasis added.]

However, this revision has two untoward consequences Engels appears not to have noticed:

(1) It makes his version of DM look even more positivistic that it already seems (at least in DN). If the appeal to forces in nature is no more than a shorthand for the relative motion of bodies, then forces will have no real counterparts in nature. The whole idea would then be little more than a "useful fiction", invented to account for the phenomena instrumentally. This would make the identification of forces with contradictions even more problematic (as will be demonstrated below); plainly, and once again: if there are no forces, there can be no DM-'contradictions'.

[DN = Dialectics of Nature, i.e., Engels (1954); UO = Unity of Opposites.]

(2) Given this re-write of the word "force", the contradictory relationship between bodies would become little more than a re-description of their relative motion. [Woods and Grant seem to be thinking along these lines, as we saw earlier.]

Unfortunately, in that case, there would be no interconnection between such bodies -- which is an essential factor, required by other DM-theses. This seems to mean that causal interactions of this sort would now be externally-motivated, and not mediated by forces, or be internally-driven. On this account, the 'unity-in-opposition' between antagonistic elements in the Totality would have been sundered; the thesis that change is the result of 'internal contradictions' would then be left without any sort of internal or mediating source.

Even the relative motion between bodies travelling in opposite directions could not supply a credible dialectical connection here, should such bodies interact, Clearly, this would fail to capture the "internal relations" that DM-theorists claim exist between such bodies. Objects behaving like this would not be internally interrelated (as part/parts of a UO), since the connection (mediation) between bodies in motion would be missing. Hence, any subsequent interaction would be difficult to account for philosophically, which would not be good news for dialecticians.9

As already noted, with events and processes sealed-off from each other in this way DM would begin to resemble CAR and/or 'crude materialism' all the more. Of course, even if Engels's version of DM could account for motion occurring along a certain line of action -- but in diametrically opposed directions --, it would be of little help because most of the bulk motion in the universe is not of this sort; it is either orbital or motion along a geodesic (depending on which version of modern Physics one attends to). In fact, as we will see, matter in general moves in complex ways which are difficult if not impossible to depict in oppositional terms.

[CAR = Cartesian Reductionism.]

Like it or not, DM-theorists need real material forces to act between bodies so that their Totality has the holistic/mediated integrity it requires; a theoretical fiction would be no use at all. Forces must exist, and reference to them as 'contradictions', 'internally-related' to one another, must be literal.10

Anyway, the figurative reading of forces as 'contradictions' runs counter to the claim advanced by dialecticians that they are offering a literal and 'objective' account of nature. It is not at all easy to see how figurative language can fill in the physical gaps in an explanation, any more than, say, the following can account for Juliet's beauty:

"But, soft! what light through yonder window breaks?
It is the east, and Juliet is the sun.

[Romeo and Juliet, Act Two, Scene Two.]

Or, at least, any more than would describing a man as a "pig" imply he has a curly tail and is a potential source of bacon.

Despite this, in view of the above difficulties -- in addition to those retailed below --, interpreting forces figuratively might prove to be the only viable way that contradictions could be regarded as 'forces', even if this compromises DM's avowedly 'objective' picture of reality.11

Of course, if this view of the nature of forces were adopted by dialecticians, it would be difficult to distinguish their theory either from Instrumentalism or from Conventionalism.

However, and once again, it is not easy to see how 'figurative forces' could account for anything; what sort of explanation would it be to say that contradictions -- already themselves suspiciously figurative -- were modelled by forces, which were figures of speech, too? Describing a man as, say, a "pig" might perhaps account for his crude behaviour (but not on the basis of his anatomy or physiology as a literal pig), but the utility of this metaphor would be virtually nil if it were now admitted that the word "man" was figurative too. Unlike iterated negations, multiple tropes do not cancel.

Nevertheless, even if this proves to be an acceptable resolution of Engels's problem, it would still not provide DM-theorists with a viable way out of their difficulties. Taken literally or figuratively, the equation of DM-'contradictions' with forces cannot work  -- whether this applies to events in nature or society. This is so for several reasons.


Contradictions As Mathematical Models?

The first of these is connected with the way that forces are already represented in mathematics, for example --, which does not appear to be even remotely appropriate for exportation and use in depicting contradictions as literal forces. Consider the following:


(A) Forces often operate according to an inverse square law. It is not easy to see how the same could be true of contradictions. Presumably, two objects, states of affairs or processes contradict each other in nature or society or they do not.12 Not much sense can be made, one presumes(!), of the idea that a contradiction could operate with, say, only 25% of its former intensity (or whatever the appropriate descriptor is here) if the distance between its oppositional elements is doubled. Do bosses really become more conciliatory if workers walk away from them? Does wealth cause less conflict if the rich move their money to the Cayman Islands? Do appearances contradict reality any the more if someone uses a microscope, or presses his/her face against a desk?13


Indeed, little sense could be given to the idea that there is a literal separation distance between such elements -- for instance, that there is, or could be, one such between Capital and Labour, or that there might be one between the "forces and relations of production", or that there is another between a body and itself as it moved along in a 'contradictory' sort of way. What could it possibly mean to suggest, for example, that the "contradiction between use value and exchange value" changes if the two are further apart? Clearly, these two 'entities' cannot be separated (except perhaps in thought), but even if they could, they would still be just as contradictory as they were before (one presumes?). And yet, no force in nature has its local or remote strength unaffected by such changes.


Sure, dialecticians speak about the "contradictions" in the capitalist system "intensifying", but this is not because the 'separation distance' between the classes has decreased. Whatever DM-theorists in fact mean by "intensification" here (which seems be that the alleged "contradictions" become more obvious, intractable or crisis-ridden), they certainly do not mean it in the same way that physicists mean it when they talk about, say, the strength of a force field intensifying. Nor is there any mathematics involved. Indeed, while a technician might be dispatched to measure the intensity of a force field in genuine scientific research, no one ever seems to have been asked to do the same with these "intensifying" 'dialectical contradictions'. They (or at least their 'strength') appear to be permanently locked in subjective space, stubbornly impervious to scientific investigation.

Odd that...

(B) Forces in nature can be represented by vectors, the use of which is governed by well-understood rules. As such, for example, they may be inclined at various angles to one another, added, subtracted and multiplied (to give inner, vector or scalar triple products, and the like) -- and by means of which, diverse quantities, such as areas, volumes, field densities, boundary flux (etc.), may be calculated. In addition, vectors may be parallel or orthogonal, to one another, or to previously defined axes, just as they may be decomposed into their components and projected onto a given direction, plane or surface. They can be used to identify and classify the mathematical properties of manifolds. Unit vectors can be defined in a given vector space, providing it with a base and spanning set. Modulii can be ascertained for any given vector, and so-called "Eigenvectors" can be calculated. Furthermore, matrices can be employed to represent vectors more efficiently, their determinants and inverses thus calculated. The ordinary and partial derivatives of vectors may be derived -- and, finally, they can be integrated (as part of line, surface or volume integrals), and so on.

It is difficult to see how any of the above (and a many others) could be true of a single DM-'contradiction' interpreted (literally or metaphorically) as a force. What, for example, is the angle between the 'contradictions' mentioned on the opening pages of TAR:

"[S]ince the Second World War there have been 149 wars which have left more than 23 million dead…. On an average yearly basis, the numbers killed in wars during this period have been more than double the deaths in the nineteenth century and seven times greater than in the eighteenth century…. Regression, by any criterion. Yet it is the very same development of human productivity that gives rise both to the possibility of life and to its destruction….

"Everywhere we look another paradox appears. How can it be, for instance, that in the richest capitalist society in the world, the United States, real weekly incomes have fallen steadily since 1973?… How is it that in Britain, where the economy, despite the ravages of recession, produces more than it has ever done…a full quarter of the population live below the poverty line?

"The contradictions are no less striking if we shift our gaze from economics to politics. The introduction of the market to Russia and Eastern Europe was supposed to bring stability and prosperity but has actually produced the opposite." [Rees (1998), pp.1-2.]

And what is the cross product between these found in Socialist Worker:

"Elvis's career illuminated a contradiction at the heart of capitalism. Capitalism needs to generate profits in order to survive. But to suck profit out of workers it also needs an ideology to ensure that workers know their place in society...." [Ian Birchall, Socialist Worker, 14/08/07.]

"However, there are contradictions in the role of prison officers.

"It is summed up by Cardiff prisoners chanting "you're breaking the law" to the strikers....

"Prison officers' work, upholding law and order, frequently pushes them to accept the most right wing ideas and actions of the system. One of their main jobs is to control prisoners –- and throughout the prison system, many officers have a proven record of racism and violence.

"Some of the contradictions can be seen in the strike. In Liverpool the POA shop steward Steve Baines responded to the high court injunction by telling fellow strikers, "Tell them to shove it up their arse, we're sitting it out."

"Yet when prisoners in the jail protested against their treatment, the POA members rushed back in to control the situation and end a roof top protest." [Simon Basketter, Socialist Worker, 30/08/07.]13a

Is it possible to find the inner product of the 'contradiction' between freedom and necessity? Is there an eigenvector applicable to the 'contradiction' between appearance and underlying essence? Is there any way of specifying the extent to which bosses and workers -- Capital and Labour -- contradict one another, individually or as classes? If so, what is the modulus of the 'contradiction' between boss NN and worker MM (or that between the classes to which they belong)? Is the 'contradiction' between ice and water orthogonal to…, well what?

But, what of the div, curl and grad of the 'contradiction' between a grain of barley and the plant that grows from it? Can we ascertain the Jacobian for the contradictory relationship between wealth and poverty? Is the 'contradiction', between "John" and his "manhood" normal to a given direction or manifold?

In her otherwise excellent book, Lindsey German says the following:

"The Working class has to have a party to overcome the contradiction between its potential revolutionary role and its actual situation. To overcome this contradiction requires a conscious struggle by an organised minority…." [German (1996), p.87.]

But, if contradictions were literal forces, we would be able to ascertain, say, the i, j and k components of "the contradiction between [the] potential revolutionary role [of the working-class] and its actual situation", differentiate them, and find out how quickly the said link was changing, and in what direction.14 The fact that we can't do this -- and no sane Marxist has ever even so much as attempted to do it (nor yet even theorised about doing this) -- suggests perhaps that in practice not even DM-fans think this analogy is at all apt, or, indeed, all that literal.

Hence, if 'contradictions' could be interpreted literally as forces, it would be possible to construct a vector algebra depicting them in nature and as part of the class struggle. Do we possess such a 'Vector Algebra of Revolution'? Has anyone ever bothered to construct one? Given the title of his book, the author of TAR was strangely silent on this issue.


Properties Of Totalities?

The second reason why this is an inappropriate way to depict 'contradictions' arises from a consideration of the sort of response that could be made to the objections outlined above; it could be claimed that it's the inter-relationship between contradictory forces that explains change, and hence that it is only within a network of forces situated in a Totality of some sort that the contradictory inter-play between them becomes clear. Indeed, it could be argued that the above interpretation of contradictions (which pictures them as seemingly isolated entities) completely misconstrues both their role in DM and their operation in nature and society.

This volunteered objection was in fact considered in Part One of this Essay -- but from a slightly different angle -- where it was pointed out that there is a serious ambiguity in DM/'Materialist Dialectics' on this issue. That is because DM-theorists are hopelessly unclear whether 'contradictions' are (1) internal to objects and processes (causing them to change as a result of an internal dynamic), or whether they (2) merely arise externally between objects (as they form part of a mediated system, group of systems or processes), or (3) if it is just our description of objects and processes which is 'contradictory' (this resulting from our partial knowledge of reality, etc.), or (4) if it is a combination of all three -- or indeed whether something else is true of these elusive DM-'contradictions'.

And as we also saw in Part One of this Essay, while each of these options faces serious difficulties of its own, they all fail to explain change since they merely re-describe it in an inappropriate and obscure form. Worse still, they become incoherent when examined closely (as we will soon see is also the case with respect to forces and 'contradictions').

In response to this, it could be argued that the problem with the sort of analysis of dialectical systems presented here is that it attempts to 'objectify' contradictions (i.e., make objects out of them). Hence, it could be pointed out that in Materialist Dialectics it is not 'objects' that are subject to contradictions -- or contain them, or which are them --, but systems/totalities in change that reveal their inner contradictions, the latter of which in turn drive change along. In that case, it could be maintained that contradictions are properties of systems/totalities in the process of change and development, but not of objects as such.

In reply to these volunteered DM-responses it is worth asking where this leaves forces if contradictions are no longer to be viewed as objects or as object-like. Forces presumably have a physical form of some sort; they are not just relations, are they?

But, even if they were, it is far from easy to see what it is that could possibly physically relate objects and processes in nature and society, that is, over and above a few Hegelian 'concepts' of dubious provenance and even more dubious content.

Indeed, in all this it seems that the idea that objects change because of an 'inner dynamic' has been lost again. If objects change only because of a set of external forces -- albeit internal to a "Totality", mediated or not by the obscure 'influence' of that "Totality" --, this can only mean that "external" has now become the new "internal". In that case, "internal contradictions" are in effect those which an object merely experiences in its external relations with other objects and processes in a given "Totality". But, once more: what is the point of arguing that change is "internally-motivated" if external mediation is the only show in town, and forces are merely "relations"?

[As we will see in Essay Three Part Three, these "relations" are 'logical' anyway, and no less bogus for all that.]

In addition, the proffered DM-response outlined a few paragraphs back fails to resolve the problems mentioned earlier. First of all, as we will also see in Essay Eleven Part One, there is good reason to question the nature of the nebulous DM-"Totality" -- or, to be more honest, there would be if we knew what 'it' was (and there was some sign that dialecticians themselves knew what 'it' was!). Its re-appearance here can only cloud the issues, therefore.

Secondly, even if a clear account of the "Totality" were forthcoming, this way of depicting forces would still not work. If contradictions are properties of totalities -- and not of their parts -- then the parts could not change, since, on this account, contradictions would not belong to them, but to the whole, taken as a whole. In that case, while the whole might change, it would do so only as a result of the rearrangement of its changeless parts. [This was argued in detail in Part One of this Essay.] Given this way of thinking, the "Totality" (or, indeed, any sub-totality) would be composed of infinitely small changeless elementary particles, or it (they) would be composed of infinitely complex further sub-systems, themselves enjoying no interconnections. [The reader is referred back to Part One for more details.]

Again, it could be objected that a Totality is constituted by its own internal contradictory processes; that is precisely what a Totality is -- a contradictory, differentiated unity. The account given above seems to want to separate the parts from the whole.

However, this reply will still not do, for on that account it would now seem that it is both part and whole which is contradictory (and in a manner that is still unclear). And yet, such parts can't be contradictory in the same way that wholes are. This is because, on this account, parts mutually condition one another; this, presumably, is the nature of their mediated unity in contradiction. However, the "Totality" is related to nothing else that could condition it (since the 'it' is not separable from its parts). So, if the "Totality" is a contradictory whole, then it would have to be such in a new and as yet unspecified sense.

In fact, as seems obvious from what little DM-theorists themselves have told anyone about their "Totality", it looks like 'it' must be an unconditioned Absolute. It certainly cannot be conditioned from the 'outside', otherwise it would not be the Whole. Of course, if on the other hand, it were conditioned from the 'outside', an infinite 'exgress' (inflation) would be implied, for, plainly, we should want to know how this 'other thing' (about which we know even less) was conditioned, and by what -- and so on.  But we have been here already.

It seems that these observations must apply otherwise, for the "Totality" to be contradictory, it would have to 'contradict' its partsEx hypothesi it would have to do this anyway, since there is nothing else for it to condition. Moreover these parts must then contradict each other in turn in the same way, after all. [The opposite supposition will be considered presently.]

And yet, if the "Totality" is composed solely of its parts (unless it is more than its parts -- that particular dead end is revealed for what it is in Essay Eleven Part Two), the contradiction between the "Totality" and its parts must (1) be the same as the contradiction between each of the aforementioned parts. In that case, it seems that the "Totality" could drop out of the picture as a shorthand for the sum total of parts in contradictory change. It, too, would become a mere fiction -- only this time a useless one.15

On the other hand, (2) if the "Totality" were more than the sum of its parts (as all dialecticians seem to believe),16 we would then be owed an explanation of the alleged 'contradiction' between this 'more' and that 'less' -- that is, between this 'more-of-a-"Totality"' and its lesser parts. But, as things stand, we have no idea whether this new 'contradictory' relation between whole and part is the same as that which operates between the parts, or if it is different.

[Anyone impatient with this nit-picking should re-direct their complaints to their local Dialectical Magus; this enforced pedantry is necessary because, even now, after 140+ years, dialecticians have yet to tell us what these 'forces' are, how they can possibly 'contradict' one another, and what their mysterious "Totality" actually is.]

However, independently of a resolution to the last series of problems ever being attempted, this 'theory' still faces other serious difficulties. If the 'contradiction' between the whole and its parts is the same as (and no more than) that which exists between the parts, then manifestly the whole would not then be more than the sum of the parts (in at least this respect), since the whole would in that case be the entire 'contradictory' whole, all of whose elements (whole and part) operate alike. But, this would be contrary to the DM-hypothesis that wholes (whether these are wholes made of 'contradictory' parts or not) are more than the sum of their parts, whose natures (including the nature of their "internal contradictions") are said to be determined entirely by (while not reducible to) the nature of their parts, and their interconnections. Conversely, if the 'contradiction' between the whole and its parts were not the same as that between the parts themselves, then we would still have an unexplained type of 'contradiction': that which exists between a whole that is more than the sum of the parts and those parts.17

Anyway, the idea that the whole 'contradicts' the parts in the same way that the parts do one another does not appear to be a viable option for DM-theorists. The parts relate to each other by "mediation, apparently; but how can the part-whole relation be one of mediation? The mutually 'contradictory' nature of the parts in development constitutes the whole; if now the whole has its own 'contradictory' relation with the parts over and above this (if it is more than the sum of the parts), then this new 'contradictory' relation cannot be one of part on part. But, if it is not this, then what is it?

Hence, as noted in Part One of this Essay, it seems that a literal interpretation of 'contradictions' as forces lapses either into some form of CAR, or expands into HEX/AIDS. Conversely, if the identification of forces with contradictions is figurative, then DM would be indistinguishable from, say, metaphysical poetry; and a rather prolix version, at that.

[HEX = Hegelian Expansionism; AIDS = Absolute Idealism; CAR = Cartesian Reductionism.]

However, in order to examine this issue more thoroughly, let us assume that the above objections are totally misguided in some as yet unspecified way. In addition, let us further suppose that some sort of solution to all the above 'difficulties' can be found -- by someone at some point, somehow.

Even then the analogy between forces and contradictions would not work

The substantiation of this latest claim brings this discussion to the third reason for questioning the connection between forces and 'contradictions'.


Contradictory To What?

Different Types Of Force Couples

In a physical system there may be several different combinations of interacting attractive and/or repulsive forces. If we abbreviate "attractive" and "repulsive" to "A" and "R", respectively, there appear to be only three types of combinations of just two of these: "AA-", "AR-" and "RR-forces".18

Many of the quotations given in Note 1 seem to imply that only AR-forces are 'contradictory'. This sort of combination will be examined later. However, AA- and RR-forces were not explicitly ruled out, and in a thoroughgoing analysis of every conceivable option available to DM-theorists, these clearly need to be considered. Hence, it is to these that we now turn.


AA- And RR-Forces

Unfortunately, it is difficult to see how AA-forces could be interpreted as unities of opposites -- let alone as 'contradictory'. They are the same, so they can hardly be opposites. But, such forces abound in nature. For example, as noted earlier, the centre of gravity of any conglomeration of matter in the universe is the result of countless such AA-forces; in systems like this, kinematic (or rather dynamic) changes are caused by non-opposites. So, when, say, a planet is in the process of formation, particles begin to gravitate together under the operation of forces of mutual attraction --, i.e., these aforementioned non-opposites.19

Similarly, it is not easy to see how RR-forces could be interpreted as 'contradictory' -- or even as opposites -- and yet these are also found throughout nature. For example, intra-atomic forces of repulsion prevent nuclei from approaching one another.20

One objection to above immediately springs to mind: this analysis ignores the fact that such forces operate as they do because they work in opposition to one another -- that is, they do so in ways that bring them into, or out of equilibrium. However, this response clearly pictures forces as AR-couples, which option will be examined later. It cannot therefore assist us in our attempt to analyse AA- and RR-forces.

Despite this, even on that interpretation a problem still persists. If it were true that A-forces are the opposites of each other, then in order for them still to be regarded as 'contradictory' they could not also be regarded as the opposite of R-forces, unless, that is, A-forces are now permitted to have two sorts of "opposites": other A- and other R-forces. But, in that case, this would make a mockery of the notion that there are "polar opposites" at work in natural systems of forces (implicated in change, equilibria and in 'contradictions'):

"All motion is bound up with some change of place…. The whole of nature accessible to us forms a system, an interconnected totality of bodies…. [These] react one on another, and it is precisely this mutual reaction that constitutes motion…. When two bodies act on each other…they either attract each other or they repel each other…in short, the old polar opposites of attraction and repulsion…." [Engels (1954), pp.70-71. Bold emphasis added.]

It is difficult to see how a particular A-force could be the "polar opposite" of another A-force while at the same time being the polar opposite of an R-force -- i.e., how A- and R-forces could have two "polar opposites" without altering the meaning of the phrase "polar opposite". Even then, if the meaning of "polar opposite" were adapted to neutralise this 'difficulty', it would succeed in doing that only because of an ad hoc subjective and conventionalised linguistic adjustment. In that case, any 'truths' that sprang into existence as a result would plainly be a by-product of yet another piece of terminological juggling, not because of the way the world happened to be (and which would mean that dialectics had been read into nature).21

However, there are dialecticians who claim that objects and processes possess many "opposites"; for example Gollobin (1986), p.122 (but even he says these are "paired").

Of course, this whole metaphysic originated in the twisted 'logic' that one finds in Hegel, who posited a unique opposite (an "other") for each and every changing item, in order to forestall the criticism that if anything could change into 'what-it-is-not' (its 'opposite'), then since everything else in the universe is 'what-it-is-not' to any given object or process, any object or process could and would change into that anything-else-whatsoever.

In which case, instead of growing into barley plants, seeds, for example, would turn into volcanoes, unexploded bombs, Stalin's moustache or your left buttock -- and much else besides.

[In Note 67 we will see that even Hegel had to abandon the odd idea that objects and processes were somehow linked to a logical(?) and unique 'opposite'/"other".

As Essay Seven also showed, this is just one of the fatal consequences of the sloppy use of language found in DM/'Materialist Dialectics', as dialecticians try to depict the changes they tell us are initiated by UOs (as part of Engels's second 'Law').]

But, if objects and processes are allowed to have many (and possibly an infinite number of) 'opposites' -- all of which they could change into --, that would demolish even this crumbling Hegelian wall (i.e., that each object/process has its own unique "other"). Naturally, if true, that would mean that any minute now you could expect to change into, say, a T Rex, and the Pacific Ocean could morph into you (and a host of other things, into the bargain). Since this sort of thing does not happen, so far as we know, then we must conclude:

(1) Hegel was right that objects and processes really do have only one unique 'other', which is either (a) (logically?) internal to that object or process (meaning that that object or process cannot turn into this 'other', since it already exists!), or, (b) external to that object or process (meaning that the cause of change cannot be internal to that object or process), or (c) external to that object or process, which object or process turns into that 'other', and thus creates it the process of change (meaning that change cannot have been caused by that 'other', which means that the whole point of this 'logical' exercise would disappear); and thus that:

(2) Forces can have only one opposite, not many.21a

Nevertheless, it could be argued that the word "opposite" really means "oppositional" in this context. This change of emphasis now underlines the active inter-relation that exists between forces rather than their passive connection, which is something the above discussion seems to have ignored. Hence, it might be natural to speak of RR- or AA-forces as contradictory in this sense --, i.e., in the sense that all and only those forces that are oppositional (which engage in, or are part of, some sort of "struggle") should be classed as contradictory.

However, this latest revision seems to be inconsistent with the claims made in several of the passages quoted in Note 1. These appear to suggest that only certain forces were to be regarded as inseparable from matter; others indicated that forces were merely the consequence of the complex inter-play between quanta of energy (or of motion). For example, Engels claimed that:

"The whole of nature accessible to us forms a system, an interconnected totality of bodies…. [These] react one on another, and it is precisely this mutual reaction that constitutes motion…. When two bodies act on each other…they either attract each other or they repel each other…in short, the old polar opposites of attraction and repulsion…. It is expressly to be noted that attraction and repulsion are not regarded here as so-called 'forces', but as simple forms of motion." [Engels (1954), pp.70-71. Bold emphasis added.]

Once again, this qualification seems to lose sight of internally-connected oppositionality. In this passage, Engels appears to edit out of the picture the dialectical interrelation between forces, replacing it/them with mere "forms of motion".

Now, "forms of motion" are not in any obvious way interconnected if the relevant forces are left out. But, DM requires bodies in motion to be inter-related; that is why intermediary forces seem to be essential. 'Contradictions' were clearly supposed to assume just such a role --, i.e., as part of the 'connective tissue' of reality (as it were). If they are now to be re-classified as little more than 'useful fictions' -- as relative "forms of motion" --,  there would seem to be nothing physical left in nature to act as either the bearer, or the mediator, of such DM-interconnections. Without a material substrate, 'contradictions' could only operate on bodies or processes magically, or,  perhaps supernaturally, it would seem.

Ignoring for the present this serious difficulty, perhaps DM-theorists mean something like the following:

F1: All and only those forces that are oppositional -- or are implicated in struggle -- are contradictory.

But, if F1 were true, motion itself could not be regarded as a product of 'contradictory forces' -- unless we confine our attention solely to accelerated motion -- since, ex hypothesi, no net forces operate in cases where there is no acceleration (in post-Aristotelian Physics, that is). Even then, accelerated motion (under gravity, say) is subject to only one force (or, rather, one resultant force) in classical Physics, and none at all in relativistic Physics.

At best, therefore, taking a classical view, most of the accelerated motion in the universe (which covers, as far as we know, all of the bulk, non-rectilinear movement in nature) is the product of only one force. Given F1, it is not easy to see how such motion could be viewed as part of a 'contradictory' Totality, if the 'classical view' is correct. If it is correct, most (perhaps all) of the motion in nature could not have been induced, caused, changed or sustained by 'contradictions'. With that observation, much of classical DM collapses.22

It could be objected to this that as a matter of fact all motion in the universe is the result of a disequilibrium between oppositional forces; that is precisely what a resultant force is. In that case, therefore, bodies would move (or their state of motion would change) because of just such an imbalance between forces. Hence, for example, the planets -- which move in apparently steady orbits around the Sun -- actually have their trajectories determined by resultant forces internal to the Solar System, the Galaxy and beyond, all of which are induced by complex inter-relating systems of forces. Or so it could be argued.

This objection will be considered in more detail later, but for now it suffices to point  out that it is difficult to see how such forces could be regarded as oppositional. Presumably, these forces do not affect each other; they simply change whatever motion is present in the system, or in certain bodies. At best, such forces could only oppose the impressed motion already present -- which motion would itself have been the result of still other forces in the system. This can be seen from the fact that if the moving bodies in question had not been in the said 'force field', the said forces would have had nothing on which they could act; hence, in 'empty space', we would see no new motion, clearly.23 Forces without bodies to operate on do not interfere with each other, as far as we know -- unless they are themselves regarded as particulate (or are carried by particles), and would then, of course, not be forces but bodies, to begin with.24

Classically, forces seem to work only on bodies by altering their motion. In which case, the supposed opposition is not between bodies, nor is it between bodies and forces, nor even between forces and forces -- it is between forces and the already impressed motion of bodies. But, this picture is difficult to square with the idea that there is a UO at work in such systems -- nor does it seem to tally with the claim that dialectically polar opposites ultimately induce all motion and change. This is because (once more) forces do not oppose each other; they oppose or augment whatever motion is already present in the system, however that was caused.

In short, on this 'revised' view, the term "contradiction" would not apply to opposing forces (i.e., to forces that oppose one another), nor to bodies; on the contrary, 'contradictions' would connect forces with movement. But, as yet, no DM-theorist has given any clear sense to the idea that a force could 'contradict' the impressed motion in a system. And quite right too; there are no opposites here for a DM-'contradiction' to latch onto. How could a force be the 'opposite' of a change of place?

It could be objected that as a matter of fact forces in nature oppose (in the sense of change) motion. Indeed, it could be argued that dialecticians examine forces as they actually operate in nature (as opposed to those abstracted from it); such opposites objectively exist and cannot be analysed away. Or, so it could be maintained, once more.

This much will not be disputed here (even if its wording might). But, in what way can this set-up be said to involve the interconnection of opposites? And, what sense can be given to the idea that motion in one direction is the opposite of a force that affects it? Certainly they are not unified opposites (i.e., opposites on the same type, so they are not logically connected, in the Hegelian sense of this word).

At best, the force concerned might tend to produce an opposite motion (or change in movement perhaps) to that which has already been impressed (or none at all). But to describe force and motion as "opposites" would appear to make about as much sense as claiming that "left" was the opposite of "television set", even if as a matter of fact someone moved a television to the left. Their actual linkage in reality has nothing to do with whether it is sensible to describe such items as unified opposites, or even as oppositional. These terms are categorically different -- as are "force" and "motion". Hence, it is not a question of whether DM-theorists are dealing with 'objective' facts, or not; it is one of asking why this proffered objection can only be made to work by mis-describing things.25

Only those who feel confident that they can provide a clear sense to the idea that forces and motion are opposites may reject the above objection with anything more than a wave of the hand.26

However, even if this could be done, it would still be bad news for DM. This is because any other allegedly oppositional force in the system could not then also be the opposite of the original duet between this force and that motion. And that would then mean that systems of opposing forces could not function in DM as is currently supposed. In that case, it would not be forces that opposed one another (as had originally been claimed); in such a set-up, forces would oppose impressed motion (not other forces), and the idea that change was the result of systematically inter-related forces would have to be abandoned.

Indeed, each item in a complex ensemble of this sort would have to be viewed as the opposite of every other. Given such an arrangement, any moving body would have countless 'opposites' (i.e., any other forces and/or moving bodies in the system).27 This would put a strain on the meaning of the word "opposite", once more, which would remain until the meaning of that word had been altered accordingly, so that several things could be regarded as the "opposite" of any one or more items. Under such circumstances, as we have already seen, the notion of a polar opposite would lose its key role in DM; indeed, it would clearly become meaningless if everything possessed innumerable "polar opposites". Not only that, as we have also seen several times, given such ad hoc linguistic tinkering, dialectics would apply to nature and society only because of a new and subjectively applied linguistic convention.

Unfortunately, this jellyfish-of-a-theory cannot be squeezed anywhere without some of it slipping through our fingers somewhere else. What had been touted all along as a grand theory that could explain change as a consequence of the 'contradictory' nature of reality -- or, as the result of the connection between opposite forces -- now seems to amount to little more than a few vague ideas about the relation between a force and the impressed motion in a system, fatally linked to the admission that the DM-Totality is a mediated system of forces only if the definition of a "polar opposite" is 'adjusted' to order. If this is what DM-theorists mean when they asserted their impressive sounding 'dialectical' theses then it seems that their theory can only be rescued by making reality Ideal -- i.e., making its 'truth' sensitive to ad hoc linguistic 'enhancement'.

However, even if the above is misguided in some way, in DM-terms, none of it makes any sense, for such opposites (force and motion) would not turn into one another, as the DM-classics say they should:

"The law of the interpenetration of opposites.... [M]utual penetration of polar opposites and transformation into each other when carried to extremes...." [Engels  (1954), pp.17, 62. Bold emphasis added.]

"Already in Rousseau, therefore, we find not only a line of thought which corresponds exactly to the one developed in Marx's Capital, but also, in details, a whole series of the same dialectical turns of speech as Marx used: processes which in their nature are antagonistic, contain a contradiction; transformation of one extreme into its opposite; and finally, as the kernel of the whole thing, the negation of the negation. [Engels (1976) p.179. Bold emphasis added.]

"Hegel brilliantly divined the dialectics of things (phenomena, the world, nature) in the dialectics of concepts…. This aphorism should be expressed more popularly, without the word dialectics: approximately as follows: In the alternation, reciprocal dependence of all notions, in the identity of their opposites, in the transitions of one notion into another, in the eternal change, movement of notions, Hegel brilliantly divined precisely this relation of things to nature…. [W]hat constitutes dialectics?…. [M]utual dependence of notions all without exception…. Every notion occurs in a certain relation, in a certain connection with all the others." [Lenin (1961), pp.196-97. Bold emphasis added.]

"[Among the elements of dialectics are the following:] [I]nternally contradictory tendencies…in [a thing]…as the sum and unity of opposites…. [This involves] not only the unity of opposites, but the transitions of every determination, quality, feature, side, property into every other [into its opposite?]…. [Ibid., pp.221-22. Last set of parentheses in the original; bold emphasis added.]

"And so every phenomenon, by the action of those same forces which condition its existence, sooner or later, but inevitably, is transformed into its own opposite…." [Plekhanov (1956), p.77.]

"Why is it that '...the human mind should take these opposites not as dead, rigid, but as living, conditional, mobile, transforming themselves into one another'? Because that is just how things are in objective reality. The fact is that the unity or identity of opposites in objective things is not dead or rigid, but is living, conditional, mobile, temporary and relative; in given conditions, every contradictory aspect transforms itself into its opposite....

"In speaking of the identity of opposites in given conditions, what we are referring to is real and concrete opposites and the real and concrete transformations of opposites into one another....

"All processes have a beginning and an end, all processes transform themselves into their opposites. The constancy of all processes is relative, but the mutability manifested in the transformation of one process into another is absolute."  [Mao (1937), pp.340-42. Bold emphases added.]

Force does not change into movement, nor does movement change into force.

Someone could object that indeed they do change into one another (perhaps via an exchange of energy, or as part of an equal and opposite reaction, etc.). But, if that were so, another problem would immediately assert itself. If force F were to turn into new movement M, then the one would follow upon the other: F would create M at a later instant in time, otherwise it could not turn into it. Plainly, if M already exists, F could not turn into it. Unfortunately, in that case, F and M cannot 'struggle' with one another, for the two would not exist simultaneously in order for that to happen. If, on the other hand, F were to change as a result of some as yet unspecified factor, say F*, then F* would have to be the opposite of F, and F would turn into F*, not into M. Howsoever we try to re-package this badly wrapped 'theory', none of it makes any sense.

[This is just a particular example of a general, but fatal defect that lies right at the heart of the DM-'theory' of change, described in much more detail here. Nevertheless, this point can be generalised, as it will be below, to show that no two (or more) forces could 'contradict' one another in the way that dialecticians imagine.]


A First Attempt At Clarification

Perhaps, then the following re-write might succeed in repairing this part of DM, which re-write also, in the event, tries to avoid undermining the thesis that UOs operate everywhere in nature:

F2: A UO involves the opposition between a force P1 and the impressed motion that another set of forces Q has produced (or would have produced) in a body B (had P1 never existed). The resultant motion of B is the final outcome of this struggle.

F2 appears to link the operation of one force (P1) with that of another set of forces (Q). However, it is difficult to distinguish what F2 says about these two from the vector resultant of two forces if we subjected this system to the usual mathematical analysis. If so, the word "struggle" would amount to little more than an anthropomorphic re-write of the functional relations that exist within the vector calculus, only now applied to just one force, the resultant. In that case, if and when P1 and Q interact, they will produce just one resultant force R, which would alone induce the recorded change in motion.28

But, if this is so, a contradiction between forces cannot arise: if there is only one force operating in the system, no contradiction seems possible. In that case, F2 threatens to introduce another fatal implication for the entire 'theory', by killing it for want of forces.29

This failure suggests we should reconsider an option left unexplored earlier; i.e., the one which argued that forces are the only legitimate candidates to be placed in such oppositional matrices, not the motion they change/induce -- contrary to what Engels seems to have believed (when he tried to replace forces with relative motion).

On this view, forces are 'contradictory' only of other forces, and not of bodies or of impressed motion. The following might, therefore, bring out this new slant slightly better:

F3: Given a body B, and a system of forces P, comprising n vectors p1-pn operating on B, a resultant force vector R represents the outcome of the struggle between these n contradictory vectors. In this, R itself need not be fixed, but could itself be subject to countless changes as body B moves under the influence of P, which would also change accordingly.

One immediate problem with this is that the specification of the forces belonging to P depends on the choice of co-ordinate system and inertial frame.30 This indicates that the representation of forces as 'contradictions' is perhaps more convention-sensitive that it is reality-driven -- making such 'contradictions' no more 'objective' than, say, latitude and longitude are.

However, even if this latest problem is put to one side, it is still worth asking whether any sense can be made of F3.

As noted above, F3 seems to bring us back full circle to the idea that forces -- not bodies, or the motion of bodies -- are 'contradictory' of each other. And yet, as we have just seen, it is not possible to depict AA- and RR-forces as 'contradictory', unless their effects are involved in some way.

Unfortunately, and once again, if "force" is just a convenient shorthand for relative motion, it would mean that at least this part of DM was consistent with a CAR-like account of reality -- in that elements of the "Totality" would now be seen as externally- (not internally-) related to one another.

[CAR = Cartesian Reductionism.]

To repeat: it is not easy to see how the motion of one body could be internally-related to that of others without re-introducing the idea that bodies exercise an effect on one another independently of how they are moving (which, to be sure, may subsequently affect their motion, but which would not itself internally-link such bodies in motion). But this issue is precisely the difficulty that exercised traditional Philosophers, as part of the classical metaphysical problem of the nature of forces; DM has merely reproduced it in an obscure form.31

Perhaps the slide into CAR may be prevented by the following re-wording of F3:

F4: Given a system of forces P, comprising n vectors p1-pn, a resultant force vector R represents the outcome of the struggle between these n vectors.

F5: This ensemble is only contradictory within a Totality of inter-related processes that mutually condition one another.

F5 is clearly dependent on the idea that the whole determines the nature of its parts, the latter of which in turn feed back into, and determine the nature of the whole. Hence, F4 and F5 appear to restore the dialectical unity that earlier paragraphs seem to have ignored.

Unfortunately, this brings us back in yet another full circle to a consideration of the relationship between the "Totality" and its parts. This is because F5 introduces its own pernicious version of HEX, for it seems impossible (on this account) to determine whether anything is 'contradictory' (or not) unless we ascertained the nature of the whole. But, since the latter is always changing, no element in this 'cosmic wild-goose chase' will ever be hunted down and trapped. We encountered this dilemma in several forms in other Essays at this site; on this see, for example, here and here.32

The most relevant aspect of this latest quandary centres on the idea (voiced by some dialecticians) that as scientific understanding grows, the 'contradictions' that now plague our knowledge of the world ought to diminish. Presumably, this must mean that at the limit (i.e., in an ideal state where human beings possess (in theory) the Absolute Truth about everything), there would be no contradictions anywhere. In its turn, this appears to mean that even if humanity never actually reaches this blessed state, we can in the here-and-now make that very inference: the Absolute truth is that not only is the world not contradictory, the motion of bodies and the operation of forces isn't either. In fact, this proposition must be true now, for if it were not now true that there were no 'contradictions' in the ultimate future state of our knowledge of the "Totality" then either the DM-view of the limit of knowledge (as ideally contradiction-free) must be wrong, or the DM-belief that humanity is converging on that limit is incorrect, since there is no such limit.33

Again, if this is what dialecticians mean by 'contradictory forces',34 then nothing may be so described until everything has been so described. But, this reverses the dialectical picture, for, as we have just seen, some DM-theorists appear to believe that things only look 'contradictory' because we do not possess the 'Big Picture', and that if ever we were to attain to such a universal overview of things, 'contradictions' would disappear (or largely disappear -- the story gets a little vague on this point). Here, in contrast, the idea seems to be that we may only depict forces in nature as 'contradictory' after the dialectical bell on judgement day has finally tolled -- that is, we may do so only at the end of time, when all (or most) 'contradictions' will have been resolved, meaning that 'objectively' they do exist and 'objectively' that they do not (or we do not know whether either of both are the case)!

So, one horn of this dilemma suggests 'dialectical contradictions' do not exist, and if they don't, they cannot induce change. The other suggests we cannot now assert that they do exist (since we are not in possession of Absolute Knowledge), so we cannot know whether they cause change.35

At any rate, if AA-, and RR-forces are oppositional to each other, or even to themselves, change would still be caused by a resultant force, which it is just as easy to interpret as 'tautological', rather than as 'contradictory' -- that is, if we insist on viewing nature in such anthropological/animistic terms.

Of course, if we resist primitivism of this sort, then both descriptors (i.e., "contradictory" and "tautological") should be fed effortlessly into the bogus concept-shredder of history. [More on that here.]

Perhaps, then, it would be wise to draw a veil over this self-imposed dialectical impasse, and turn to a more likely source of 'contradictions': AR-forces.



In the previous section, it became clear that little sense could be made of AA- or RR-forces serving as models for 'contradictions', and this turned out to have nothing to do with the difficulty of seeing whether such 'dynamic duos' contained opposites or not -- which they manifestly don't. An A-force is not the opposite of another A-force; the same can be said for R-forces.

However, a prima facie case could be made for regarding AR-force couples as apt exemplars of the polar opposites DM-theorists require (in order to depict 'contradictions' in DM and HM).

Unfortunately, as we will see, this slender straw once clutched soon turns into a millstone, drowning this already sinking 'theory'. Quite apart from the considerations outlined above, no clear sense can be made of the idea that AR-forces can model 'contradictions', anywhere, anyhow.36

An initial serious difficulty with this whole idea is that AR-couples do not appear to operate in nature in quite the manner this handy prefix seems to suggest: i.e., as AR-forces.

Consider a straightforward case involving, say, the accumulation of matter that formed the stars, planets and their moons (etc.). Here, R-forces (operating at the nuclear level) apparently prevent (for a time) the catastrophic collapse of these growing masses into 'singularities' by balancing-out the A-forces that presumably set the whole thing in motion. The problem with these R-forces is that, while they look as though they oppose any other A-forces in the system, they are not their polar opposites (in the way that, say, the North and South poles of a magnet are said to be) -- that is, they are not opposite manifestations of the same force type. So, the inter-atomic forces preventing this collapse are not of the same type of force as the gravitational forces that initiated the process.37 While a case might be made for depicting North and South poles of a magnet as polar opposite magnetic forces (or as 'creating' them -- but on this see below), gravitational and nuclear forces are not opposites of the same type, and so cannot, it seems, 'contradict' each other.

However, even that description is prejudicial, for, as noted above, these forces change the motion of bodies; they do not directly confront each other as opposing forces. Admittedly, they can be represented in a vector calculus, but we have already seen that this translation is of little assistance to DM -- this is because the relevant forces would disappear, to be replaced by a single resultant force, which causes all the action.

Perhaps these initial difficulties could be defused if emphasis were once more placed on the oppositional nature of AR-forces as a way of explaining change?

Unfortunately, this detour is no more successful here than it was when it was considered above in relation to AA- and RR-forces.

Even if this further difficulty is shelved, it would still be difficult to see how AR-forces could be interpreted literally (or figuratively) as 'contradictions' (especially in HM). This is because of they way in which they can combine and augment one another.

For example, consider, two forces operating in diametrically opposite directions tangentially placed around a rotating body. These two forces -- although 'opposites' at their point of action -- exercise a combined and augmented effect on the angular acceleration of that body, thus ceasing to be oppositional.38

This is a familiar feature of force vectors. In some instances, they seem to 'oppose' -- in others they appear to 'augment' -- one another, while in still others they look like they do both at once.39

Cases like these illustrate that forces are not rigidly fixed as permanent opposites, nor are they always oppositional, even when they are supposedly opposites. Hence, it is difficult to see how a DM-picture of forces operating (in nature) only as polar oppositional pairs could accommodate this property of natural forces.40 But in that case this is unwelcome news, for little sense can be given in DM to the idea that opposites can switch in this way.41

It could be objected here is a gross distortion since the above phenomena are actually consistent with DM. Dialecticians themselves reject the idea that there are fixed and unchanging forces in nature. Hence, the recognition that forces can change and operate in 'opposite directions' is one of DM's strengths, not one of its weaknesses. Or so it could be maintained.

However, this volunteered reply does achieve one thing: it helps focus on what has been a recurring problem throughout these Essays: DM is so vague and equivocal that it is impossible to say what its consequences are, or even if it has any. The claim that 'contradictions' in nature must be understood as opposing forces has under close examination turned out to mean that such forces might not actually oppose each other -- indeed, according to Engels, the concept of a force could simply be a convenient shorthand for the complex relative motion of bodies. Now, it seems that even this is incorrect, for oppositional forces may actually augment one another, but only if they are not now viewed as shorthand for the relative motion of bodies.

It is thus impossible to decide which DM-type forces are or were genuine opposites (or, indeed, which are or were polar opposites, if any are or were), or distinguish those that are from those that aren't. But, if all forces can work in any manner whatsoever, then it becomes deeply mysterious why only some are depicted as opposites. And anyway, what has become of the AR-typology Engels regarded as fundamental?

Given such slippery terminology, little meaning may be given to a single DM-concept in this area; still less to the idea that DM force 'laws' operate anywhere in nature.

Imagine a Chemist, say, who identified an element as having just so many protons in its nucleus, except it didn't really have this number, and these alleged protons weren't really protons, and the element rarely if ever had a nucleus, and anyway it wasn't an element in the first place. Suppose further that this chemist claimed that he knew what he was talking about (even if no one else did) because he was an expert player of the 'Nixon Card', and skilled in the art of "grasping contradictions", which unfortunate lack of 'flexibility' prevented his critics from seeing the truth as he saw it.

Few, I think, would take him seriously.

Naturally, such discursive and theoretical 'contradictions' are grist to the DM-mill, but this is not something about which dialecticians should feel the least bit proud. For if Capitalists, say, (as a social force) can indeed operate in such a contradictory manner, who is to say whether a revolution is necessary to overthrow them? Perhaps -- as result of a 'dialectical inversion' -- the class enemy could become the strongest ally of the working class? In such a topsy-turvy world anything might happen. Capitalism might end by being reformed away, Imperialists could assist in the abolition of injustice, the Nazi's might one day help create 'racial' harmony, and the Ku Klux Klan could advance the struggle for Black Liberation. Who knows? The Bosses might even overthrow themselves!42

If it is a central postulate of the theory that 'contradictions' are oppositional forces, and that these can change in 'contradictory' ways to become 'non-oppositional', then reformism, centrism, class collaboration (and the prospect of having the Fascists (etc.) as allies) cannot be ruled out. On the other hand, if these possibilities are to be rejected (as surely they must), then the importation of such 'contradictory' DM-ideas into HM contexts must be resisted equally forcefully.

Of course, it could be pointed out that forces operate in history in more complex ways than those that work in nature, so the analogy with natural forces (and the KKK, etc.) is inapt -- especially if it is applied in the "crude" manner illustrated above. Unfortunately, if this attempted rebuttal were itself correct then it would be misleading to describe natural and social forces as 'contradictory', for if the analogy between forces and 'contradictions' is inapt, it is inapt. Of course, that admission would amount to the abandonment of this unhelpful analogy in its entirety: that 'contradictions' may be depicted as oppositional forces.43

Nevertheless, even if all of the above points turn out to be incorrect in some way, there are other, more fundamental reasons for ruling-out the identification of opposing forces with 'contradictions'.


 A Contradictory Theory?

'Literal Forces' In Opposition

Many of the above remarks were aimed at demonstrating that the analogy between forces and 'contradictions' might not be at all apt. However, it could be argued that this does not affect the view that the identification of forces with 'contradictions' is in fact literal, not figurative.

However, the truly remarkable thing is that despite its centrally-important role in DM, as far as can be ascertained, the precise details of the literal connection between forces and 'contradictions' have never been worked-out by dialecticians. One reason for this might be that they consider this identification to be so obvious that the specifics either do not matter or they are deemed trivial.

On the other hand, it could turn out that nothing could have been said in this direction by anyone desirous of defending this aspect of DM, which would more obviously explain the deafening silence. As seems apparent, and as will presently be advanced beyond the mere 'seeming' stage, the latter option is indeed correct: this omission is not the least bit surprising, for the imagined connection between forces and 'contradictions' turns out to be entirely illusory.

In order to substantiate this claim, it might help if we back-track a little. Part of the argument in favour of the identification of forces and contradictions appears to depend on an initial analogy: that drawn between literal contradictions and conflict (which, as we will see in Essay Twelve, is a throw-back to an animistic confusion -- a conflation of various forms of social conflict with the imputed activities of ancient 'gods'/personified forces at work in nature -- perpetrated by (Greek) ruling-class theorists; summary here).

Mere contradictions are ostensively verbal wrangles, which themselves look oppositional; when one person asserts "p" and another person denies it (or asserts "not p", where "p" stands for a proposition token), at the level of discourse at least some sort of opposition seems to be implied (but on that, see here). So, analogously, a 'contradiction' in nature might appear to signify the existence of a real material opposition (but, alas, only to those who are happy to fetishise social relations as if they were, or which represented, real relations in the non-social world).

Clearly, DM-theorists view material 'contradictions' as their primary concern, compared to the secondary instances found in merely verbal wrangles --, since matter precedes mind (etc.). Even so, the argument in general is clearly analogical, for we were certainly aware of the latter well before the former. In that case, the argument must have proceeded from the human case to the natural -- which is indeed what the history of the subject reveals: materialist dialecticians did not exist in pre-historic times, but people have been arguing for tens of thousands of years.

Hence, DM-theorists must (at least initially) have relied on an analogy drawn between the way human beings argue (and/or fight) and the way conflict appears in the natural world. Unfortunately, this makes the literal interpretation of forces as 'contradictions' still dependent on the use of analogical and figurative language, but, with no clue as to what that literal meaning could possibly be; we still lack the material grounding that DM-theorists require.

Now we certainly have a very clear way of explicating contradictions in language and logic, but we have none at all for those that allegedly occur in nature -- save we continually use a typographically identical word (i.e., "contradiction") and equate it (in the absence of any justification, save perhaps on Hegel's say-so) with forces.

Nevertheless, this would at least account for the figurative way that contradictions are continually used in DM (and overused in HM), and why dialecticians regularly conflate social with material forms.44

Even if we ignore this latest problem, one thing is clear: for DM-theorists verbal contradictions represent perhaps the least significant type of opposition. Changes in nature and society are (for them) the result of much more fundamental 'contradictions' than those occasioned by the mere gainsaying of another person's words. As noted above, in many cases anyway, discursive contradictions might turn out be the 'reflection' of more basic conflicts in the real world, and it is the latter that are of interest to DM-theorists.

However, once this superficially 'neat picture' is examined a little more closely much of it disintegrates.


The Revenge Of The Non-Existent

As has already been noted, DM-theorists have as yet failed to provide a clear account of the precise nature of the connection between 'contradictions' and opposing forces. In that case, once again, one will have to be supplied for them.45

Presumably, when DM-theorists claim that 'contradictions' are represented in nature by opposing forces they have something like the following in mind (if they but knew it):

F6: Let force P1 oppose force P2 in configuration C1 in nature.

F7: Here, opposition amounts to the following: the normal effects produced by P1 in C1 (had P2 not been present) are the opposite of the effects P2 would have produced in C1 (had P1 similarly not been operative).

F8: Let P1's normal effects in C1 be elements of an event set E1, and those of P2 be elements of E2. For the purposes of simplicity let E1 and E2 be disjoint.

F9: By F7, E1 and E2 contain only opposites.46

[Here, the content of C1 could include any other ambient forces and processes operating in the system; alternatively, the forces themselves may even be 'edited out' on the lines envisaged by Engels (as a sort of shorthand for relative motion, etc.). In addition, all the internal mediations between these forces and/or events in the Totality (T) may also be incorporated into the picture. Other 'dialectical' caveats could, of course, be stirred into the mix, as seems necessary and/or appropriate.]

It is worth emphasising at this point that P1 or P2 must operate 'independently' in C1.47 This seems to be an essential assumption to make so that sets E1 and E2 may be determinate themselves.

[Anyway, this 'independence' need not suggest a CAR-like scenario since it could form part of the 'dialectical development' of new forces and processes as C1 and the rest of T develop. Naturally, this simplifying assumption could be modified at a later stage, as the need arises.]

The first problem with the above account centres on the term "opposites", in F9. Something a little more precise than merely an "opposite" seems to be required here in order for DL to surpass FL in its ability to account for change, etc.48

Unfortunately, the difficulty here is seeing whether even this minimal condition is actually implied by F6-F9, and whether the rather weak concept of an "opposite" is capable of bearing all the weight that is usually put on it.

However, quite independently of these annoying opening niggles, far more problematic is the fact that given F6-F9, it would be impossible to say what the 'contradictory' state-of-affairs here is meant to be.

This is because F6-F9 imply that E1 and E2 do not in fact obtain together, for if just one of P1 or P2 is in fact operative, then just one of E1 or E2 will be instantiated.

Clearly, in such circumstances there could be no 'contradiction' -- even given the loose DM-notion of one -- since, at least one 'half' of the alleged contradiction would not actually exist for it to contradict anything else, it having been prevented from occurring by the operation of either one of P1 or P2!49

Anyway, I shall examine later the question whether E1 and E2, even though 'opposites', can legitimately be said to be 'contradictory'. In what follows, I shall simply assume that they are.50


Prevention And Its Discontents

Despite this, it could be claimed that the following propositions are all that DM really requires:

F10: P1 prevents E2, and P2 prevents E1.

F11: Anything that prevents something else happening contradicts it.

F12: Therefore, P1 and P2 contradict each other's effects.

If this is so, then plainly P1 and P2 do not actually contradict each other, just each other's effects. In that case, it is not too clear whether or not DM-theorists -- keen to maintain the orthodox view that forces contradict each other -- will want to embrace F10-F12.

In addition, it has already been conceded (for the purposes of the argument) that E1 and E2 are 'contradictories'. But, it now appears from the above, and from F10-F12, that not only does E1 'contradict' E2, but also that P1 'contradicts' E2, and P2 'contradicts' E1, as well. I shall return to consider these added complications, later.

However, there appears to be no good reason for accepting F11, and every reason for rejecting it. Consider the following scenario -- aimed at illustrating why F11 is unacceptable (even given the truth of other DM-theses):

F13: NN saved child MM from drowning.

F14: NN prevented the drowning.

F15: So, NN contradicted the drowning (by F11).

[F11: Anything that prevents something else happening contradicts it.]

The problem here lies not so much with the non-standard use of language these sentences contain, but with the fact that if a drowning (or if anything) is prevented from happening then it never actually took place. In that case, if the said incident did not happen it could not have been 'contradicted' by any of the forces or events doing the preventing, since there would be no 'it' for anything to contradict. Unless we are prepared to envisage forces 'contradicting' things that do not exist, or we allow them to 'contradict' unrealised possibilities -- or even ideas (perhaps those in the mind of NN above) --, the word "contradiction" can gain no grip here, even in DM-terms.

Of course, it could be objected that this hypothetical action did indeed contradict the said drowning by stopping it from happening. But, to repeat, since the said drowning had been prevented, it did not take place, so it never existed to be contradicted.

One obvious fall-back position for dialecticians to occupy would be to argue that the actions mentioned above halted a series of events that would have led to the said drowning. In that sense, those actions contradicted that series of events. This objection will be looked at more closely later, and below.

However, just in case this latest counter-example is considered prejudicial, or contentious (in that it does not deal with real forces, or with the sort of forces DM-theorists are interested in), then perhaps the following considerations might prove more acceptable. Let us begin with this obvious sentence:

F16: Any process that is prevented from occurring does not exist (or take place).51

It is clear that while F16 is a truism, it seems to ignore events and processes that have an extended life, so it might not in fact be acceptable as a clarification of the processes that are of interest to DM-theorists. Consider, then, the following emendations:

F17: Event E consists of a set of inter-connected sub-events E1-En.

F18: Events E1-En form complexes of material interactions (of a sufficiently mediated and contradictory nature) within T, if ever they occur.

F19: Let P2 prevent some or all of E1-En from taking place.

F20: Therefore, some or all of E do not exist (or will never exist), or do not take place.

It is quite plain from this that because of the operation of P2, certain events failed to manifest themselves. But that simply generalises the point made in the drowning example above. Even if it is assumed that the vague notion of a 'contradiction' employed by DM-theorists is viable, it is difficult to see how something could 'contradict' something else if the latter does not exist/take place (and perhaps never will).

This objection appears to be fatal to DM; if forces are genuinely oppositional then they actually prevent 'contradictions' from arising, and so cannot be equated with what they thwart. So, far from being DM-friendly, forces/'contradictions' seem to be its worst enemies.

In that case, if this serious difficulty is to be neutralised, a new and more conducive account of the relationship between 'contradictions' and forces must be found.52


A Balanced Account Of Prevention?

In order to construct a more viable account, we need to return to a difficulty we met earlier, which was put to one side temporarily: the claim that it's forces (not forces and effects, or simply effects) that are directly contradictory to one another. Consider then the following:

F21: P1 contradicts P2 in so far as it prevents P2 acting, and vice versa.

Again, this perhaps puts too much weight on the term "prevent"; it could prompt F21 to self-destruct just as fast as F17-20 did, for if one of these forces fails to operate, no 'contradiction' would ensue.

However, perhaps this conclusion is a little too hasty. For example, both of the above forces could still exist even if one ceased to operate in an F21-style scenario, and no problem need arise because no appeal would have been made to the non-existent effects of one of them in this case.

This means that even though either one of P1 or P2 might have been prevented from acting, they could both still exist in some form or other. If so, F21 might appear to be the viable option that dialecticians require. One further advantage would be that F21 connects forces directly with 'contradictions', rather than linking 'contradictions' to the effects of forces. Could this be the lifeline that DM requires?

Alas, upon closer examination, this lifeline soon turns into a noose.

The fatal consequences this option creates for DM become apparent when we attempt to unravel what it means for a force to be 'prevented' from operating.

Despite disclaimers, it seems that if a force no longer operates, it no longer exists. Perhaps the problem lies not so much with the precise physical form that forces take (which is mysterious in itself, even to this day), but with the fact that the word "operate" is ambiguous. Consider the following examples of forces that are capable of being rendered inoperative:

F22: The electromagnetic force ceased to operate once worker NN threw the switch.

F23: An aerofoil produces the lift necessary to keep an aeroplane in the air provided that there is sufficient relative velocity between that aerofoil and the ambient medium to prevent the force of gravity from operating normally, pulling the aircraft to the ground.

In F22, the relevant force simply ceased to exist (or it was converted back into another force, 'potential' force, or form of energy, etc.) once the switch had been thrown. But, in F23, a second force (lift) 'cancels out' the effects of the first force (gravity) -- which, of course, still exists (perhaps as part of the resultant force in this system).

Could F21 now be interpreted along lines similar to those suggested in F23? This way of viewing the relation between P1 and P2 would see them both as still existing, even while they counterbalanced each other. In which case, it might prove helpful to re-write F21 in the following manner:

F24: P1 contradicts P2 only if it counterbalances P2.53

[F21: P1 contradicts P2 in so far as it prevents P2 acting, and vice versa.]

Now, F24 does not seem to face any of the existential problems that F21 encountered since the relevant forces actually co-exist, counterbalancing each other. Perhaps, at last, we have a clear statement of what DM-theorists require?

Alas not.

A new difficulty arises once we ask why only counterbalancing forces should be considered 'contradictory'. This is relevant since F24 simply restricts our attention to situations where there is an equilibrium between forces, and ignores dis-equilibria.54 But surely, it is largely as a result of the latter that change occurs -- meaning that 'contradictions' should be connected with these rather than with equilibria. If so, F24 must be re-written in the following way:

F25: P1 contradicts P2 whether it counterbalances P2 or not.

Unfortunately, F25 cannot now provide the clarity that was missing from previous attempts to explicate this part of DM. This is because F25 fails to distinguish between equilibria and disequilibria. F24 seemed to express a clear definition of 'contradictory' forces, but in order to make it applicable to the real world, F25 had to be recruited in support, completely undermining F24. This is because F25 informs us that forces are 'contradictory' whether F24 is true or not. Worse still, F25 could be true even when F24 is false:

F24: P1 contradicts P2 only if it counterbalances P2.

F25: P1 contradicts P2 whether it counterbalances P2 or not.

Hence, if the following were true:

F26: P1 contradicts P2 even though it does not counterbalance P2.

[F25 would be true, but F24 would be false (or vice versa).]

Now, anyone reading these three sentences (and taking them for an accurate exposition of this part of DM) would rightly complain that nothing had actually been explained, since there is nothing about the relationship between the forces mentioned that indicates what the overall theory is committed to.

In response, others could argue that this latest problem is spurious and is solely the result of the phrase "only if" occurring in F24. Perhaps its removal would eliminate the difficulty? Unfortunately, the removal of the "only if" in F24 would plunge the theory back into all the existential problems it had been introduced to eradicate. This can be seen if we try to re-word F24 in the following manner:

F27: P1 contradicts P2 if it counterbalances P2.

Although F27 might look acceptable, it is merely a sufficient condition; hence, it does not rule out the following:

F28: P1 contradicts P2 in so far as it prevents P2 acting, and vice versa.54a

[F21: P1 contradicts P2 in so far as it prevents P2 acting, and vice versa.]

But, F28 is just a resurrected version of F21, which we found did not rule out F22, and non-existent forces. What was required here instead was a description of 'contradictory' forces that does not imply that one of the forces operating ceased to exist as a result of the action of any other forces in the system. And we also required an account that does not rely on forces merely 'contradicting' effects -- because of the serious difficulties that alternative encountered earlier.

This is why an appeal had to be made to forces that counterbalance each other, since (clearly) they must exist to do this -- hence the introduction of the "only if", making this a necessary condition. But, as we then discovered, this more restricted version ruled out forces that did not counterbalance one another, which DM seems to need; reintroducing these at a later stage ruined this neat picture.

Unfortunately, F24 and F26 seem to divorce 'contradictions' from equilibria, since the presence or absence of the latter is in no way affected by the former.

F24: P1 contradicts P2 only if it counterbalances P2.

F26: P1 contradicts P2 even though it does not counterbalance P2.

This means that if F24 and F26 reflect the real nature of things, then 'contradictions' are in fact unrelated to the balancing effects of forces. As paradoxical as this might seem, DM-theorists must deny the truth of the conjunction of F24 and F26 if they want to maintain their belief that there is a connection between forces, equilibria and disequilibria. But, alas, in order to account for the 'contradictory' nature of reality, DM-theorists can't afford to do this. For, as soon as F24 and F26 are adopted, DM ceases to be explanatory; but the minute these two are rejected, this attempt to understand the nature of DM-forces collapses.

Nevertheless, this annoying conclusion might appear to some to be a little too hasty -- or, for that matter, contrived. And yet, with so little in the writings of DM-theorists to guide us, how would it be possible for anyone to decide if this is the case? Indeed, how could dialecticians themselves arrive at a decision here, without some form of theoretical (shock, horror!) innovation, an option that has so far been complete anathema to the 'orthodox'?

Nevertheless, if we adhere to the requirement that 'contradictions' explain change -- when pictured as opposing forces (that is, if we give 'contradictions' some sort of material bite) --, then the theory must self-destruct, by the above argument. This is because the theory maintains that forces are 'contradictory' whether what its theorists claim about them is true or not (if this is indeed what they might claim!).

Naturally, all this is independent of the far more fundamental worry whether the idea that contradictory forces are capable of counterbalancing each other can itself be explicated without referring to those 'prevented'/non-existent effects we met earlier. If it can't then this latest detour would prove to be another dead end, since 'prevented' effects do not exist to be contradicted. On the other hand, if this can be explained without referring to such effects, then it would be difficult to say what material impact such a scenario might have on the physical world. How could such forces be described as "material" if they had no effect on anything material --, that is, except on those seemingly insubstantial 'non-existent' effects?

Well, this is another dialectical hole DM-fans can dig themselves out of. I am merely content to remind them that it is a hole, and not part of a viable theory, as they fondly imagine.


Yet More S&M?

Perhaps even this is too hasty? Maybe we should begin again?

To that end, it might help to re-examine a passage from Cornforth, quoted in Part One of this Essay:

"The unity of opposites in a contradiction is characterised by a definite relation of superiority-inferiority, or of domination, between the opposites. For example, in a physical unity of attraction and repulsion, certain elements of attraction or repulsion may be dominant in relation to others. The unity is such that one side dominates the other -- or, in certain cases, they may be equal.

"Any qualitative state of a process corresponds to a definite relation of domination. Thus, the solid, liquid and gaseous states of bodies correspond to different domination-relationships in the unity of attraction and repulsion characteristic of the molecules of bodies....

"Domination relationships are obviously, by their very nature, impermanent and apt to change, even though in some cases they remain unchanged for a long time. If the relationship takes the form of equality or balance, such balance is by nature unstable, for their is a struggle of opposites within it which is apt to lead to the domination of one over the other....

"The outcome of the working out of contradictions is, then, a change in the domination relation characteristic of the initial unity of opposites. Such a change constitutes a change in the nature of a thing, a change from one state to another, a change from one thing to another, a change entailing not merely some external alteration but a change in the internal character and laws of motion of a thing." [Cornforth (1976), pp.97-98.]

Now, the above argument might appear to work when applied to human social systems, where agents (individually or in groups) can 'upset' any number of 'balanced' situations, and which do not need too much in the way of external motivation to do so (although, in order to be able to say even this much with any clarity, the reader will note that Cornforth found he did not need to use any of the obscure jargon invented by Hegel). However, when it is applied to nature as a whole it cannot work. Consider the following:

F29: Let FD be a set of force 'elements' in a 'dominant' relation to FS, which is 'submissive' accordingly (i.e.,  FD > FS), and let both operate in system S, however defined.

F30: Now, for this relation to change so that a qualitative transformation occurs in the overall system S, one or both of FD and FS will have to change first.

F31: If the change occurs in FD it will have to do so because of the latter's own 'internal contradictions', otherwise the theory must fail at least here. [The same applies to FS, or indeed to both taken severally or together.]

F32: But, if that is so, then the same analysis will apply one more level down, as it were: whatever causes FD to change will have to be the result of further dominance/submissive relations inside/internal to FD itself. In turn, the pre-conditions noted in F31 will also apply at, or to, these lower level relations; they must change because of their own 'internal contradictions'.

F33: This must continue forever, or it will halt at some point.

F34: If it halts at some point, then there must be fundamental units that do not change through 'internal contradictions', and so the theory fails. [These fundamental units can have no effect on each other, for reasons spelt-out in detail in Part One of this Essay.]

F35: If this process continues forever, then there would be nothing to condition anything internal to anything else, just more and more layers, tailing off to infinity (i.e., to "who knows where?"). DM would thus have its own "bad infinity". [We saw that this was a non-viable option in Part One, too.]

F36: All this is independent of whether or not an external cause (or causes) initiated these internal changes in FD or FS. While the latter may be influenced by external causes (according to Cornforth), external causes cannot bring about the internal qualitative changes required (again, according to Cornforth). The latter must be internally-generated in the last analysis.

It looks, therefore, like there is no way of rescuing this 'theory' along these particular lines.


Hole To Let -- Previous Occupant Self-Destructed

Howsoever we try, there seems to be no way out for this self-destructing theory -- killed-off by its own internal obscurities.

In short: if a force prevents something from happening it cannot contradict it; once prevented, the latter does not exist.55

On the other hand, if forces affect one another externally (as they seem to do), then change cannot be the result of 'internal contradictions'. Alternatively, if they have internal effects on one another (in some as yet unspecified way), and they change as a result of their own 'internal contradictions', then either they are composed of simple units that do not change, or they are infinitely complex, and nothing internal to them can condition anything else internally, for there would be no such things.


Too Many Forces Spoil The Broth -- Or Is It Too Few?

It could be objected that the above results have been deliberately tailored to fit the desired end -- by the choice of, say, F24. A much better way, therefore, of representing this aspect of oppositional forces might be the following:

F37: Contradictory forces are those that enter into opposition in such a way that they (dialectically) partially or totally cancel each other out.

[F24: P1 contradicts P2 only if it counterbalances P2.]

This means that the 'contradictory' relation between two or more forces would operate along a sort of continuum -- as it were -- with no fixed relation between them. The account given earlier clearly makes the link between 'contradictory' forces an "either-or", all-or-nothing, sort of affair -- or so the counter-argument could go.56

At this point, an example from mechanics might help illustrate the complex relationship that is intended here: un-damped simple harmonic motion. [This particular link requires JAVA -- or try here if you have no JAVA installed.]

Consider a particle set in motion under the operation of two forces, such that its acceleration is proportional to its displacement from the point of equilibrium, and directed toward that point. Since the acceleration of such a particle changes in proportion to its position, the net force operating on it must also change accordingly. This is due to the fact that the resultant force in this system is the vector sum of these two distinct but changing forces, which at the equilibrium point counterbalance one another, but at other points they either augment or partially cancel each other out, depending on the physics of the situation. Because these two forces work in opposite directions and cause the impressed acceleration (achieving this by their 'dialectical interaction', let us say for now) we appear to have here an example of F37-type motion.

In this highly simplified picture of just one type of motion, the forces present in the system appear to 'contradict' one another in complex but changing ways, as DM seems to require. But, if this scenario actually does illustrate F24- (or F37-) type 'contradictions' then several untoward consequences follow:

(1) This analogy would mean that 'contradictions' (like forces) operate on a continuum. Hence, at any point along the path of the above particle the net force operating is unequal to that at another point (in one cycle). This means that given a certain displacement, the modulus of the net force might be, say, only 1% of its maximum, at another it would be, say, 99% of it -- while at a symmetrical location past the point of equilibrium, the same would be true but in an opposite sense. However, it is not easy to see how such a picture may be fitted seamlessly into the DM-view of 'contradictions', and as we saw above, such a model would have unacceptable consequences in HM (involving, for example, the Nazis fighting racism!).

(2) This trope depends on forces being viewed as basic units of reality, as opposed to the product of the relations between bodies in motion.

[Recall that the latter option appears to have been one that Engels himself preferred when he spoke of relative velocities replacing forces. However, if the term "force" is just a shorthand for relative motion (or if it depends on the presence of a "field"), then, as we have also seen above, the 'dialectical' unity of nature would be thrown into question. On that basis, the links between bodies and processes would be external, whereas DM seems to require the existence of forces to provide the 'connective tissue' of reality. If now forces themselves depend on bodies in relative motion, then reality must be discrete, not continuous.]

But, DM-theorists have yet to say what the physical nature of a force is. Physicists themselves have ceased to use this word (except as a sort of shorthand, as noted above). If forces have no physical nature, can they be part of material reality?

(3) This neat picture, tailor-made for F37, obscures the complexity that occurs in nature. Even so, it is not easy to see how such a tidy model could cope with systems of forces, which, given this view, indicate that several things must be 'contradicted' all at once by countless others, or, indeed, which suggest that bodies and/or processes could have innumerable 'contradictories'. That would, of course, divorce DM-type 'contradictions' completely from FL-contradictions and from Hegelian 'contradictions'. While this might not be a totally unacceptable outcome, it would mean that the former would be even more tenuously linked to the latter (or even with contradictions that appear in everyday discourse), and in that case the meaning of the word "contradiction" used in DM would be even more indeterminate than it already is. In addition, it would imply that any object or process in nature had more than one opposite at any point in time. The word "opposite" would cease to have any clear meaning. But, we have been here already.

Despite these niggling problems, it might be felt that F37 suitably modified could still capture essential features of the 'contradictory' nature of forces.

In order to investigate this alternative more closely, let us imagine that the two forces operating in the above scenario are aligned so that the angle between them is 180°, once more.57

F38: Let the first force be F1, and the second, F2.

F39: At t1, let F1 + F2 < 0.

F40: At t2, let F1 + F2 = 0.

F41: At t3, let F1 + F2 > 0.

[F24: P1 contradicts P2 only if it counterbalances P2.

F37: Contradictory forces are those that enter into opposition in such a way that they (dialectically) partially or totally cancel each other out.]

F39 and F41 imply that there is a net force operating in the system in either direction; F40 expresses the background condition to F24, where no net force exists.

But, as we saw earlier, we face immediate problems with this way of depicting forces -- difficulties encountered above in relation to the inappropriate analogy drawn between 'contradictions' and mathematical objects -- such as, forces represented by vectors.

Ignoring this 'problem' too, it is worth pointing out again that F40 in fact implies that there are no forces operating in the system (unless we regard the zero vector as a force by default), and F39 and F41 both mean that there is only one force -- the resultant -- at work. On that basis, F37 would collapse for want of forces. No contradiction seems possible if only one (resultant) force is present; still less if no forces are (as in F40).

It could be objected here that in the above, both of the original forces (F1 and F2) still exist, since it is they that create the zero vector and/or any resultant force(s) in the system (as they do in F39 and F41).

The problem with this reply is that it is not easy to see how the two original forces may also be said to exist alongside this third force -- the resultant --, whether the latter is zero or not. If they do exist in this way, we would plainly have three forces in the system, not one, or two.

This would, of course, create energy out of nowhere.58

To be sure, as part of our way of calculating resultants, we apply some mathematics to the relevant components, but that does not mean that nature does the same -- if it did, that would clearly imply nature was mind! No one, it is to be hoped, thinks that in nature there are three forces where once there were only two. And yet, it is this third force that does all the work.

Now, if an F37-type model is in fact applicable in HM, we ought to conclude that the 'contradiction' between Capital and Labour (or that between the forces and relations of production), say, produces a resultant third social force, the nature of which has to this day remained completely obscure. Since, on this model, all motion in the Capitalist system is produced by this "third force", its identification by revolutionaries is, to say the least, of the utmost urgency!59

Moreover, on this view, forces are 'contradictory' when and only when they produce a third resultant force. This might provide DM-fans with a certain amount of aesthetic satisfaction (in that this picture is triadic), but it would in fact sink the theory faster than a lead-lined diving suit sinks a diver. This is because change would then be a result not of contradictory forces, but of resultant forces.

And, as we have seem already, it is just as easy to depict this set-up as 'tautologious' as it is to describe it as 'contradictory' -- even though both descriptors rightly belong in the mystical concept-crusher as hopelessly anthropomorphic.

Howsoever we twist and turn, the equation of forces with 'contradictions' seems to be as misconceived as anything could be. When interpreted metaphorically it turns out to be inappropriate (if not paradoxical and animistic); when interpreted literally it crumbles into incoherence and inconsistency.

So, in order to avoid all these difficulties, we need to return to an alternative that was considered briefly, earlier -- one that could provide DM-theorists with a successful way of interpreting forces as 'contradictions'. However, before this alternative is aired, it is necessary to counter an objection that should by now have occurred to the reader: this whole analysis is abstract and fails to consider "real material forces".59a


'Real' Contradictions

Sinking In Concrete

As noted above, considerations like these would stretch the patience of most dialecticians; indeed, they would probably be the first to point out that this Essay fails to consider real material and empirically verifiable contradictions. When they say things like this they generally (but not exclusively) mean those 'contradictions' that appear in HM, and which help account for the dynamic we see in class society.

However, and in response, it is worth pointing out that many of the examples considered earlier were eminently concrete, and undeniably material!

Nevertheless, if no sense can be made of 'contradictory forces' in nature (as we have seen), then that automatically throws into question their appearance in HM.

Now, as is easy to demonstrate, revolutionaries seriously overuse the word "contradiction" in their endeavour to depict not just capitalism, but the class war in general. In fact, comrades seldom bother to justify their almost neurotically profligate application of this word to everything and anything they attempt to analyse.59b Indeed, it seems to operate almost as a sort of code word that serves merely to identify them to others as one of like mind, or as belonging to the same 'speech community' (with its own jargon, which defines an 'in-group' and excludes those of the 'out-group'), rather than acting as a concept which genuinely applies in every case, or in any case -- or, indeed, which actually means anything at all.

[We shall see why they do this in Essay Nine Part Two and Essay Fourteen part Two.]

But, perhaps this is unfair? In order to substantiate the above allegations, it would be wise, therefore, to consider examples of the "real material contradictions" which supposedly underpin and drive social development.60

[TAR = The Algebra of Revolution (i.e., Rees (1998); HM = Historical Materialism.]


TAR And Concrete Forces

TAR, for example, opens with several apposite and well-observed illustrations of the irrational and destructive nature of Capitalism. As John Rees correctly points out, while life expectancy, for instance, has increased dramatically over the last century or so (even in the poorest regions of the planet), forces have grown alongside this that tend to cancel such advances:

"[S]ince the Second World War there have been 149 wars which have left more than 23 million dead…. On an average yearly basis, the numbers killed in wars during this period have been more than double the deaths in the nineteenth century and seven times greater than in the eighteenth century…. Regression, by any criterion. Yet it is the very same development of human productivity that gives rise both to the possibility of life and to its destruction….

"Everywhere we look another paradox appears. How can it be, for instance, that in the richest capitalist society in the world, the United States, real weekly incomes have fallen steadily since 1973?… How is it that in Britain, where the economy, despite the ravages of recession, produces more than it has ever done…a full quarter of the population live below the poverty line?

"The contradictions are no less striking if we shift our gaze from economics to politics. The introduction of the market to Russia and Eastern Europe was supposed to bring stability and prosperity but has actually produced the opposite." [Rees (1998), pp.1-2.]

First of all it needs emphasising that in what follows the validity of the above comparisons will not be questioned -- nor will the explanation given by Rees for these and other intolerable features of Capitalism. The sole aim here is to ascertain what if anything he (or any one else, for that matter) means by calling these irrationalities "contradictions", and why he and other dialecticians insist on linking the latter term with material forces in nature and society.


The Impertinent Explanation

Of course, the trite and impertinent answer would be that DM-theorists do this simply because it is part of the 'Marxist tradition' to do so (and hence it helps define an 'in group', noted earlier). As seems plain from the record, the use of this word is part of Materialist Dialectics solely because of contingent events in the lives of Marx and Engels (i.e., those that are related to when and where they were born, in which class they found themselves, and how they were educated). And, as fate would have it, their view of the world would likewise have been conditioned by their own "social being" -- to use Marx's term.

In fact, had Hegel died of Cholera 45 years earlier than he did, does anyone think we would be using this term?

[The effect on dialecticians in general of this sort of background will be examined in more detail in Essay Nine Part Two.]

However, because of the towering authority of Marx and Engels, all subsequent dialecticians have been constrained to think and reason along similar lines. They have to use the same vocabulary or risk being be accused of 'Revisionism', branded 'anti-Marxist', and perhaps suffer expulsion, political isolation, or worse. [Or, of course, the sort of ignorant abuse I constantly receive.]

In short, it is quite clear that revolutionaries like Rees use such obscure Hegelian terms derived because prominent comrades did so, and they are merely aping them.

Naturally, the impertinent nature of this 'trite' explanation will not win over many dialecticians (but since a less impertinent one stands no chance either, there is little to lose from advancing one such here).

In that case, there is a pressing need to try to find a better reason why hard-headed materialists should want to anthropomorphise nature and society in this manner, using terms drawn from mystical theology.

Unfortunately, as we will soon find out, there isn't in fact a better explanation as to why such hard-boiled materialists allowed themselves to be conned into accepting and using Hermetic jargon like this (and then employing it quite indiscriminately).

We have already seen how every attempt to render viable the analogy between forces and 'contradictions' fail, hence, it should come as no surprise to see the very same thing happen in HM.

To spoil the ending: the result of all this will be that the impertinent reason is the only one left standing.

[The ideological background to all this will, of course, be elaborated upon and extended considerably in Essay Nine Part Two, and more generally in Essay Twelve.]


Conflict Resolution

The underlying cause of the many absurdities found in Capitalism is -- as TAR rightly points out -- the complex and changing interplay between the "material productive forces of society" and the ambient "relations of production". [Ibid., p.2, quoting Marx.]

That account of the driving force of capitalism (but, interpreted humanistically in terms of the class struggle), I fully accept.

However, this brings us no closer to understanding what it is about opposing (social) forces that merits calling them "contradictions". Why turn a clear deployment of an ordinary word, drawn from the vernacular (with a few easily explained technical terms thrown in) into an obscure doctrine peppered with impenetrable jargon lifted from mystical Idealism (i.e., in this case, "determinate negation", "identity of opposites", "negation of the negation", "mediate", and the like)?

In HM, we can certainly make sense of the term "force" -- and even of "opposing" and "struggle" --; but what is there to gain by calling one and all "contradictory"?61

Some might regard it as a harmless use of this word, but, as we will see in Essay Twelve (summary here), in this instance there is no such thing, just as there is no such thing as a neutral use of the word "oppression". And, as we will also see in Essay Nine Part Two, this particular word allows, and has allowed, assorted Dialectical Gurus to impose contradictory policies, strategies and theses on the faithful, and to 'justify' class collaboration, murder, splits and expulsions (and more) on this basis: if reality is contradictory, the Party must be so too. [An excellent example of which is the way that Trotsky used dialectics to justify the revolutionary defence of the former USSR (on the basis of its contradictory nature), and thus also the heinous invasion of Finland. Another, is the way that Ted Grant, for instance, used 'Materialist Dialectics' to construct his confused theory of 'Proletarian Bonapartism' (sic), which allowed him to rationalise the substitution of the Maoist ruling-class for the Chinese working class -- a topic I have debated here.]

So, these mystical concepts are not simply 'innocent bystanders'; they have helped turn Marxism into a murderously unsuccessful disaster area.


Where The Shoe Pinches

Nevertheless, part of the argument in TAR appears to be the following:

F42: Capitalism seems to offer unprecedented possibilities for human development.

F43: But, in reality Capitalism delivers only partial or faltering advancement.

F44: Alongside this progress we have witnessed major regression.

F45: Hence, Capitalism actually delivers a mixture of development and retreat.

For Rees, the "contradiction" appears to be based on the fact that Capitalism holds out certain possibilities, which it either cannot fully deliver, or cannot provide at all; almost invariably the opposite of what it promises actually unfolds.

Rees clearly believes that the involvement of opposites is important here: instead of peace we find war; in the place of prosperity we find poverty (where it need not be); the growth in human need is not catered for by the incessant search for profit; the waste of human potential conflicts with the increased capacity society has for augmenting and satisfying its members needs, and so on. "Contradictions" seem to arise either from the incongruity that exists between what might be expected of Capitalism (by those who do not understand its nature, presumably) and what it actually delivers --, or from the yawning gap that exists between its potential to satisfy human need and its obvious inability to do so. In that case, forces that seem capable of freeing humanity from want seem to be inextricable combined with others that merely intensify it.

However, these by now familiar observations leave the import of the alleged equation between forces and 'contradictions' still rather vague. In order to clarify Rees's point we perhaps need to consider various plausible interpretations of what he might have meant.

There appear to be several distinct possibilities here:

F46: Capitalism offers A, but delivers only not A.

F47: Capitalism offers A, but delivers both A and not A.

F48: Capitalism offers A, but delivers only B, where A and B are opposites.

F49: Capitalism offers A, but delivers A and B, where A and B are opposites.

F50: Capitalism offers A, but delivers C instead, where C is a paradoxical outcome.

F51: Capitalism offers A, but delivers A and not A as well as B and C.

Doubtless there are many other combinations that could be imagined along similar lines, but they would, I think, be elaborations on these six possibilities. I propose, therefore, to examine each of these in turn, beginning, naturally, with the first.


Not What The System Ordered

The first option was:

F46: Capitalism offers A, but delivers only not A.

But, F46 presents us with a scenario we have seen before; it resembles several earlier unsuccessful attempts to solve this overall problem. As we discovered above, whatever forces there are in the system that actually produce "not A", no contradiction can arise between "A" and "not A" because "A" itself does not exist, since only "not A" will have been actualised in place of "A". Nor can any forces which are at work in the system contradict what they themselves actually produce (viz., "not A" in this case) --, especially if whatever they 'offer' does not exist.

F46 is of no use, therefore, in our search to find a viable way of equating forces and 'contradictions' in HM.


An Apparent Contradiction  -- At Last!

The second alternative went as follows:

F48: Capitalism offers A, but delivers both A and not A.

This seems to be a little more promising since "A and not A" certainly looks like a genuine contradiction. However, because F48 appears to depict contradictory outcomes it cannot illuminate the alleged contradictory connection between forces in society and nature that exist prior to their emergence. This is because F48 is manifestly not about the forces themselves, but about their results.

So, even here, we do not seem to have contradictory forces.

Nevertheless, this section is aimed at considering the last few remaining options left open to DM-theorists to make their ideas comprehensible, so F48 will not be abandoned just yet.

In fact, F48 corresponds to a relation depicted abstractly in an earlier section (i.e., that between E1 and E2, in F6 to F9, above, reproduced below) -- but interpreted here concretely (if schematically). Hence, it looks like we might at last have found a genuine interpretation of E1 and E2 that is undeniably 'contradictory'.

F6: Let force P1 oppose force P2 in configuration C1 in nature.

F7: Here, opposition amounts to the following: the normal effects produced by P1 in C1 (had P2 not been present) are the opposite of the effects P2 would have produced in C1 (had P1 similarly not been operative).

F8: Let P1's normal effects in C1 be elements of an event set E1, and those of P2 be elements of E2. For the purposes of simplicity let E1 and E2 be disjoint.

F9: By F7, E1 and E2 contain only opposites.

Unfortunately, this appearance is illusory since the conjunction of "A" and "not A" cannot be considered contradictory until it is clear what interpretation is to be given to each schematic letter "A".

It is worth recalling that we are looking for a literal interpretation of the term "contradiction" which will allow DM to surpass FL -- not a metaphorical or analogical sense of the word -- still less one that possesses a secondary or derivative sense (or even the 'special' DM-sense that has yet to be explained). As should be obvious, this search is of the utmost importance if we are to rescue from oblivion the idea that forces and 'contradictions' may be equated objectively -- and not poetically.

Clearly, there are several different ways of reading the expression "A and not A"; some of these will be contradictions, others not.

In what follows, I shall employ a further example taken from TAR (quoted above), which seems to many DM-theorists to be a genuine contradiction (i.e., between wealth and poverty). In that case, this involves interpreting "A" as "wealth", and "not A" as "not wealth" (it clearly cannot be "not poverty"!). In that case, "A and not A" would cash out as "wealth and not wealth".62

Unfortunately, the problem with this way of taking "A and not A" is that it actually creates a phrase and not a clause, indicative sentence or proposition.63 As such, it cannot be a literal contradiction.

[Most DM-fans miss this point since their knowledge of logic rivals that of George W Bush. That, of course, does not stop them pontificating on the subject.]

The only apparent way to situate this phrasal conjunction in a propositional context would be to interpret it a little more loosely -- perhaps along the following lines:

F52: Capitalism produces wealth and not wealth.64

As such, F52 is a paraphrase of:

F52a: Capitalism produces wealth and Capitalism produces not wealth.

Or perhaps even:

F53: Capitalism produces wealth for some and not wealth for others.65

Again, F53 itself is short for:

F53a: Capitalism produces wealth for some and Capitalism produces not wealth for others.

None of these look at all promising; they are not just stylistic monstrosities, their import is rather unclear. Anyway, F53 and F53a are not contradictory -- that is, no more than, say, a bottle would be contradictory if it supplied drink for some but not for others, or any more than the claim that "forces are contradictory" would itself be 'contradictory' if it convinced some but not others. No one would think they had been contradicted if they asserted that a certain factory, say, produced a few batches of defective Widgets, and someone else clamed it also produced some that were non-defective.66

Anyway, F52a is far too vague as it stands -- it is certainly no more of a 'contradiction' than F53 and F53a are, and probably for the same reason. If sentences like these have no clear meaning they cannot possibly assist in a clarification of DM. Hence, a further widening of the interpretation of "A and not A" is called for if we are to gain a clear view of the implications of F47.

F54: Capitalism produces Capitalists who are wealthy and workers who are not wealthy.

As was the case with F53 and F53a, F54 is not even a contradiction. Again, anyone asserting the first clause of F54 who was then confronted with the second would not feel that they had been contradicted -- this is because the first clause is about Capitalists, while the second is about workers. To be contradictory F55 would have to be written as:

F55: Capitalism produces worker W1 (or Capitalist C1), who is both wealthy and not wealthy at the same time and in the same respect.

But, quite apart from the fact that no one would assent to, or even think to assert F55, it possesses no clear sense. The situation would be no better if it were re-written as:

F55a: Capitalism produces a set of workers W (or Capitalists C), who are both wealthy and not wealthy at the same time and in the same respect.

It is reasonably certain that Rees meant neither F55 nor F55a. On the other hand, if he had intended either, it would be unclear what he could possibly have meant by one or both. At best, F55 and F55a might be re-interpreted in a comparative sort of way, as follows:

F55b: Capitalism produces a set of workers W that is both wealthy (in comparison to a set of peasants P) and not wealthy (in comparison to a set of Capitalists C), at the same time and in the same respect.

But, F55b is no more contradictory than, say, a proposition about the length of a copy of TAR would be if it were compared with another proposition about the length of a copy of The New York Times (i.e., that the first is longer than the second) and then with another proposition about the length of a copy of Das Kapital (i.e., that the first is shorter than the third). Hence, the observation that TAR is both long compared to The New York Times and short compared to Das Kapital is not, one imagines, what most DM-theorists mean by "contradiction". If it were, their theory would be based on linguistic naivety, and little else. That, of course, is the whole point of the phrase "and in the same respect", tacked on the end of several of the above propositions. Consequently, it rather looks like F47 cannot be squeezed into this particular dialectical boot after all.

More problematic: is either of these options going to turn into the other?

In the above example, is W going to turn into C, and C into W? Indeed, is wealth going to turn into poverty? But, if these were 'genuine' 'dialectical opposites/contradictions', they most surely should.

[On this, see here and here.]

Further attempts to interpret "A and not A" can be extended almost indefinitely. DM-enthusiasts are welcome to play around with them as much as they like, the end result will be no different. There are no literally true contradictions that can be manufactured out of "A and not A" in this context. This is because, if a contradiction were true, it would cease to be a literal contradiction. As indicated in Essay Five, if and when such 'contradictions' were encountered, they would normally be viewed as either figurative or the result of an ambiguity of some sort. There is no way around this convention this side of altering the meaning of the word "contradiction". And, even this would be a little help to DM-enthusiasts since that would 'solve' the problem by means of yet more subjective ad hoc linguistic reform.67


Opposite Tendencies I

In that case, perhaps F48 is the reading we are searching for?

F48: Capitalism offers A, but delivers only B, where A and B are opposites.

Unfortunately, as we have seen several times already, since A does not exist -- Capitalism not having delivered it --, it cannot 'contradict' B. This means that F48 is not a viable reading of TAR's intentions, either. Even if B 'contradicted' forces and/or processes which were already present, that would just return us to where we were when we considered several examples earlier, such as this:

F6: Let force P1 oppose force P2 in configuration C1 in nature.

F7: Here, opposition amounts to the following: the normal effects produced by P1 in C1 (had P2 not been present) are the opposite of the effects P2 would have produced in C1 (had P1 similarly not been operative).

F8: Let P1's normal effects in C1 be elements of an event set E1, and those of P2 be elements of E2. For the purposes of simplicity let E1 and E2 be disjoint.

F9: By F7, E1 and E2 contain only opposites.

Another dialectical dead-end, I fear, for here we have yet more non-existents being 'contradicted' by existents.


Opposite Tendencies II

Does, therefore, F49 provide DM with a lifeline?

F49: Capitalism offers A, but delivers A and B, where A and B are opposites.

If we now read "A" as "wealth" and "B" as "poverty" once more, we would have the following:

F63: Capitalism offers wealth, but delivers wealth and poverty, where wealth and poverty are opposites.68

However, there are several problems with this paraphrase. One of these concerns the supposition that capitalism actually does offer wealth. Admittedly, for propaganda purposes, its ideologues often claim that it does -- but who believes them? Certainly, blatant lies like this cannot serve as part of a socialist analysis of capitalism.69

Perhaps then we should re-interpret F56 in the following manner?

F57: Capitalism develops productive forces capable of delivering wealth to all, but it actually delivers wealth to a minority, and poverty to most of the rest, where wealth and poverty are opposites.

However, in F57 we are confronted with a subtle change in the way that the "A" of F49 has been interpreted in the opening clause: it now stands for something like the system's capacity to "develop productive forces capable of delivering wealth". But in the last clause it simply stands for "wealth", as before. Hence, F57 is actually equivalent to the following:

F49a: Capitalism develops D, but actually delivers B and C, where B and C are opposites.

Or perhaps:

F49b: Capitalism develops D (which has the potential to produce B), but actually delivers B and C, where B and C are opposites.

Here, the 'contradiction' would seem to be that between either (1) Capitalism's capacity to deliver wealth and its actual deliverance of poverty, or (2) the wealth it delivers to some and the poverty it delivers to the rest.

In the first case, clearly we don't have a contradiction. This is because, a capacity is an unrealised potentiality, and as such it cannot contradict something which does exist -- no more than, say, a woman's un-actualised capacity to play the flute contradicts her actualised skill with the piano, or even her actualised state of living without a flute -- or, indeed, of not being able to play the flute while she has to make do with that piano.

The second option is no contradiction either, however much it offends our sensibilities. It is no more a contradiction than, say, £10,000 ($20,000) in one pocket contradicts £0.01 ($0.02) in another, or no more than a £5 ($10) note in a millionaire's wallet (assuming this is all she has on her at the time) contradicts the £1000 ($2000) in a worker's pocket (who has just won a compensation claim, say) -- even if these two are sat next to each other at a UK New Labour rally. To call these "contradictions" would be bizarre -- even on DM-terms. [Are they struggling? Do these turn into one another?]70

As we saw earlier, anyone who thought otherwise would be openly advertising their own linguistic naivety, if not perversity, but not advancing the cause of science.

In any case, there can be no literal contradiction between something that does not exist (i.e., the prospect of wealth under Capitalism, where this is meant to be wealth for all) and something that does exist (i.e., the mixed fortunes of the people who have to endure conditions as they are).

Despite this, it might still be felt that the situation is not as bad as the above makes out; the emphasis in F49 is on what Capitalism actually delivers, not on what it genuinely (or otherwise) offers. If "wealth" and "poverty" are real opposites, F49 could still serve in the way DM-theorists intend -- or so it might seem.

Again, this desperate alternative diverts attention once more away from allegedly contradictory forces and onto their effects. In that case, the nature of the direct relation between whatever forces produced these effects is still obscure, and not the least bit contradictory.

Nevertheless, even when we consider these effects, a nagging question remains: just what is so contradictory about wealth and poverty existing side by side? Admittedly, to any socialist, this state of affairs is as intolerable as it is indefensible, but there still does not seem to be a literal contradiction involved here. True, this state of affairs may be paradoxical (but not to a Marxist); however, the presence of one of these alleged opposites does not entail that an assertion that the other opposite also obtains is false, as it would have to do if a literal contradiction were intended.71

If, on the other hand, we wish to re-define the word "contradiction" so that it becomes the equivalent of "paradox", "unjust", "something contrary to expectations", "deplorable" (and so on), all well and good. But then that would concede the point being made here that social reality is only 'contradictory' because of linguistic tinkering to that effect, and the claim that DM-'contradictions' (in HM) are literal would have to be abandoned. Seen in this way, DM-'contradictions' would either be figurative, or they would depend on the use of a word ("contradiction") that has been 'redefined' in order to produce the right result.72

On the other hand, if the word "contradiction" possesses a special, literal DM-sense, which allows for its legitimate use here, then DM-theorists have yet to say what that is.

It might be volunteered here that one such sense is that "contradiction" implies opposition and tension. But, even though "wealth" and "poverty" are opposites in the ordinary sense, they do not seem to oppose each other in an active way, as one would expect they should if they genuinely illustrated the validity of the equation of 'contradictions' with forces. Admittedly, poverty acts as brake on development of the productive forces at certain points in history (warping the development of those who have to endure it, etc.), it stokes up resentment, class hatred and foments struggle. But, over and above the influence these states of affairs have on human agents, these lifeless concepts appear to have no active connection with one another. Sure enough, the material situations they express might indeed create tension in those who have to endure them, but none of the latter would describe what they feel by using the word "contradiction", unless, of course, a fast-talking and allegedly materialist disciple of Hegel had sold them on the idea. In ordinary language, the word cannot be given such a meaning without altering the sense it already has.73

Furthermore, if this set of consequences is meant to be taken as a new gloss on F56 (by way of illustrating the alleged 'contradiction' between E1- and E2-type events discussed earlier) then it would soon collapse into the claim that it is the effects of effects that are 'contradictory', and not the original effects themselves. Down this road there lies, I fear, yet another "bad infinity" --, which ends "who knows where?"

The second difficulty with this reading is that although wealth and poverty are genuine opposites (again, in the ordinary sense), they do not appear to be classic examples of dialectical-UOs (even if we knew what those were!). To be sure, under Capitalism the wealth of one class is connected with the poverty of others, but this is a familiar causal connection. They are not internally-, or logically-, related in reality, despite claims to the contrary. That this is so can be seen from that fact that were this not the case, we would find we could not agree (with Engels) that under Capitalism poverty exists "where it need not be".

If there were a 'dialectical' (or "internal") "unity in difference" connecting poverty and wealth (like that which dialecticians allege between, say, the north and south poles of a magnet, or that between Capitalist and Worker (as classes), then we would not be able to argue that socialism will eliminate one without abolishing the other. But, the whole point of a socialist society is that all should become as wealthy as the productive forces will allow. If there were a logical link between these two states (poverty and wealth) then they would be inseparable in all modes of production and we would have to temper our slogans somewhat. We might then have to point out that in eradicating poverty, workers would be eradicating wealth, too. That we do not so argue -- we actually claim the opposite that socialism can produce wealth for all -- indicates that the relation between wealth and poverty is not a logical (or internal) connection, but is causal.

Of course, it could be argued that there is an internal/logical link between "wealth and poverty under capitalism" and "wealth under socialism"? This objection will be dealt with below, and in Note 74.74

The basic problem here, of course, derives from the anthropomorphism implicit in the idea that concepts can enter into struggle with one another. This mystification appears as part of the belief that because wealth and poverty are opposites they are actively oppositional and cause struggles, of themselves. On this account, it is the opposite nature of concepts that creates struggle, whereas in reality it is clearly material conditions that cause it. Only by confusing a causal connection with a conceptual one does DM get off the ground here, as elsewhere (if this is what dialecticians mean, of course!). But, as we have seen, this is just one more consequence of LIE and the RRT (defined in Essay Twelve -- and which was a conclusion of Part One of this Essay).75

[LIE = Linguistic Idealism; RRT = Reverse Reflection Theory.]

The animated DM-contrast that is imagined to exist between dead concepts like these seems plausible only because they are viewed as the idealised equivalents of the real relations between human beings, reified in an inappropriate metaphysical/linguistic form. Human beings give life to the concepts they use, but under circumstances not always of their own choosing, and they do so as a result of their practical activity, modified by ambient class relations. The reverse does not happen; 'concepts' do not give life to human relations, although their use by human agents might affect the roles that such concepts can play in material life (and they certainly could modify the ideas that individuals from antagonistic classes form of their oppositional connections and their own material interests, etc.). Unless we suppose concepts to be agents (in a sort of inverted Hegelian form, wherein perhaps they walk the earth in place of human beings), they cannot 'reflect' things that human beings haven't sanctioned for them, by means of the above constraints. History is after all the result of the class war, not a consequence of the struggle between concepts.

As should seem obvious, the above comments are based on theoretical considerations drawn from HM, but this is precisely where that scientific theory can provide the interpretative sophistication that DM and/or 'Materialist Dialectics' lack, obscure and invert in an idealised/fetishised form.76

This shows, once again, that the inversion DM-theorists say they have inflicted on Hegel was merely formal; their system can only 'work' in his Ideal universe.


Final Round-Up

In that case, the only options left open are F50 and F51. They were: 

F50: Capitalism offers A, but delivers C instead, where C is a paradoxical outcome.

F51: Capitalism offers A, but delivers A and not A, as well as B and C.

However, since these two are clearly variations upon F48 and F49, they do not appear to be viable alternatives. DM-apologists are welcome to make of them what they can.


Dialectics In ER

We have thus seen that concepts drawn from Hermetic Philosophy (and deployed in DM) fail badly when an attempt is made to apply them to, or connect them with, the forces operating in nature and society. In that case, the impertinent answer (to the question why hard-boiled revolutionaries use such mystical terms in HM) offered above is the only one left in the ring: dialecticians use mystical jargon like this simply because it is traditional to do so.

This means that this part of DM (already under intensive care in the Emergency Resuscitation ward) is ready to be measured for its pine overcoat and lowered 6 feet closer to the Earth's core.


A Last Desperate Attempt

However, before we call for a Hermetic High Priest to read DM its last mystical rites, we should make one last desperate bid to resuscitate this moribund 'theory'. In fact, we are now in a position to return to several earlier abandoned alternatives in a vain attempt to rescue this part of DM from its long overdue burial.


Back To The Drawing Board

Here, I present an interpretation based upon the one expressed in F6-F9, above:

F6: Let force P1 oppose force P2 in configuration C1 in nature.

F7: Here, opposition amounts to the following: the normal effects produced by P1 in C1 (had P2 not been present) are the opposite of the effects P2 would have produced in C1 (had P1 similarly not been operative).

F8: Let P1's normal effects in C1 be elements of an event set E1, and those of P2 be elements of E2. For the purposes of simplicity, let E1 and E2 be disjoint.

F9: By F7, E1 and E2 contain only opposites.

To these we need to add the following:

F58: Force P1 contradicts P2 in so far as some or all of E1 and E2 are contradictory (internally, or to one another).

Unfortunately, this latest re-interpretation cannot work, either. This is because if one or both of E1 and E2 do not exist (as a result of the operation of P1 and P2) there can be no contradiction; as we have seen several times already, F58 would imply a 'contradiction' between sets of events that do not co-exist.77

It looks, therefore, like this particular interpretative seam has been thoroughly worked-out. There is no gold left, only slag -- indeed what little gold there was that had been mined by Hegel & Co., unfortunately turned out to be nothing but Iron Pyrites.

We need to find a new approach to save this rapidly fading 'theory' from being sent to the morgue.


DM And The Revival Of Teleology

The only avenue of escape for DM-theorists seems to rely on yet another interpretation which was postponed from earlier, wherein 'contradictions' were said to exist between the effects of forces (or between forces and the effects of other forces),  rather than between forces themselves. One alternative involved Engels's suggestion that forces should be edited out of the picture, leaving behind just the relative motion between bodies to give some content to the idea that 'contradictions' cause change.

However, the first of these options had to be abandoned because it meant that forces 'contradicted' prevented effects, implicating this part of the theory with the idea that forces could 'contradict' non-existent entities. The second option appeared to undermine the dialectical unity of nature.

Nevertheless, I now propose to examine a re-vamped version of the first of these alternatives, one aimed at circumventing the difficulties noted above. The good news is that this new interpretation solves the problem created by the second option; the bad news is that it introduces far worse difficulties of its own.

This earlier attempt was based on the following:

F17: Event E consists of a set of inter-connected sub-events E1-En.

F18: Events E1-En form complexes of material interactions (of a sufficiently mediated and contradictory nature) within T, if ever they occur.

F19: Let P1 prevent some or all of E1-En from taking place.

F20: Therefore, some or all of E do not exist (or will never exist), or take place.

As we saw above, an existing force P1 appears to 'contradict' a non-existent event (or series of events), which rendered this interpretation useless. The following re-vamped version of these sentences now aims to fix this bug:

F59: Event E consists of a set of inter-connected sub-events E1-En.

F60: Events E1-En form complexes of material interactions (of a sufficiently mediated and contradictory nature) within T, if ever they occur.

F61: Let P1 prevent some or all of E1-En from taking place.

F62: Therefore, some or all of E do not exist (or will never exist), or take place.

F63: Hence, propositions that express the fact that one or more of E1-En have been prevented from taking place contradict propositions that express an expectation that they will occur.

Since, an expectation can exist alongside a realisation that it has been thwarted (in some cases), this might appear to solve the problem.

However, F63 is clearly of little assistance since, not only would be inapplicable throughout the Universe at all times, it does not even record a contradiction. [The propositions it expresses to are of the form 'p and q', not 'p and not p', as required.]

Perhaps F63 could be altered to circumvent this difficulty?77a

F64: Propositions that express the prevention of one or more of E1-En taking place contradict propositions that depict the dispositional properties of Pn, the set of forces that would have produced all of E1-En, but for the presence of P1.

One immediate problem with F64 is that it is not at all clear what the "dispositional properties" of forces are. Objects certainly have dispositional properties as a result of their microstructure and of their relationship with other bodies -- if, that is, the term "dispositional" is not read anthropomorphically, as it usually is.

Even so, since forces are not obviously bodies (although they can apparently be carried by them -- if we accept certain parts of modern Physics --, but even then this is apparently cashed out in terms of transferred momentum, i.e., along neo-Engelsian lines),78 the ascription of dispositions to forces themselves amounts perhaps to a disguised reference to the affect forces have on such bodies. In that case, we would have here an explanation of contradictions that appealed to the effect of effects, yet again.

[Anyway, F64 does not even record a contradiction since the propositions it expresses to are of the form 'p and q', not 'p and not p', once more.]

Nevertheless, perhaps F64 can be re-jigged -- maybe along the following lines:

F65: Propositions that express the prevention of one or more of E1-En taking place contradict propositions that depict the normal operation of Pn, the set of forces that would have produced all of E1-En, but for the presence of P1.

Unfortunately, not only does F65 fail to record a contradiction (since, yet again, the propositions it expresses to are of the form 'p and q', not 'p and not p'), what it says brings us back once more to a consideration of the inter-relationship between forces as a way of understanding 'contradictions', as opposed to the present model, which sought to interpret 'contradictions' as the relationship between forces and the effects of other forces.

Anyway, F65 is of little use: if the normal operation of Pn is disturbed (so that it does not take place) there would be nothing for P1 to 'contradict'. This annoying but recurring fact is precisely what required the current consideration of the actual effects of forces, since they do exist -- as opposed to the prevented effects of forces, or even forces which cease to operate, which don't.

It now seems that unless we can specify how the effects of forces can 'contradict' other forces (or other effects), this part of DM will be as good as dead, but not yet buried. Maybe the following option will help revive it:

F66: Propositions that express the prevention of one or more of E1-En taking place contradict propositions that express the operation of Pn, in that the presence of E1 (the effect of P1) excludes some or all of E2-En.

However, this is no use, either, since it matters not how effectively some or all of E2-En are excluded; E1 may only 'contradict' that which exists, and, ex hypothesi, once excluded, effects E2-En would no longer be around to be 'contradicted'.

The next suggestion constitutes, in my view, the only way to keep this critically ill part of DM alive:

F67: The prevention of one or more of E1-En taking place contradicts the aims of Pn, the set of forces that would have produced all of E1-En but for the presence of P1.

[F67 will need to be re-written in a 'propositional' form, but since that would make this example even more unwieldy than it already is, that has not been attempted here.]

Since aims can exist where results and effects do not, we seem at last to have a genuine 'contradiction' (even if it is still figurative!).

The bad news is that this apparent tonic soon turns into yet another dose of strychnine. This is because, of course, not only does F67 not record a contradiction (for reasons given several times already), we cannot attribute aims to forces unless we wish to introduce teleology back into nature. F67 can only therefore apply to forces under the control of human agents, or to their animistically projected counterparts in reality --, that is, if we genuinely want to go down the latter route and regard nature in this ancient/mystical manner.

It is no coincidence then that the only interpretation that appears to render this part of DM viable is one that reveals the anthropomorphism implicit in its concepts.

Alternatively, it is equally unsurprising that this is the one option that underlines the only reading that works in HM, one that puts forces under human control (all the while clearly distinguishing them from literal contradictions).79

Unfortunately, this now means that F67 cannot help revive the DM-corpse.


Coup De Grace

It was noted earlier that there is a general problem afflicting the identification of forces with 'contradictions' -- i.e., if these are viewed as dialectically-united 'opposites'. In connection with that, we also saw that DM-classicists argued that such opposites all turn into one another. But is it even plausible to suppose forces can do this? Is it credible that a gravitational force, say, can turn into a magnetic force, or into an electrical force? Do all R-type forces turn into A-type forces? Where in Physics is it postulated that gravity can become a repulsive force?

Undoubtedly, electricity and magnetism are inter-linked on modern Physics (and are in fact manifestations of one of the four fundamental forces in nature, in electromagnetism), but they do not struggle with one another, and neither do the particles on which they depend. Such forces, so we are told, are created by exchange particles, but they are not an expression of a 'struggle' between particles.

To be sure, magnetic fields are reversible, as are electrical fields, but this is not true of all fields (even though all four forces can change in many different ways), but it is far from clear that this is because of any 'struggle' going on between them, either. For example, the origin of the reversal of the Earth's magnetic field may lie deep inside the core, or, perhaps, inside the crust --, or it may even be external (with one set of theories blaming meteor impact); scientists are not sure. But not one geophysicist, to my knowledge, is investigating the 'contradiction' between North and South to find its cause.

If that is so, then even if all of the objections voiced in this Essay are misguided in some way, the 'dialectical' equation of forces and contradictions does not work even in its own terms!

Do the Relations of Production really turn into the Forces of Production?


For Dialectics, Truth Is A Hole --, And it's Six foot Deep

Since there appears to be no way that DM-'contradictions' can be given a literal or figurative interpretation as forces which survives a moment's scrutiny -- when applied in nature or society, in abstract or concrete form --, this part of DM can at last be given a decent burial. Indeed, we can even call its time of death: August 27th, 1770.

It won't be missed -- well, not by us materialists.

Please..., send no flowers.80



1. For example, Engels declared:

"Motion is the mode of existence of matter…. All rest, all equilibrium, is only relative, only has meaning in relation to one or another form of motion…. Matter without motion is just as inconceivable as motion without matter…. Each separate movement strives toward equilibrium, and the total motion puts an end to the equilibrium.... [Engels (1976), pp.74-77.]

"So long as we consider things at rest and lifeless, each one by itself…we do not run up against any contradictions in them…. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence. Then we immediately become involved in contradictions. Motion itself is a contradiction…. [T]here is a contradiction objectively present in things and processes themselves, a contradiction is moreover an actual force.... [Ibid., pp.152-53.]

"Processes which in their nature are antagonistic, contain internal contradiction; transformation of one extreme into its opposite…. [This is] the negation of the negation…. [which is a] law of development of nature, history and thought; a law which…holds good in the animal and the vegetable kingdoms, in geology, in mathematics, in history and in philosophy…. [D]ialectics is nothing more than the science of the general laws of motion and development of nature, human society and thought." [Ibid., pp.179-80.]

"The great basic thought that the world is not to be comprehended as a complex of ready-made things, but as a complex of processes, in which the things apparently stable…go through an uninterrupted change of coming into being and passing away…. [T]he transformation of energy, which has demonstrated to us that all the so-called forces operative in the first instance in inorganic nature -- mechanical force and its complement, so-called potential energy, heat, radiation (light, or radiant heat), electricity, magnetism and chemical energy -- are different forms of manifestation of universal motion…. [W]e have now arrived at the point where we can demonstrate the interconnection between the processes in nature not only in particular spheres but also the interconnection of these particular spheres on the whole…by means of the facts provided by empirical natural science itself." [Engels (1888), pp.609-11.]

"All motion is bound up with some change of place…. The whole of nature accessible to us forms a system, an interconnected totality of bodies…. [These] react one on another, and it is precisely this mutual reaction that constitutes motion…. When two bodies act on each other…they either attract each other or they repel each other…in short, the old polar opposites of attraction and repulsion…. It is expressly to be noted that attraction and repulsion are not regarded here as so-called 'forces', but as simple forms of motion.... [Engels (1954), pp.70-71.]

"All motion consists in the interplay of attraction and repulsion. Motion, however, is only possible when each individual attraction is compensated by a corresponding repulsion somewhere else…. Hence, all attraction and all repulsions in the universe must mutually balance one another…. Dialectics has proved from the results of our experience of nature so far that all polar opposites in general are determined by the mutual action of the two opposite poles on each other, that the separation and opposition of these poles exist only within their mutual connection and union.... [Ibid., p.72.]

"All natural processes are two-sided, they are based on the relation of at least two operative parts, action and reaction. The notion of force, however, owing to its origin from the action of the human organism on the external world…implies that only one part is active, the other part being passive…[and appearing] as a resistance.... [Ibid., p.82.]

"Dialectics…prevails throughout nature…. [T]he motion through opposites which asserts itself everywhere in nature, and which by the continual conflict of the opposites…determines the life of nature.... [Ibid., p.211.]

"[A]ttraction is a necessary property of matter, but not repulsion. But attraction and repulsion are as inseparable as positive and negative, and hence from dialectics itself it can already be predicted that the true theory of matter must assign a place to repulsion as to attraction, and that a theory of matter based on mere attraction is false…. Equilibrium is inseparable from motion…. All equilibrium is only relative and temporary…. Motion of the heavenly bodies [is an] approximate equilibrium of attraction and repulsion in motion." [Ibid., pp.243-46.]

This is how Bukharin put things:

"[T]he world consists of forces, acting many ways, opposing each other. These forces are balanced for a moment in exceptional cases only. We then have a state of 'rest', i.e., their actual 'conflict' is concealed. But if we change only one of these forces, immediately the ‘internal contradictions’ will be revealed, equilibrium will be disturbed, and if a new equilibrium is again established, it will be on a new basis, i.e., with a new combination of forces, etc. It follows that the 'conflict,' the 'contradiction,' i.e., the antagonism of forces acting in various directions, determines the motion of the system…." [Bukharin (1925), p.74.]

And here are Lenin's thoughts:

"The identity of opposites…is the recognition…of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature…. Development is the 'struggle' of opposites." [Lenin (1961), pp.357-58.]

Comrade Cornforth argued as follows:

"If we consider the real, complex movements and interconnections of real complex things, then we find that contradictory tendencies can and do exist in them. For example, if the forces operating in a body combine tendencies of attraction and of repulsion, that is a real contradiction…. [C]ontradiction is the driving force of change…. [O]nly the presence of contradictions in a process…provides the internal conditions making change necessary…. The real universe is…full of contradictions –- the contradictions of attraction and repulsion studied by physics…." [Cornforth (1976), pp.92-95.]

The author of TAR had this to say:

"The conservatism of Hegel's system is thus buried in his notion of contradiction. Contradictions in Hegel are merely intellectual contradictions to be resolved by merely intellectual methods…. The dialectic is therefore only a pseudo-dialectic; its contradictions are never those of opposed material forces capable of doing real damage or of effecting real progress…. Marx was, however, obliged to transform completely the terms of the dialectic when he altered its starting point from abstract concepts to real material forces…. The contradictions are no longer simply between concepts but between real, material forces…. Marx and Engels's dialectic is utterly different from Hegel's. It starts from real, material, empirically verifiable contradictions." [Rees (1998), pp.67-69, 83.]

Woods and Grant put things thus:

"Dialectics explains that change and motion involve contradiction and can only take place through contradictions.... Dialectics is the logic of contradiction....

"So fundamental is this idea to dialectics that Marx and Engels considered motion to be the most basic characteristic of matter.... [Referring to a quote from Aristotle] [t]his is not the mechanical conception of motion as something imparted to an inert mass by an external 'force' but an entirely different notion of matter as self-moving....

"The essential point of dialectical thought is not that it is based on the idea of change and motion but that it views motion and change as phenomena based on contradiction.... Contradiction is an essential feature of all being. It lies at the heart of matter itself. It is the source of all motion, change, life and development. The dialectical law which expresses this idea is the unity and interpenetration of opposites....

"The universal phenomena of the unity of opposites is, in reality, the motor-force of all motion and development in nature. It is the reason why it is not necessary to introduce the concept of external impulse to explain movement and change -- the fundamental weakness of all mechanistic theories. Movement, which itself involves a contradiction, is only possible as a result of the conflicting tendencies and inner tensions which lie at the heart of all forms of matter....

"The opposing tendencies can exist in a state of uneasy equilibrium for long periods of time, until some change, even a small quantitative change, destroys the equilibrium and gives rise to a critical state which can produce a qualitative transformation. In 1936, Bohr compared the structure of the nucleus to a drop of liquid, for example, a raindrop hanging from a leaf. Here the force of gravity struggles with that of surface tension striving to keep the water molecules together. The addition of just a few more molecules to the liquid renders it unstable. The enlarged droplet begins to shudder, the surface tension is no longer able to hold the mass to the leaf and the whole thing falls.

"Attraction and Repulsion

"This is an extension of the law of the unity and interpenetration of opposites. It is a law which permeates the whole of nature, from the smallest phenomena to the largest. At the base of the atom are immense forces of attraction and repulsion....

"Engels points out the universal role of attraction and repulsion:

"'All motion consists in the interplay of attraction and repulsion. Motion, however, is only possible when each individual attraction is compensated by a corresponding repulsion somewhere else. Otherwise in time one side would get the preponderance over the other and then motion would finally cease. Hence all attractions and all repulsions in the universe must mutually balance one another. Thus the law of the indestructibility and uncreatability of motion is expressed in the form that each movement of attraction in the universe must have as its complement an equivalent movement of repulsion and vice versa; or, as ancient philosophy—long before the natural-scientific formulation of the law of conservation of force or energy—expressed it: the sum of all attractions in the universe is equal to the sum of all repulsions.'

"In Engels' day, the prevailing idea of motion was derived from classical mechanics, where motion is imparted from an external force which overcomes the force of inertia. Engels was quite scathing about the very expression 'force,' which he considered one-sided and insufficient to describe the real processes of nature. 'All natural processes,' he wrote, 'are two-sided, they are based on the relation of at least two operative parts, action and reaction. The notion of force, however, owing to its origin from the action of the human organism on the external world, and further from terrestrial mechanics, implies that only one part is active, operative, the other part being passive, receptive.' (38)

Engels was far in advance of his time in being highly critical of this notion, which had already been attacked by Hegel. In his History of Philosophy, Hegel remarks that 'It is better (to say) that a magnet has a soul (as Thales expresses it) than that it has an attractive force; force is a kind of property that, separate from matter, is put forward as a kind of predicate -- while soul, on the other hand, is this movement itself, identical with the nature of matter.' This remark of Hegel, approvingly quoted by Engels, contains a profound idea -- that motion and energy are inherent to matter. Matter is self-moving and self-organising." [Woods and Grant (1995), pp.43-45, 47, 68, 71-72. Their reference (38) is to Engels (1955), pp.95-96, 110. Formatting altered to conform to the conventions adopted here. Bold emphases added.]

It is interesting to note that Woods and Grant blithely record Engels's approving reference to Hegel's depiction of magnets as having 'souls' while failing to notice its mystical implications. How could this notion -- i.e., 'having a soul' -- be given a 'materialist spin', aimed at putting it back on its feet/'the right way up'? Presumably a soul is a soul, upside down or not.

In addition, we have already noted that an on-line dictionary 'defines' contradiction in somewhat similar terms, but since that is has already been commented upon, no more will be said about it here.

True Contradictions?

However, several comrades have tried to argue that there are indeed 'true contradictions' in reality. By far and away the most sophisticated of these is Graham Priest. But, it is far from clear whether the contradictions he considers are dialectical, that is, should we ever be told what a 'dialectical contradiction' is. Priest's work will be considered in more detail in an Additional Essay, to be posted at this site in the next year or so.

Despite this, Cornforth himself made an attempt in this direction when he aired an argument intended to show that contradictions actually 'exist' in the world -- contrary to the view endorsed here that a contradiction (in logic, and in its simplest form) is merely a certain sort of truth-functional relation between a proposition and its negation: 


"The contradiction in things is a very familiar state of affairs. There is nothing in the least abstruse about it, and it is often referred to in everyday conversations. For example, we speak of a man as having a 'contradictory' character, or as being 'a mass of contradictions'…." [Cornforth (1976), pp.92-93.] 

In which case, presumably, when we describe someone as a "bit of a puzzle" Cornforth thinks we mean that he or she (or parts of them, at least) may be purchased in a magic shop or toy store, and then solved with some difficulty -- or that when we read this:

"All the world's a stage,

And all the men and women merely players;

They have their exits and their entrances." [William Shakespeare, As You Like It, 2/7.]

we should all try and remember our lines, and make sure the audience (what?) can hear us.

Clearly, Cornforth has never heard of metaphor. [Why this is not a literal use of "contradiction"/"contradictory" is considered below.]

Now, even Cornforth admits that describing people as "contradictory" in fact involves a reference to their dispositions (or "tendencies"): 

"This means that [they evince] opposed tendencies in [their] behaviour, such as gentleness and brutality, recklessness and cowardice, selfishness and self-sacrifice." [Ibid., p.93.] 

If this concession is meant to commit his theory to a dispositional account of contradictions, then much of classic DM would become obsolete. The fact that someone might have a disposition to be, say, brave in certain circumstances, and cowardly in others, in no way suggests they are both at once. What is in doubt is whether the joint actualisation of these dispositions (in certain states or performances) may be expressed by means of true propositions (without ambiguity), and in the same respect.

Hence, the fact that an iron bar could be red hot at one end and icy cold at the other is not a contradiction (even though an iron bar is at any time disposed to be both). Asserting that the entire bar is both of these (at the same time) might be thought by some to be contradictory (but, that will depend on the circumstances); and yet even that would merely be an inconsistency (for both descriptions could be false if the said bar was merely warm).

[It is worth recalling here that two contradictory propositions cannot both be true, and cannot both be false, at once. Dialecticians in general appear not to be aware of the latter condition (possibly because Hegel appears not to have been, either!).]

Anyway, as noted above, such contrary ascriptions would merely be inconsistencies. For example, if NN is said to be both angry and calm (i.e., not angry) all at once, that would only be a contradiction if it could not be false to assert NN was both. But, it could be false to assert this if NN were slightly agitated (in which state NN would neither be angry nor not angry), say. Now, if NN could be described (without ambiguity) as follows:

N1: NN is both angry and not angry in the same respect and at the same time, and with respect to the same object of that anger,

we might have a genuine contradiction here. But, it is unlikely that Cornforth meant what he said to be taken in this way --, and it is even more doubtful whether he would have been able to say under what conditions he or anyone else would/could hold N1 true -- or attribute to NN such an odd disposition/actualisation.

For example:

N2: At time t, NN is both angry with MM for lying to her, and not angry with MM for lying to her.

Someone could object and argue that it is possible to have mixed emotions at one and the same time. Perhaps, then, they would mean this:

N3: At time t, NN is both angry with MM for lying to her (because it is a violation of trust), and not angry with MM for lying to her (because she understands the pressures on MM at the time he lied).

In that case, N3 is really this:

N4: At time t, NN is both angry with MM for φ-ing, and not angry with MM for ψ-ing.

Here we in effect have two different objects of NN's emotions: anger at MM lying because it is a violation of trust (i.e., "φ-ing"), and lack of anger at MM lying because of extenuating circumstances (i.e., "ψ-ing"). Which is, of course, why caveat N1 was included earlier:

N1: NN is both angry and not angry in the same respect and at the same time, and with respect to the same object of that anger.

To be sure, some might still object, but they will (like Cornforth) find it hard to say what the content of that objection amounts to without editing out of the picture some object or other of the said anger.

In fact, by his use of the word "tendencies", Cornforth himself seems half ready to concede this point, anyway. But, not even he would want to describe the same action (performed by the same person) as, say, literally both gentle and brutal at the same time (and without equivocation). While it is possible to ascribe contrary properties to the same object (e.g., one part of the aforementioned iron bar being hot while another part is cold), a 'contradiction' may only be extracted from such familiar facts by someone who has never heard of ambiguity.

And once more, any description saying of the same action that it was literally both gentle and brutal at the same time (and without equivocation) would merely be an inconsistency -- since both alternatives could be false if the said act was neutral (i.e., if it was neither gentle nor brutal).

[Just as both parts of the assertion that NN as angry and not angry could be false at once, and in the same respect, if NN was only slightly miffed.]

However, in the end, the concrete Communist Block finally caught up with Cornforth; in one of his last works [Cornforth (1980)] he systematically retracted most of the theses he had declared were cornerstones of the "world view of the proletariat".

[To be sure, the entire proletariat sent him billions of cards expressing their thanks for his changing their minds for them. (More on 'contradictory' emotions below.)]

Another benighted comrade tried to argue along similar lines in 'debate' with me over the recent UK Prison Workers' Strike:

"I can contradict someone's statements. Can I also have contrary interests to yours? Could it reasonably be said that someone's behaviour was contradictory? Or that someone's interests were contradictory (in relationship perhaps to some goal they had)? Or that my interests contradicted yours? Certainly some data might appear contradictory in relationship to some enquiry we have about it.

Does this not suggest that the notion of a contradiction is not exhausted by what might go on inside a proposition? In ordinary usage?"

Of course, contraries are not contradictions. As indicated earlier, concerning two contrary propositions, both cannot be true (i.e., in this case, they are merely inconsistent with one another), but they could both be false.

For example, these contraries, "All swans are white" and "No swan is white", cannot both be true (in a non-empty domain), but they could both be false -- for instance, if 'Some swan is not white' or "Some swan is white", respectively, were themselves true. But, two contradictory propositions cannot both be true and they cannot both be false, at once. Dialecticians invariably ignore such "pedantic" details.

Now, the above comrade vainly tried to defend the employment of this obscure notion (i.e., "dialectical contradiction") by appealing to an everyday use of "contradiction": in connection with contradictory behaviour. But, what does he mean by this? Perhaps someone who stands and sits all at once? Or maybe someone who strikes and refuses to strike at the same time?

In relation to the August 2007 UK Prison Officers' strike, he seems to have meant workers who support the state one minute, but act against it the next (or who hold odd beliefs about one or both). In fact, there is a rather good example of this sort of confusion in Simon Basketter's recent article in Socialist Worker:

"However, there are contradictions in the role of prison officers.

"It is summed up by Cardiff prisoners chanting 'you're breaking the law' to the strikers....

"Prison officers' work, upholding law and order, frequently pushes them to accept the most right wing ideas and actions of the system. One of their main jobs is to control prisoners –- and throughout the prison system, many officers have a proven record of racism and violence.

"Some of the contradictions can be seen in the strike. In Liverpool the POA shop steward Steve Baines responded to the high court injunction by telling fellow strikers, 'Tell them to shove it up their arse, we're sitting it out.'

"Yet when prisoners in the jail protested against their treatment, the POA members rushed back in to control the situation and end a roof top protest."

Once more, what is the 'contradiction' here? Maybe, it has something to do with the following:

P1: Prison officers uphold the law.

P2: This either results from, or leads them into, holding right-wing ideas.

P3: But, this strike has forced some to defy and/or disrespect the law.

P4: However, later, when some prisoners protested, the same officers rushed back to work to control them.

Now, I have already commented on the loose and indeterminate way that dialecticians like to use the offending word (i.e., "contradiction"), but even given this conceptual morass what precisely is the contradiction here?

Let us try again (using "NN" this time to stand for the name of any randomly chosen prison guard who thinks and acts along the above lines):

P5: NN upholds the law.

P6: NN has adopted a number of right-wing ideas.

P7: One day, as a result of the strike, NN says "Screw law L1!"

P8: Later that day he acts in support of a totally different law.

Once more, where is the contradiction?

Now, if NN had said, "Screw all laws!" we might be able to cobble-together an inconsistency here (such as "Screw all laws!" and "No laws ought to be screwed!"), but not even that is implied by the above story.

In fact, a contradiction in this case would be something like: "All laws should be screwed" and "There is at least one law that should not be screwed." Or, perhaps: "No laws should be screwed" and "There is at least one law that should be screwed."

To be sure, people say all manner of odd things, and it is relatively easy to utter contradictions. Who has ever denied that! Look, I have just posted two in the previous paragraph. The question is, can both be held true, or false (or in this case, advocated and repudiated as a moral or political code), at the same time? Well, did anyone from Socialist Worker try to ascertain from the aforementioned prison guards if any of them would have assented to and rejected either of these at the same time: "All laws should be screwed" and "There is at least one law that should not be screwed", "No laws should be screwed" and "There is at least one law that should be screwed"? Apparently not.

Indeed, if NN in fact assented to "No laws should be screwed", then we could safely infer from his later strike action that he no longer held it true, for by his actions he must have advocated this in its place: "There is at least one law (namely, law L1) that should be screwed". [And this could be the case even if tomorrow NN went back to believing the former again. Dialecticians, least of all, should need reminding that people and things change!]

Unless, that is, we actually think NN holds to this odd idea: "I do not believe that there is at least one law that should be screwed and I also believe there is at least one law that should be screwed." Or, perhaps "Screw law L1 and do not screw it!" Even so, it is reasonably clear that we could only attribute schizoid beliefs like this to NN if he were about to go insane. We certainly could not rely on such a confused character to help win a strike -- nor report his genuine beliefs to us with any accuracy.

But, let us examine what the above benighted comrade had to say, to see if anything useful can be extracted from it. Is it possible, therefore, for an individual to have contradictory interests in a relationship, say? Perhaps this comrade meant the following:

B1: NN has interest (A in relationship R).

B2: It is not the case that NN has interest (A in relationship R).

[The brackets have been inserted to ensure the same scope is operating here for the negative particle -- another "pedantic" detail our superfine 'dialectical logicians' also ignore.]

Now, this seems to be is a genuine contradiction (if the two are conjoined). Did he mean this?

Apparently not. Well, what about this?

B3: NN has interest (A in relationship R).

B4: NN has interest (B in relationship R).

B5: Interest (A in relationship R) contradicts interest (B in relationship R).

But, if we are talking about literal contradictions here (and not those unexplained 'dialectical contradictions') then A and B (in relationship R) can only contradict one another if they are expressed in propositions (or, at the very least, in clauses), as B5-B7 below indicate.

Hence, A and B (in relationship R) would contradict each other if they were expressed in something like this form (if, in B5a, we ignore for the moment the "pedantic" detail included above):

B5a: Interest A contradicts interest B.

B6: "A" stands for "I must love my partner".

B7: "B stands for "It is not the case that I must love my partner".

Can anyone assent to such beliefs all at once? Well, as we saw with NN above, people can hold all manner of odd ideas in their heads, so there is nothing to suggest that B6 and B7 could not form the content of someone's overall belief system/emotional make-up. But, and unfortunately, this just tells us that contradictions in ordinary language and in logic are built around the content of propositions, and the logical links we hold between them -- thus, destroying this particular comrade's point.

The question now is, has anyone ever held the quoted propositions in B6 and B7 both true and both false at the same time? Or anything like them? Perhaps they have (who can say?), but how that shows that there are in fact 'true contradictions' in nature and society is still somewhat unclear. [As should seem obvious, the fact that some individuals believe something does not make it true!]

However, it could be argued that the fact that NN holds, say, the quoted propositions in B6 and B7 both true, when coupled with the fact that NN is an individual who exists in the real world (should we actually find a genuine NN-type person somewhere), shows that it is at least possible to assert the existence of true contradictions. Once such a possibility has been admitted, the objections set out in this Essay can be seen for what they are: empty rhetoric. Or, so it might be claimed.

An argument somewhat like this was indeed put forward by Roy Edgley a few years back:

"Since thought and theory are also part of reality and thus real objects that can be thought about, contradictions in thought, thought not true of reality, certainly exist in reality; and it is only because they do exist in reality that they can be the object of criticism -- criticism for failing to be true of reality. Moreover, it is because two contradictory theories cannot both be true that each bears a critical relation to the other: instantiated in actual thought this relation of logical opposition is in fact a critical relation of real opposition, Kant notwithstanding. It is no less logical opposition and no more simply natural 'conflict of forces' for taking the form of real historical and social struggle." [Edgley (1979), pp.24-25. Italic emphases in the original.]

The following would presumably be one such contradiction (although Edgley himself was interested in more overtly scientific propositions), and one such existential claim:

B8: Let "p" be "I must love my partner and it is not the case that I must love my partner".

B9: In so far as "p" exists, contradictions exist in reality.

As Edgley admits, while a proposition like "p" could not actually be true, but it would still exist, and hence contradictions certainly exist (at this minimal level). Now, it is an entirely different matter whether "p" is true; I will return to this later. But, what about the claim that the above shows that contradictions at least exist? Well certainly those words exit, but this is no more illuminating than the following would be:

B10: Let "G" = "God"

B11 In so far as "G" exists, "God" exists in reality.

The question would still remain as to whether there is a 'God' or not.

[As those who know their logic will also know, Edgley has confused a propositional sign with a proposition. B10 and B11 partially bring this out.]

Furthermore, no one has questioned the existence of inscriptions of contradictions (indeed, these Essays contain scores of them), but that sheds no light at all on the DM-claim that there are 'real contradictions' in nature and society. If the mere thought of a contradiction, or its actual  inscription on the page (or screen), were enough to show that DM-contradictions exist in the real world, then we should have to admit that there were 'real tautologies', too. But worse, we should have to accept LIE, that is, the doctrine that from thought alone, or from words, ontological conclusions may be drawn. [More on that in Essay Twelve.]

[LIE = Linguistic Idealism; FL = Formal Logic.]

But signs and inscriptions do not have such existential implications; plainly, if they did we should all have to believe in Bigfoot.

Edgley goes on to argue:

"Though a system of thought that is contradictory cannot be true of its real object, this isomorphic relation between the structure of a society's thought and the structure of its material life thus gives sense to the idea that such thought is true to that material life: in being contradictory it 'reflects', and so discloses, though its content does not explicitly assert, the contradictory structure of the material life of that society." [Ibid., p.25. Italic emphasis in the original.]

But, one may wonder how Edgley knows this is indeed an "isomorphism" if none of his contradictions are true of capitalism. And his claim that this theory is "true to" capitalism is far from clear; how something can be "true to", but not "true of", a social system is something Edgley failed to explain.

Now, Edgley asserts that these linguistic contradictions (or at least the more theoretical examples to which he refers) are a "reflection" of "real oppositions" in society. That claim is partly defused below, and will be further laid to rest throughout this Essay, and in an Additional Essay on the nature of science to be published at this site in the next few years. [See also here.]

Independently of all that, Edgley makes a serious mistake (one that seems to be as endemic in, as it is ubiquitous among, dialecticians): that of confusing contradictions in FL with what might or might not exist. FL makes no existential claims. To be sure, logicians as individuals may make such claims, but logic itself is neutral in this regard. Moreover, certain logical systems might need an ontology (or even a model) in order to work, but that is not so in general. Anyway, even there, contradictions do not make existential claims. The 'ontology' does that.

To repeat: in its simplest form, a contradiction in logic is merely the conjunction of a proposition with its negation, such that they cannot both be true and cannot both be false, at once. So, the fact that inscriptions of contradictions exist has no bearing on that logical principle. Furthermore, FL does not rule out the existence of contradictions (for it is not a science), it is merely concerned with the truth-functional connection between a proposition and its negation. [The fact that there are many different and varied definitions of "contradiction" in logic will be discussed in a later Essay. In the meantime, one need only reflect on the fact that none of these alternative definitions of contradiction make existential claims, either.]

In that case, contradictions cannot "reflect" anything, for they represent one form of the disintegration of the expressive power of language.

[More on this here, here and in Essay Twelve Part One.]

But, wait! The earlier comrade has a powerful ally: none other than that outright charlatan Freud:

"Perhaps someone is in the midst of an unhappy love affair and says 'I love him but I also hate him'. Its not just the statement but the feeling which is a contradiction surely? If Freud is held to describe the human individual not as a unified subject but a bundle of contradictory drives and desires, might one not imagine contradictory drives (if not desires) in a particular social system?

"Can I not have contradictory emotions about a subject, situation or person (I know I do about all sorts of things!)."

Thus, on the back of some egregious pseudo-science, this comrade has built his 'case'.

But, is there anything in such fraudulent Freudian fancies anyway (even if we put to one side all the lies, deceit, client abuse, intellectual bullying, cocaine addiction, paranoia, and fabrication of evidence that marked Freud's career)?

Well, once more, can people have contradictory emotions? Perhaps these examples will suffice:

B12: NN hates Blair.

B13: It is not the case that NN hates Blair.

However, I rather think that the aforementioned comrade did not mean a contradiction like this. Perhaps he intended then the following?

B14: NN both hates and loves Blair.

This is entirely possible, if unusual. However, it is worth noting that love and hate are not contradictory (when put in a propositional context) unless, say, hating someone implies not loving them; but, as the above quotation concedes, it does not imply this here.

Nevertheless, (1) the reader will need to re-read the caveats posted earlier, and (2) note that in order to give content to this idea (if it is what was meant, or if these ideas mean anything at all), we had to use a proposition once more. This rather makes a mess then of the following rash assertion:

I'm just very puzzled about what it means to restrict the meaning of the term contradiction to a rule of formal logic. Its always been the least compelling of your arguments it seems to me. I don't understand the linguistic scandal that is supposed to be involved in talking about the human subject as a 'bundle of contradictory drives and desires' or talking about the capitalist system as encompassing contradictory tendencies (how TRPF [the tendency of the rate of profit to fall -- RL] is held to operate inside a concrete capitalist social formation for example)....

"I don't see how there can be anything ipso facto absurd or meaningless about such statements to anyone familiar with ordinary language." [Bold emphasis added.]

No "scandal"; this comrade's badly thought-out examples themselves imply the above conclusions -- that is, if we are to make sense of them.

[The alleged 'contradictions' in capitalism will be dealt with here, and here.]

Now, it could be argued that certain brain states and/or underlying psychological or social forces are what lie behind these contradictory emotions, and it is here that the contradiction lies.

Unfortunately, the thesis that there are such things as 'contradictory forces' has been laid to rest in this Essay, but the overall idea is susceptible to the next series of objections, anyway.

[The argument below also applies to the claim that there might be certain brain states/process and/or psychological and social forces at work, of which we are as yet unaware, that constitute such 'material contradictions'.]

Let us, therefore, call "F*" the brain state/process and/or psychological and social force that results in, or from which "emerges", the following:

B15: NN loves Tony Blair,

and label that which 'opposes' or "mediates" the following "F**":

B16: NN hates Tony Blair.

So "F*" stands for the social force (etc.) that mediates, or from which "emerges", "NN loves Tony Blair" and "F**" stands for that which mediates (etc.) "NN hates Tony Blair".

Let us further assume that F* 'contradicts' F**, i.e., that they are 'dialectically-united opposites'. Now, given these assumptions, even this will not work.

[Of course, if they are not 'dialectically-united opposites', then the above comrade's objection falls by default.]

According to the DM-classics, where we are told that all things change into their opposites, and because of their opposites, F* must change into F**. But, F* cannot itself change into F** since F** already exists! If it didn't already exist, according to this theory, F* could not change, for there would be no opposite to make it do so!

And, once more, it is no good propelling F** into the future so that it now becomes what F* will change into, since F* will do no such thing unless F** is already there to make it happen!

Now, it could be objected that love can turn into hate, and vice versa; sure enough, but the whole point of introducing F* and F** was to show that if and when this happens, dialectics cannot account for it!

[For those interested, this argument is developed in greater detail here (where 'social contradictions' are also considered).]

Finally, at least here, the following section contains an exchange between myself and a far more reasonable comrade (whose name has been omitted):

Comrade M (commenting on the dialectical use of the word "contradiction"):

"I mean what most people mean -- conflict, inner tension..."


Do they really? Give me one sentence drawn from ordinary language (the vehicle most people do in fact use, so what you say should appear there, somewhere) where such an interpretation could be put on the word "contradiction" -- i.e., one not infected with the sort of idealist guff you read in Hegel. An idealist will have no problem with asserting such things; if reality is mind it can argue with itself. Not so a materialist who bases his science on the material language of ordinary workers (ordinary language).

But, even so, why call such things "contradictions"? What link does this use have with the "gain-saying" of someone, which is what the word usually means? How is a conflict in society a contradiction?

Sure, you can re-define the word to mean what you like, but if we all did that we could re-define anything to mean anything, and we'd lose touch with meaning altogether.

Apart from that, you'd be forcing a view onto reality (contrary to what 'dialecticians' always claim they do) not reading one from it. Linguistic Idealism -- as I asserted in those parts of my work I sent you -- would then automatically have raised its ideal head. Society would be 'contradictory', not because it really was so, but because we merely re-defined it to be so. A linguistic dodge would have created a few empirical 'truths'; science on the cheap...

Comrade M:

Rosa said:

"Give me one sentence..."

Okay, what about "don't you contradict me you little bastard!" Or "that's a contradiction in terms".

Suppose someone says 'military intelligence' is a contradiction in terms. What they mean is that there is a conflict or a tension between the first and the second word, thus conjugated.

At any rate, you are berating a new convert. I can't be expected to know everything at once, much less know it as wisely as the central committee (you).


First, the phrase "contradiction in terms" is either a misnomer or a rhetorical device (i.e., it is, say, metaphorical). Why? Well, since contradiction has to do with truth and falsehood as much as it has to do with "gain-saying", and since one term on its own cannot be true or false (only sentences and clauses can be), no term can contradict another. 

In that case, "contradiction in terms" means something like "incompatible phrase(s)", as in "round square". However, "AB is round and it is square" would be a contradiction if "AB is round" were taken to mean "AB is not square", but then you would not now have a contradiction in terms, just a plain contradiction with no "conflict (or) inner tension". [There can be no "conflict" here, since words cannot "conflict" (they are not agents -- except, of course, to idealists they are), and there can be no "tension", for the same reason.]

And, if the above were rejected (for some reason), you still would not have a 'contradiction in terms' that was itself indicative of "conflict (or) inner tension", since, once more, words cannot conflict (or be tense, or be in tension), because they are not agents. Moreover, anyone who uttered a 'contradiction in terms' would not necessarily be in "conflict (or) inner tension", just confused. And even if they weren't confused, the 'contradiction in terms' they uttered would not of itself indicate "conflict (or) inner tension"; it could be a sign of all manner of things (ranging from lack of clarity to playfulness). 

As to the idea that such a phrase could indicate the presence of "conflict (or) inner tension" I have no doubt, but if a 'contradiction in terms' meant that a "conflict (or) inner tension" had to be present, it would mean this, not merely could mean this, just as the truth of "not p" would mean the falsehood of "p" (as opposed to merely "not p" could mean the falsehood of "p"). So they cannot be synonymous, as you allege.

[Apologies for the prolixity of this paragraph, but logic is a pain in the dictionary!] 

But even if this were not so, "contradiction" here would not mean "conflict (or) inner tension", merely "gainsaying oneself", which could be true without an inner conflict being implied. It might be a joke, an attempt to puzzle, a game, a mistake… The possibilities are endless. The attempt to squeeze this into an idealist mould can only succeed if the almost endless possibilities allowed for by ordinary language are ignored. 

As to "Don't you contradict me you little bastard!", the term "contradiction" in this command (it's not in fact a proposition, so it cannot itself be a contradiction, literally speaking -- not that you suggested it was) clearly means "gain-say". No quibble. But, if it meant "conflict, inner tension", you would have: 

"Don't you conflict/inner tension me you little bastard!", which is meaningless. 

Even if we were to edit this to: "Don't you conflict with me you little bastard!" it would not mean the same as "Don't you contradict me you little bastard!"

One can conflict with someone without contradicting them, and vice versa (e.g., two friends could contradict each other (out of fun) without conflicting with each other, say). Hence these cannot mean the same.

However "Don't you inner tension with me you little bastard!" cannot be beaten into shape at all.

2. Engels, for example, went to great lengths to qualify what he meant by "force". Cf., Engels (1954), pp.69-86.

3. This was established in Essay Two.

Nevertheless, as we saw there, assertions like those given in Note 1 function as "forms of representation", not as summaries of the available evidence. In many cases, such broad generalisations are made on the basis of little or no evidence at all. For example:

"Dialectics…prevails throughout nature…. [T]he motion through opposites which asserts itself everywhere in nature, and which by the continual conflict of the opposites…determines the life of nature." [Engels (1954). p.211.]

"Processes which in their nature are antagonistic, contain internal contradiction; transformation of one extreme into its opposite…[is] the negation of the negation…. [This is a] law of development of nature, history and thought; a law which…holds good in the animal and the vegetable kingdoms, in geology, in mathematics, in history and in philosophy…. [D]ialectics is nothing more than the science of the general laws of motion and development of nature, human society and thought." [Engels (1976) pp.179-80.]

Now, Engels is quite happy to call this sketchy, half-formed sub-hypothesis, a "law" even though it was based solely on a superficial examination of a limited range of examples -- all specially selected and highly simplified --,  drawn from the science of his day. And, even then, they are often badly-described or misconstrued.

Their role as a "form of representation" is outlined in the section dealing with the RRT, in Essay Twelve.

[RRT = Reverse Reflection Theory.]

[The phrase "form of representation" is taken from Wittgenstein; a brief outline of its meaning can be found in Glock, pp.129-35. We will see Engels use one such in Note 7 below.

Also follow the link to "norm of representation" given in Note 25.]

4. However, in one of these quotations, Engels seems to qualify this identification away:

"All motion is bound up with some change of place…. The whole of nature accessible to us forms a system, an interconnected totality of bodies…. [These] react one on another, and it is precisely this mutual reaction that constitutes motion…. When two bodies act on each other…they either attract each other or they repel each other…in short, the old polar opposites of attraction and repulsion…. It is expressly to be noted that attraction and repulsion are not regarded here as so-called 'forces', but as simple forms of motion." [Engels (1954), pp.70-71. Bold emphasis added.]

[Engels elaborated on this theme in the succeeding pages of DN.]

[DN = Dialectics of Nature; i.e., Engels (1954).]

Nevertheless, this re-interpretation of the term "force" as a sort of shorthand for "simple forms of motion" has serious consequences for DM that Engels appears not to have noticed. Several of these are examined in the main body of this Essay, and below in Note 25. I consider some of his other, more important comments, in greater detail in Essay Seven.

5. Admittedly, this is a highly simplified picture, for even in such circumstances there could be several forces operating on an orbiting body -- the resultant motion will therefore be a function of the vector sum of all the forces acting in the system. The point at issue here is that relative to the centre of mass of the orbiting body, motion is not the result of two different sorts of forces -- those of attraction and repulsion -- but the consequence of just one resultant force. In that case, orbital motion is produced by the action of one force only (i.e., in Classical Physics).

Furthermore, any secondary motion (resulting from the effect of other forces operating in the system), which happens to be superimposed on the primary action, only complicates the picture, it does not alter it. This extra activity might also be the result of other attractive -- but, not repulsive -- forces (in Classical Physics, once more), which admittedly affect the said resultant; while they might change it, they do not turn it into two or more resultants. [This topic and these and several other options are examined again in more detail here.]

Nevertheless, it could be argued that the motion of such a body around another is determined by the operation of the two forces of attraction that pass between them: body A attracts body B, and vice versa.

Even so, it is difficult to see how two attractive forces could be regarded as opposites or as 'contradictories'. Anyway, Engels himself argues that oppositional forces are those of attraction and repulsion, despite the fact that with respect to the vast amount of the bulk motion in nature these seem to have little or no part to play. Not only that, but the motion of, say, planet A around, say, star B, is caused by forces originating in B, not A. While, the forces originating in A may affect B, they do not affect A itself, or its motion around B.

It could be argued once more that the interconnected and reciprocal 'effect chain', as it were, in play between A and B shows that such forces are dialectically-linked. Hence, on this view, B would affect A's motion while A reciprocates; this in turn alters B's own motion which must then affect A's and so on. But even here, these attractive forces do not confront each other as oppositional or as contradictory. At best, such forces affect the motion of the two bodies in tandem, which motion in turn then affects any forces in play, and so on. In fact they appear to augment each other. On that basis, should we not (and with more justification) say that such forces are --, not contradictory --, but tautological? [On this see Note 38, below.]

And, once more, these forces do not turn into one another, which either means that they are not opposites, or the DM-classics were wrong.

6. Again this simplifies the picture considerably, but the point is still valid. Even if it could be shown that gravity is a property either of matter (as a result, perhaps, of the activities of the by now legendary "graviton"), of Spacetime, or of something else, 'motion' through that latter would still not be a function of attractive and repulsive forces. [On this, see Jammer (1999), pp.iv-vi. This has been challenged in Wilson (2007). More on that below.]

[In the previous paragraph, the word "motion" is in 'scare' quotes, since it is a moot point whether anything actually moves in four-dimensional Spacetime.]

6a. This, of course, is not how things are pictured in school or college Physics, where "force" is still used for heuristic purposes. But, as Jammer notes, in higher Physics, "force" has been edited out, replaced by exchange particles.

This is re-iterated by Nobel Laureate, Professor Wilczek (of MIT):

"The paradox deepens when we consider force from the perspective of modern physics. In fact, the concept of force is conspicuously absent from our most advanced formulations of the basic laws. It doesn't appear in Schrödinger's equation, or in any reasonable formulation of quantum field theory, or in the foundations of general relativity. Astute observers commented on this trend to eliminate force even before the emergence of relativity and quantum mechanics.

"In his 1895 Dynamics, the prominent physicist Peter G. Tait, who was a close friend and collaborator of Lord Kelvin and James Clerk Maxwell, wrote

"'In all methods and systems which involve the idea of force there is a leaven of artificiality...there is no necessity for the introduction of the word 'force' nor of the sense−suggested ideas on which it was originally based.'" [Quoted from here.]

[The above now appears in Wilczek (2006), pp.37-38.]

This view has been criticised quite effectively in Wilson (2007). More details on this will be added here at a future date.

7. For example, see Engels (1954), pp.73-80.

Nevertheless, it is not at all clear what Engels was driving at in these passages. If he meant to say that heat operates as a repulsive force then that would have been a desperate and unconvincing move. Not only do cold bodies have satellites (e.g., Neptune), hot bodies swallow matter up all the time. It is possible that Engels simply copied this idea from theorists of the previous century. [Hesse (1961), Williams (1980).]

Admittedly, Engels did consider other repulsive forces that could operate in a planetary system, but his ideas were speculative, fanciful and clearly ad hoc. I can find no evidence that anyone else (DM-fan or otherwise) has followed-up on -- or developed -- any of these ideas in any way in the intervening years.

For example, Engels appeals to the original repulsive properties of the "individual particles of the gaseous sphere" from which the Solar System was formed (as a result of "contraction"), to account for its origin by means of an "interplay of attraction and repulsion." [Engels (1954), pp.73-74.]

It would be difficult to find a better example than this of how the dialectical method has been imposed on nature -- and not deduced from the phenomena. And we can say this with some confidence; even if this 'theory' weren't so obviously fanciful, it certainly could not have been deduced from the phenomena since the alleged incidents took place billions of years ago. Admittedly, there were theoretical considerations that recommended this 'hypothesis' to Engels as a tentative 'explanation' of how the solar system might have been formed -- although even that is questionable since Engels explicitly based his ideas on the old Kant-Laplace model, itself nearly 100 years old at the time --, but even granted all this, Engels's account is superficial, impressionistic and lacks both mathematical and evidential support. It was clearly motivated by his desire to find some force -- any force -- to counterbalance gravity just because DM requires it, not because the phenomena dictate it. This is a classic example of Engels using the ideas he inherited from Hegel as a "form of representation".

To be sure, such formal devices are used all the time in science; Engels however turned this one into a metaphysical thesis.

[The difference between Metaphysics and science will be outlined in a later Essay. On Metaphysics and DM, see Essay Twelve Part One.]

Indeed, Einstein himself was not above inventing forces to suit his needs (as, indeed, was Newton), introducing "the cosmological constant" to account for the fact that the Universe has not collapsed in on itself. Cf., Lerner (1992), pp.131-32. There are countless examples of this sort of move in the history of science. Kuhn calls these "paradigms" (a none-too-happy term). On this see Kuhn (1970, 1996), and Sharrock and Read (2002).

Incidentally, an appeal to so-called 'centrifugal forces' (a bogus notion found in Classical Physics) will not save Engels's theory either -- such forces do not 'exist'. If anything they are the result of a misleading shorthand for the way that rectilinear motion would tend to be re-asserted if forces responsible for centripetal acceleration cease to operate, subjectively experienced in certain rotating systems.

8. In that case, for once, Engels's views would seem to be consistent with modern Physics (as indicated by Jammer)!

Engels also noted the anthropomorphic origin of this concept (something Woods and Grant, for example, failed to spot -- even though they quoted this passage!):

"All natural processes are two-sided, they are based on the relation of at least two operative parts, action and reaction. The notion of force, however, owing to its origin from the action of the human organism on the external world…implies that only one part is active, the other part being passive…[and appearing] as a resistance." [Engels (1954), p.82. Bold emphasis added.]

On the animistic/anthropomorphic origin of the concept of force, see Hesse (1961), Jammer (1999), and Agassi (1968), who references Bacon's Novum Organum (Book One: Aphorisms; Aphorisms XXXVII-LXVIII) as a locus classicus of this avenue of criticism.

DM-theorists are not alone in finding their theses embarrassed by the use of anthropomorphic concepts; the ideas of metaphysically-motivated Philosophers and scientists have been similarly compromised. The material and ideological source of this phenomenon is discussed in Essays Twelve and Fourteen (summaries here, and here).

9. Classical problems associated with the ontology of interaction will be posted here at a future date. However, there is an outline of these issues in Note 24. See also Note 6a.

10. It could be argued that forces are 'abstractions' constructed to assist in the scientific study of nature. However, once again, when viewed this way, the concept "force" becomes little more than a "useful fiction", only now situated in a metaphorical universe of its own, located somewhere between genuine fictions (such as apparitions) and mathematical fictions (like the centre of mass of the huge galactic system to which our galaxy belongs, the Virgo Supercluster). In that case, naturally, the 'objective' status of forces would be fatally compromised. They would have no physical counterpart, and the real material correlates of DM-'contradictions' (which was the whole point of this Part of Essay Eight to investigate and perhaps locate) would be non-existent.

11. Once more, this is not a problem confined to DM-circles; scientific theories are shot-through with metaphor, and scientists use analogical reasoning all the time. On the nature and use of metaphor and analogy in the sciences, cf., Baake (2003), Brown (2003), Benjamin, et al (1987), Guttenplan (2005), Hesse (1966), Ortony (1993), and White (1996). [Several of these base their ideas on those of Max Black, whose theory is destructively criticised in White (1996).]

However, there is as yet no satisfactory treatment of the import, role and significance of the use of figurative language in science anywhere in the literature. Naturally, given the ubiquity of such language, the precise nature of scientific knowledge is poorly understood. [I hope to say more on this in an Essay on science to be published in 2008 or 2009.]

12. This might be one particular use of the LEM that DM-fans would be wise not to question. If objects, states of affairs and processes were held to be both non-contradictory and contradictory at the same time, little sense could be made of the theory even before it was examined.

[LEM = Law of Excluded Middle.]

Nevertheless, as with any application of the 'laws' of FL to complex situations, some sensitivity is required. In that case, it could be argued that DM is only committed to the view that parts of one system/process 'contradict' parts of another, while still others do not.

To be perfectly honest, it is impossible to give a clear answer to this volunteered response since DM is far too imprecise and sketchy for anyone (supporter or opponent) to decide whether or not this is a legitimate reading. Perhaps it is both and neither at the same time?

However, dialecticians do in fact speak about contradictions growing and intensifying, or even lessening and being "resolved"; but this is clearly qualitative speech since they supply us with no units by which they can be measured, and no data to support their contention; nor do they attempt to quantify them in any way (which, on its own, is a rather odd thing for an alleged science to omit).

If DM-apologists decided to invent a unit here, we might make some progress. May I suggest, therefore, the 'Neg'?

So, one Neg could be defined as that strength/level/intensity of contradiction necessary to make either a stick (of arbitrary size) look bent in water, an object (again of arbitrary dimensions) look smaller as it recedes from the viewer, or maybe even that required to make at least one capitalist/employer look fair.

In that case, a Nanoneg would be enough to make an electron move, and a Piconeg would allow it to be a wave and a particle all at once. Further: a Millineg would be strong enough to move a millipede. [The reader can decide for herself what a Centineg would be capable of setting in motion.] A Decineg would be sufficient to depict a formal contradiction in logic, while a Decaneg (colloquially, "A Blair") would be enough to spin a pack of capitalist lies (about the affordability of, say, pensions) or write at least one 'dodgy' Iraq dossier.

Perhaps then, a Hecto(r)neg would set off a factional dispute in yet another dialectically-distracted Trotskyist sect, while the class war itself would need a Kiloneg to initiate a strike, a Meganeg to motivate a huge anti-war movement, and a Giganeg to prompt an insurrection. Moving up the scale, a Teraneg would be needed to keep the Earth in orbit around the Sun, and, of course, a Yottaneg to kick-start the 'Big Bang' (if the latter actually happened).

We could even introduce a special unit to measure the contradictory stench created in the nostrils of most working-class people by the sectarian in-fighting, oppression, mass murder and counter-revolutionary activity this misbegotten theory has helped inflict on Marxism: the Rottaneg.

All we would need then is an intrepid dialectician (i.e., one of those who claim to be able to discover fundamental scientific truths in thought alone, by simply juggling with obscure Hegelian jargon) to invent a Negometer (and they could do this if they saved time by not writing yet another identical version of DM/'Materialist Dialectics' by just cutting and pasting large sections from the 'classics') to measure these super-scientific 'dialectical contradictions'. That done, and Mystical Marxism might at least begin to look precise for a change.

[To be honest, I would have suggested the 'Con' here as a suitable unit with which to measure the strength of DM-'contradictions', but when I typed "Megacon" into an earlier version of the above, that seemed to me to be a little too obvious -- and a mite too facetious.

Compare the above comments with the suggestions made about dialectical "nodes"/"leaps", here.]

13. This, of course, assumes that 'contradictions' have metaphorical 'geometric centres' and possess figurative 'separation radii'. Well, maybe they can be photographed, weighed and given new paint job?

Cheap debating points? Perhaps so; but if all parts of nature (animate and inanimate, macroscopic or microscopic) behave as if they can argue over the metaphysical garden fence, as it were -- which is how things are depicted in DM, picturing them as 'contradicting' themselves and one another, bickering all the time (that is, if the word "contradict" is taken literally) --, the cheap shot above is hardly worth mentioning in comparison. DM takes the piss out of itself; it needs little help from me.

13a. Indeed, when asked to explain why this is a 'contradiction', Ian Birchall failed to respond. However, in a later thread, he tried again unsuccessfully to do so, as did a few other confused comrades. [The reader is encouraged to read this lengthy exchange on this topic; my thoughts on the 'arguments' of one of the egregious participants in this 'debate' can be found here and here, and now in a revised form above, in Note One.]

Unfortunately, the same always seems to happen whenever I ask other dialecticians to explain why these are 'contradictions'. [On the best response ever given to this question, but not as asked by me, see here.]

Several more examples of this DM-tendency to label anything and everything as "contradictory" can be found here, and in Note 14.

14. We might also want to know how something actually existing (i.e., the current state of the working class) can 'contradict', in a dialectical sense (involving forces), something that does not (i.e., the latter's potential revolutionary role). As we have seen, dialecticians are won't to use the word "contradiction" in inappropriate circumstances to depict things that are quirky, odd, contrary to expectations, and so on -- as the mood takes them, it seems. [See, for instance, here.]

However, what Lindsey might have had in mind in the quoted passage is that there is a seeming contradiction in revolutionary theory, which on the one hand depicts the proletariat as the revolutionary class, while on the other, they are often quiescent (or relatively so) for long periods. But this is no more a contradiction here than it would be in Physics if, say, an unsupported heavy object near to the surface of the earth does not actually fall toward the ground. As soon as we learn that the heavy object is maintained in place by magnets, for example, the phenomenon puzzles us no more. To be sure, this stretches the meaning of "unsupported" almost to breaking point, but as that word has no strict definition, it will probably survive that particular semantic trauma.

The moral here (if there is one) seems to be that no law in physics is 'true' on its own, and all are hedged about by all manner of ceteris paribus (i.e., "all things being equal") clauses. On this, see Cartwright (1983). [However, there is  a forceful rebuttal to this way of seeing things here. Naturally, it would be out of place to pursue this topic in this Essay. See also, Earman et al (2002). ]

Hence, as soon we know what is holding the working class back, this puzzle also disappears.

In that case, Lindsey's worry about overcoming this 'contradiction' can now be shelved: there isn't one to overcome.

That does not mean that socialists must just let things drift, and fail to intervene, or wait for workers to organise themselves, but since this is to stray into areas covered by HM, no more will be said about this topic here.

15. It may be felt that this completely misconstrues the relation between parts and wholes as it is interpreted in DM-circles (wherein "the whole is more than the sum of the parts", etc.). However, this dialectical doctrine is examined in extensive detail in Essay Eleven Part Two, where it is exposed as no less confused than other DM-theses are.

16. E.g., Rees (1998), pp.5-8.

17. Of course, it could be argued that this objectifies the Totality, once more, thereby distorting it. But, if the Totality is not a kind of object (even if it is a changing 'object'), how can 'it' have any relation to 'its' parts, and how could 'contradictions' be properties of 'it'?

It could be objected that the Totality is a process, and hence it could be an 'it' (or a sort of 'it') in that sense. Naturally, the answer to these (and other) questions about this mysterious entity/process (the "Totality") will have to be put to one side until DM-advocates tell us (if ever) what (if anything) they think 'it' is.

[They might find a few useful ideas (consistent with much else in DM)  here.]

Despite this, it could be further objected that abstract reasoning like this demonstrates nothing since DM is concerned with verifiable, concrete material contradictions, which occur in the real world. That option is examined here, and here.

18. Naturally, this assumes that these relations are symmetrical -- that is, that AR = RA, which seems reasonable enough. Another simplifying assumption is that these forces are part of binary systems -- that is, the discussion in the text concentrates exclusively on force-couples. It is clear, I take it, that this contraction does not materially affect the conclusions drawn. Anyway, further complications will be introduced and examined later.

In addition, most of the comments in this part of the Essay have been deliberately restricted to the use of DM-terminology, the employment of which does not imply I either accept its validity or that it makes any sort of sense.

Naturally, a comprehensive scientific account of the concept of force would have to include modern ideas about gravity, the strong nuclear, weak and electroweak forces, etc. [As I noted earlier, this concept is now explicated by the use of exchange particles.]

However, it is possible that as science develops reference to forces (even in school Physics) will progressively disappear; cf., Jammer (1999), pp.iv-vi (quoted earlier). In that eventuality, if DM-theorists maintain their adherence to the doctrine that forces give 'contradictions' a material grounding of some sort, their theory would become 'unscientific' by default. Either that, or they will have to abandon talk about the 'objective' nature of forces and join with Engels in regarding them as shorthand for relative motion. Of course, forces would then not just be "useful fictions", they'd be entirely fictitious.

Should this scientific development fail to materialise (i.e., the editing out of all forces from nature), it would be interesting to see how DM-theorists would try to harmonise their 'attraction-repulsion' scenario with successful attempts to unify the four fundamental forces in a Grand Unification Theory (or even in Superstring/M Theory, etc.). It might finally kill-off informed talk in DM-circles about the existence of 'contradictory' forces in nature. Clearly, if there is only one force, it can hardly 'contradict' itself, one supposes.

19. This is, of course, to adopt the vocabulary of Classical Physics.

[However, no inference should be drawn from this to the present author's views concerning the 'ontological' status of forces. As noted elsewhere, this terminology is only being used here as a way of exposing the confusions that abound in DM. It is up to scientists to tell us what the world contains, not Philosophers --, and definitely not RL.]

Nevertheless, with respect to the comments in the text, it is assumed that R-forces prevent the collapse of accumulated matter into 'singularities' under the action of ambient AA-force couples. Clearly, this simply complicates the point, without altering it, once again. In such a scenario, we would have an ARA-system-of-forces, which would be even more difficult to interpret as 'contradictory'. As pointed out in the text, the meaning of the word "opposite" would have to be altered so that systems of three or more forces could then have any number of their constituent parts considered as 'opposites' of any (or all) the rest. If so, such 'contradictions' would be artefacts of an arbitrary choice of words, not 'objective' realities.

Moreover, and once again, given the classical picture, motion itself is altered by the operation of a single resultant force. This is even more difficult to square with the idea that forces are 'contradictions'. [More on this later, too.]

20. This simple picture is, of course, ruined by the complexities found in nature. However, the more complications there are, the less applicable DM-concepts seem to be. In this case, we find that we would have an RARA-system-of-forces. Again, a choice would now have to be made whether we should widen the meaning of the word "opposite" to accommodate DM, or change DM in order to accommodate reality. [To date, DM-theorists have generally preferred the former over the latter alternative.]

Since AR-forces are discussed below, I will postpone comment on them until then.

21. This need not be as serious a problem as is indicated in the text. As pointed out elsewhere in this Essay, scientists do this sort of thing all the time. Unfortunately, this is bad news for DM since it confirms the view that science is a conventionalised social practice, and further substantiates the claim made here that metaphysical theses merely result from a misconstrual of conventionalised grammatical forms (the latter of which gain their sense from material practices), as if they represent fundamental aspects of reality. In short, the conventions we use to represent the world are confused with material truths about it.

This is as crass an error as, say, assuming that reality itself must have an edge to it simply because every photograph has one.

This topic is examined in detail In Essay Twelve Part One.

21a. Or perhaps even:

(3) This way of looking at the world is really quite as loopy as it looks.

[This topic is examined more thoroughly later on in the present Essay.]

22. It might be felt that this Essay is so heavily biased against any way of interpreting forces as 'contradictions' that scientific facts and theories have constantly been prejudicially twisted/slanted -- this latest allegation being an excellent example of this tactic. Surely -- it could be argued -- accelerated motion in the real world is the result of several forces operating on a body; the ensuing motion simply follows as their oppositional effect.

However, this volunteered response will be examined presently in the main body of the Essay.

23. Once more, it could be objected that there is no such thing as "empty space". But even if this were so, and the bodies referred to in the text were not in the said force field, any forces present would not operate on each other, but only on the bodies in that system (if there were any). Hence, forces seem to affect bodies not each other.

24. It could be pointed out here that force fields do in fact interact, and they certainly alter one another. This will be examined presently.

This, of course, is the source of the classical ontological problem concerning the exact nature of forces, and it is partly why it is so difficult to understand their nature. Indeed, their detection seems to depend only on the effects they have on bodies, or on instruments (or, rather, a 'force' seems to be little more than the way scientists depict certain relationships between bodies, as Engels, in a more sober mood, actually put it; on this, see Note 4), or on other fields.

However, if forces are viewed as particulate (that is, if certain particles are viewed as the 'bearers' of forces), the problem would simply reappear at a new level, and we would be no further forward -- a fact Leibniz was, I think, among the first to point out.

Hence, this sort of confrontation between forces could only take place if they were particulate in some way -- that is, if they registered some sort of resistance to one another. If, on the other hand, they were not particulate, it would be hard to see how they could interact in any way, let alone 'contradict' each other. Continuous media have no rigidity and no impenetrability to exert forces of any sort (except, of course, as part of a figurative extension to particulate interaction). [This has been questioned in Smith (2007). More on that presently.]

But, there are well-known classical problems associated with the idea that forces are particulate (referenced here) -- not the least of which is the observation that if forces were particulate then they could only interact if they exerted still other forces (contact forces, cohesive forces, forces of reaction, and so on, which held them together), so that they could act on other particulates (and thus not disintegrate), initiating an infinite regress. That is, in order to account for the ability of particles to resist one another, we would need to appeal to forces internal to bodies to stop, say, one body penetrating the other, or to prevent distortions tearing that body apart, etc. But, if the forces internal to bodies are particulate too (as it seems they must be), we would thus need further forces to account for the internal coherence of these new (and smaller) 'force-particles', and so on. Alternatively, if these 'internal forces' are continuous (or non-particulate), they would not be able to generate inner coherence (since they have no rigidity).

In the end nothing would be accounted for since at each level there would be nothing to provide the required resistance/coherence.

So, reducing the interaction between forces to that between bodies means that particles could not 'contradict' one another without exerting non-particulate forces on their operands -- which would once again mean that such entities were incapable of exerting forces, having no rigidity to do so, etc., etc.

Unfortunately, even the exchange of particles (in QM) would succeed in exerting forces only if there were reaction forces internal to bodies, which were themselves the result of rigidity, cohesion, contact, etc, to stop the force carrier particle passing right through the target particle. Of course, Physicists these days appeal to fields, energy gradients and the like (and reject such mechanistic notions), but if these are continuous, too, the above problems will simply re-emerge at a new level. On the other hand, if they are particulate, after all, this merry-go-round would merely take another spin around the metaphysical dance floor.

[QM = Quantum Mechanics.]

Of course, it could be objected that the above adopts an out-dated mechanistic view of interaction, and hence is completely misguided. However, the 'modern' mathematical approach surrenders the possibility of giving a causal, or physical account of forces -- or, at least, one that does not itself depend on a figurative use of the sorts of verbs we employ in everyday life to give a material account of why things happen in the macro-world.

So, if a particle is seen as a 'carrier' of a force, and that 'force' can be given no physical content, but is still regarded as being capable of 'making' things happen, 'forcing' particles to 'divert' from their line of action (etc.), then those very words must themselves lose contact with seemingly identical everyday words like "make", "force", "divert", as and when the latter are used to depict macro-phenomena.

Now there is no problem with this; but then such an account would thereby become merely descriptive (or even metaphorical), not explanatory. Differential equations and vectors cannot make things move, or alter the path of a single particle. To be sure, we can describe such things with these mathematical forms, and guarantee thereby that the 'books' of nature balance; but the downside to this is that such models cannot explain why anything actually happens in the physical world. [For more recent qualms on this, see Note 30.]

Perhaps, this helps explain Engels's own suspicion of forces; ontologically, they appear to be deeply mysterious, if not animistic. He is not alone. [Other relevant aspects of the nature of forces are discussed here.]

Clued-in physicists seem already to be aware of this (i.e., that it is a problem of language). Here is David Peat:

"IT HASN'T been a great couple of years for theoretical physics. Books such as Lee Smolin's The Trouble with Physics and Peter Woit's Not Even Wrong embody the frustration felt across the field that string theory, the brightest hope for formulating a theory that would explain the universe in one beautiful equation, has been getting nowhere. It's quite a comedown from the late 1980s and 1990s, when a grand unified theory seemed just around the corner and physicists believed they would soon, to use Stephen Hawking's words, 'know the mind of God'. New Scientist even ran an article called 'The end of physics'.

"So what went wrong? Why are physicists finding it so hard to make that final step? I believe part of the answer was hinted at by the great physicist Niels Bohr, when he wrote: 'It is wrong to think that the task of physics is to find out about nature. Physics concerns what we can say about nature.'

"At first sight that seems strange. What has language got to do with it? After all, we see physics as about solving equations relating to facts about the world -- predicting a comet's path, or working out how fast heat flows along an iron bar. The language we choose to convey question or answer is not supposed to fundamentally affect the nature of the result.

"Nonetheless, that assumption started to unravel one night in the spring of 1925, when the young Werner Heisenberg worked out the basic equations of what became known as quantum mechanics. One of the immediate consequences of these equations was that they did not permit us to know with total accuracy both the position and the velocity of an electron: there would always be a degree of irreducible uncertainty in these two values.

"Heisenberg needed an explanation for this. He reasoned thus: suppose a very delicate (hypothetical) microscope is used to observe the electron, one so refined that it uses only a single photon of energy to make its measurement. First it measures the electron's position, then it uses a second photon to measure the speed, or velocity. But in making this latter observation, the second photon has imparted a little kick to the electron and in the process has shifted its position. Try to measure the position again and we disturb the velocity. Uncertainty arises, Heisenberg argued, because every time we observe the universe we disturb its intrinsic properties.

"However, when Heisenberg showed his results to Bohr, his mentor, he had the ground cut from under his feet. Bohr argued that Heisenberg had made the unwarranted assumption that an electron is like a billiard ball in that it has a 'position' and possesses a 'speed'. These are classical notions, said Bohr, and do not make sense at the quantum level. The electron does not necessarily have an intrinsic position or speed, or even a particular path. Rather, when we try to make measurements, quantum nature replies in a way we interpret using these familiar concepts.

"This is where language comes in. While Heisenberg argued that 'the meaning of quantum theory is in the equations', Bohr pointed out that physicists still have to stand around the blackboard and discuss them in German, French or English. Whatever the language, it contains deep assumptions about space, time and causality -- assumptions that do not apply to the quantum world. Hence, wrote Bohr, 'we are suspended in language such that we don't know what is up and what is down'. Trying to talk about quantum reality generates only confusion and paradox.

"Unfortunately Bohr's arguments are often put aside today as some physicists discuss ever more elaborate mathematics, believing their theories to truly reflect subatomic reality. I remember a conversation with string theorist Michael Green a few years after he and John Schwartz published a paper in 1984 that was instrumental in making string theory mainstream. Green remarked that when Einstein was formulating the theory of relativity he had thought deeply about the philosophical problems involved, such as the nature of the categories of space and time. Many of the great physicists of Einstein's generation read deeply in philosophy.

"In contrast, Green felt, string theorists had come up with a mathematical formulation that did not have the same deep underpinning and philosophical inevitability. Although superstrings were for a time an exciting new approach, they did not break conceptual boundaries in the way that the findings of Bohr, Heisenberg and Einstein had done.

"The American quantum theorist David Bohm embraced Bohr's views on language, believing that at the root of Green's problem is the structure of the languages we speak. European languages, he noted, perfectly mirror the classical world of Newtonian physics. When we say 'the cat chases the mouse' we are dealing with well-defined objects (nouns), which are connected via verbs. Likewise, classical physics deals with objects that are well located in space and time, which interact via forces and fields. But if the world doesn't work the way our language does, advances are inevitably hindered.

"Bohm pointed out that quantum effects are much more process-based, so to describe them accurately requires a process-based language rich in verbs, and in which nouns play only a secondary role....

"Physics as we know it is about equations and quantitative measurement. But what these numbers and symbols really mean is a different, more subtle matter. In interpreting the equations we must remember the limitations language places on how we can think about the world...." [Peat (2008), pp.41-43. Bold emphases added; quotation marks altered to conform to the conventions adopted here.]

Now, I do not want to suggest for one moment that I agree with the above comments about the nature of language (or even of scientific language), but they certainly indicate that scientists themselves are aware of the problem.

[To be sure, Peat follows Bohm and suggests we need to learn from native American languages, which seem to have rather odd grammars; but it is to be doubted whether a culture that has produced no science or technology of any note has anything to teach one that has.]

25. Admittedly, when viewed as vectors, velocities, accelerations and forces can, in some circumstances, be represented as 'opposites', but this is given within vector algebra and follows from certain definitions. However, unless we are prepared to admit all the absurdities outlined earlier, this approach cannot lend any support to DM. In addition, it is argued below that mathematics can in no way be regarded as an abstraction from reality.

[Issues related to this will be examined in Essay Thirteen, and in an Additional Essay. However, this topic is intimately connected with the idea that motion is caused by resultant forces, which is discussed in more detail here.]

To be sure, when forces are represented as vectors they can produce accelerations that appear to 'oppose' impressed motion in the system. Ignoring for the present the fact that the use of such language is arguably anthropomorphic, in such cases we would be linking items drawn from the same category (i.e., vectors connected with movement), which clearly makes sense. In this way, any force could be replaced by relative acceleration (by means of Newton's Second Law, etc.). But, even here, an acceleration in an opposite direction does not oppose the original velocity; an acceleration (in vector algebra, which is what we are speaking of here!) just is a description of that changing velocity. Even in reality, accelerations are not disembodied beings that haunt the material world, throwing their weight about, bullying velocities to do their bidding. They are just changing velocities --, no more, no less.

However, in vector algebra no sense can be made of the addition (or subtraction) of force and velocity vectors unless this is mediated by the Second Law (etc.), once more. Even then, the relation between acceleration and velocity vectors has to be established by well-known equations. The various physical quantities represented by these equations can only be linked by means of translations like these, which set up analogies between categorically different items (but in a dimensionally consistent fashion). That is one reason why no sense can be given to 'equations' such as the following:

(1) F = -v

(2) a = kv

Equations like these would be regarded as dimensionally incoherent (unless further dimensions were built into the constant "k", for example). Compare these with the next batch:

(3) s = ut + ½at2

(4) a = -w2s

(5) F = -mw2s

By means of translational/analogical equations like these (or, to make the same point more clearly, by the use of algebraic rules that sanction the inferences we make about physical quantities, in which forces appear as part of a "norm of representation"), we can convert forces into accelerations, compare physical quantities, and account for the motion of bodies (etc.).

Unfortunately, this is of little help to DM-theorists since the translation of forces into relative accelerations would mean that forces are indeed "useful fictions" once more, which would re-introduce all the difficulties noted earlier.

[This is not a problem for the account presented here, for reasons hinted at in the previous paragraph but one.]

However, even if the above were rejected for some reason, this would still lend no support to DM, for such representations are not oppositional; they do not slug it out on the page or the blackboard. And, manifestly, they do not turn into one another (as we are told they should by DM-classicists).

Hence, if two ('opposite') forces in equilibrium (inclined at θo to the x axis, say) are resolved (into their i components), and then equated as follows:

F cosθ - G cosθ = 0

no one would suppose that these symbols are locked in a life-or-death conflict, and will one day change into each other.

Naturally, the above conclusions are not affected in any way of these forces are not in equilibrium:

F cosθ - G cosθ > 0

F cosθ - G cosθ < 0

And it would be little use arguing that while it is true that the above representations may be lifeless (and thus incapable of struggling, and turning into one another), what they actually represent in the real world most certainly can, and does. This is because, the above considerations were expressly aimed at forestalling the claim that the vector calculus is 'dialectical' (and no more). The allegedly dialectical nature of forces in reality is an entirely separate issue, which is demolished throughout the rest of this Part of Essay Eight (and here). [However, on the Calculus in general, see here.]

Readers may be puzzled by the use of the word "analogical" in an earlier paragraph. The use of this word is connected with the history of the development of mathematical terminology in this area, and with the way we make sense of such equations. More particularly, it originated in the reservations expressed by ancient Greek mathematicians over the relationship between so-called "incommensurables" (physical quantities from different qualitative categories, which could find no common noun/predicate to 'co-measure' them) and how these reservations were resolved by European mathematicians in the High Middle Ages. Conceptual barriers between disparate categories were beginning to be broken down by the introduction of concepts (and thus new grammars) at this time, which followed (and were based) on the development of market economies in Feudal society.

So, in earlier times, categorical differences were believed to hold between certain physical terms, which meant they could not be linked mathematically. In that case, whole new grammars had to be introduced by the above mathematicians before incommensurable quantities could be compared analogically (so their exchange values could be calculated). Innovations like these permitted theorists to move beyond earlier 'commonsense' approaches to motion encapsulated in Aristotelian Physics, enabling them to lay the foundations of modern kinematics.

This emphasis on the analogical nature of modern algebraic forms depicting motion follows from an approach to mathematical development that sees the latter as dependent on contingent Historico-economic factors, and which thus bases it firmly and exclusively on human practice and thus on material relations. This view of mathematical development also helps undermine the idea that mathematics is concerned with the study of 'abstractions', and is thus about the Ideal. Hence, it also neutralises yet another core DM-thesis: that scientific development is predicated on the ability of theorists to abstract concepts into existence. [This doctrine has already been picked apart here.]

There is a detailed discussion of these issues in Hadden (1988, 1994), upon which many of the above comments are based. Hadden's pioneering work is only prevented from being Marxist classic by the absence of a clear account of the nature and role of language and of the logic of analogical reasoning.

[However, in view of the fact that the logic of analogy has not advanced much since Aristotle's day, this is hardly Hadden's fault.]

Hadden's conclusions are themselves a development of ideas found in Borkenau (1987), Fleck (1979) and Grossmann (1987). Cf., also Sohn-Rethel (1978).

Clagett (1959) contains many of the original medieval sources. See also  Zilsel (2000), and Kaye (1998).

[CAR = Cartesian Reductionism; UO = Unity of Opposites.]

In that case, the admission that forces can be edited out of the picture (so that relative acceleration and motion may be regarded as opposites) might succeed in winning this particular battle, but only at the cost of losing the war. Once again, this is because it would imply that the universe was much more CAR-like than DM-theorists are prepared to admit. On this account, any reference to a DM-UO would be little more than a confusing way of referring to relative acceleration/velocity. The connection between events could then only be explicated in one of two ways:

(1) By an appeal to the topology of Spacetime, or:

(2) By means of a detailed analysis of the vector and scalar fields in which the said processes were taking place.

In either case, the connection between natural events would not be governed by any sort of physical mediation between elements of the Totality in the process of change -- as DM requires -- since, on this view, moving bodies (with or without opposite velocities (or accelerations)) would have no internal connection with other bodies in motion.

At least an appeal to forces has the merit of appearing to supply a vaguely mediational link between bodies in motion/change, which DM requires; forces seem to connect the latter in dialectical union -- but only because a literalist interpretation of forces like this depends on a prior endorsement of an animistic view of nature.

So, any attempt to edit forces out of the picture would result in the disappearance of the dialectical 'connective-tissue' of reality (as it were); and with that DM would become indistinguishable from the mechanical materialism (i.e., CAR) it sought to replace.

[AIDS = Absolute Idealism; DN = Dialectics of Nature.]

As noted in the text, DM-theorists require forces to be part of the ontological fabric of the universe (which is why they become rather defensive, if not emotive, when the existence of forces is questioned -- except they tend to ignore Engels when he did just this!). Their theory needs a world suffused with anthropomorphic concepts like these -- those that are themselves the result of the fetishisation of the products of social interaction as if they were real objects/processes in nature; which is just another poisonous spin-off of the much touted 'inversion' of Hegelian AIDS.

Hence, whether DM-fans like it or not, the language of dialectics suggests that objects/processes in nature are quasi-intelligent, and engaged in what can only be described as some sort of mystical conversation/shouting match with other objects/processes, as they 'contradict' and 'negate' one another.

As has already been pointed out, in parts of DN, Engels pictured motion in dynamic terms, portraying it as simply the transfer of energy. [Engels (1954), pp.69-102.] This seems to connect his comments with more recent theories of motion, depicted by the use of vector and/or scalar fields, or with the laws of Thermodynamics -- or even with concepts derived from non-Euclidean Spacetime (where talk is no longer of forces) --, constructed a generation or so after he died. But, once again, such a re-write of DM would mean that familiar DM-concepts (such as "contradiction", "polar opposite", "UO" etc.) would become just as obsolete as "natural place", "substantial form", "accident" and "substance" are now --, notions that were once used in ancient scientific theories.

Indeed, it is difficult to imagine how, say, an energy gradient (depicted as a scalar field) could be interpreted as 'contradictory', even though these often feature in modern accounts of motion. Well, no more perhaps than, say, a ladder should be regarded as contradictory if someone fell off of it.

Far worse: it is even more difficult to regard states of affairs involving vector and scalar fields, the geodesics of Spacetime -- or even the strings of Superstring Theory -- as part of a material universe. If everything in nature is just a complex array of energy gradients, vector fields and differential curvatures in Spacetime -- spruced up with a few probability density functions -- there would seem to be no place left for anything that even looks remotely material. Given this 'modern' mathematical account of reality, matter itself would simply become a "useless fiction", explanatory of nothing at all. Small wonder then that Lenin was highly suspicious of the Idealism implicit in the Physics of his day (even if he had no answer to it). [On this, see Essay Thirteen Part One (summary here).]

Quite apart from all this, the 'ontological status' of 'energy' itself is highly obscure -- and this situation is unlikely ever to change. Energetics is thus no friend of 'Materialist Dialectics'.

Of course, in DM-writings, a clear definition of "matter" is about as easy to find as is an honest UK Prime Minister (as we will also see in Essay Thirteen Part One).

26. Those who still think that forces can oppose motion, and therefore, contradict it, should consult the arguments constructed in Note 25 above, and presently in the main body of this Essay, where this idea is finally laid to rest.

However, it is worth pointing out to such individuals that if they were correct, then the idea that forces are oppositional to one another will have gone out of the non-dialectical window, for if forces oppose motion, they cannot oppose each other.

27. In which case, it might be wondered whether only those bodies that approach each other along the same line of action (wherein the angle between their trajectories is 180°), or which operate in a force field (where the lines of action of that field are similarly orientated at 180°) are to be counted as opposites.

If not, will any angle (other than 90°) do? In that case, clearly, since forces and velocities are vectors, they can be resolved to get around this difficulty.

Even so, any solution sought along these lines would clearly be conventional, since the components of vectors do not exist in nature in any meaningful sense; they are just calculating devices that help make sense of motion. On this see Notes 24 and 25 above, and Note 30, below.

28. Anyone who thinks that the vector calculus is a description of reality would be suffering from the same sort of confusion as someone who thought that the weather, say, is just the wavy lines and/or tangent fields on a map because the weather forecast on TV uses them. [On this see Notes 25, above and 40, below.]

29. This section of the Essay might be dismissed as just one more unsympathetic reading of yet another artificially-manufactured set of DM-theses. Perhaps so, but the reader will find that dialecticians themselves consistently fail to examine their own theory in anything like the detail attempted here, despite the fact that DM/'Materialist Dialectics' is supposed to represent the best, if not the very epitome of scientific thought. The present Essay, in contrast, has endeavoured to set-out in more detail than has ever been attempted before the implications of this particular DM-thesis; as such, it ventures into entirely unexplored territory. Hence, it is impossible to say whether it misrepresents DM or not -- indeed, DM-theorists would be hard-pressed to decide among themselves whether this is so. For one thing, they cannot even decide what matter is! [As Essay Thirteen seeks to show, their 'materialism' is a rather like, say, Hamlet without the Prince.]

In addition, it is worth pointing out yet again that F2 was motivated by the idea that forces contradict impressed motion. Unfortunately, since change in motion is the consequence of just one resultant force (if considered classically), the alleged 'contradiction' between two forces disappears.

F2: A UO involves the opposition between a force P1 and the impressed motion that another set of forces Q has produced (or would have produced) in a body B (had P1 never existed). The resultant motion of B is the final outcome of this struggle.

It would take an especially alert and eagle-eyed dialectician, therefore, to spot 'contradictory' forces when there is only one force responsible for the said change in motion!

Worse still, F2 postulates a 'contradiction' between a force and the motion that is (or might be) produced as the counterfactual result of the action of other forces, but since some or all of the latter's effects won't have been actualised (having been prevented from occurring by P1), the alleged 'contradiction' here contains only one real term.

Even the most avid DM-fan might find it difficult to visualise (let alone explain) a 'contradiction' between something that is real and something that is unreal (in that it never existed): i.e., the motion that would have occurred if the impeding force P1 above had not acted.

30. Admittedly, some vectors are invariant under certain transformations, but the physical interpretation of the operation of forces is not a given; it is set by convention.

On this topic, cf., Ellis (1963, 1965, 1976).

[Ellis (1976) was written in response to Hunt and Suchting (1969). See also Hanson (1965a, 1965b), and Jammer (1999).]

Mysteriously, however, Ellis has backtracked on his earlier views (for what appear to be instrumentalist reasons); cf., Bigelow, Ellis and Pargetter (1988), and the response to this in Jammer (1999), pp.iv-vi.

The difficulty with finding a physical analogue for a vector space (worse: for any tensor extension to it) is examined in Cartwright (1983), pp.54-73; see also Hesse (1961). A recent challenge has been mounted to this way of seeing forces, in Jones (2007); on this see Note 6a.

31. On this, see Notes 24, 25 and 30 above.

32. This was discussed in more detail in the sections devoted to something I have called the Dialecticians' Dilemma. See also here.

33. On this, see, for example, here.

Either this (i.e., that there is no limit toward which knowledge is converging), or it must be the case that as knowledge advances, external reality alters accordingly!

However, that can't be so. We are not to suppose that our knowledge of the world alters the 'objective contradictions' that allegedly power it along, so that as the former grows the latter slowly disappears. But if not, it must now be true that absolute knowledge of the world (even if we never attain to it) implies that nature is not contradictory. [However, on this see here.]

Of course, it may be incorrect to assume that dialecticians believe that as science advances all contradictions will be resolved, but it is not easy to see how they can deny this. Faced with yet another contradiction -- and committed to the view that science can only advance if it overcomes/resolves contradictions in knowledge --, with respect to this new contradiction, dialecticians must believe it can be resolved. Otherwise they will have to admit that science cannot advance beyond a certain point. But this they deny, too. So unless they hold both of these true (that is, they believe that there is no limit to scientific advance, and that there is a limit (i.e., because there are irresolvable contradictions in nature) --, which in itself would represent a contradiction in their own theory, so DM can only advance if this is resolved!), they must hold that all contradictions are resolvable, and hence none are 'objectively' true.

Thus, in terms of DM's own theses, it would seem that nature cannot be fundamentally contradictory.

Again, the only apparent way of avoiding this dilemma (that is, in the form in which it appears here, at least) is to deny either that (1) science advances by resolving all contradictions, or that (2) Absolute Truth 'exists'.

(1) The denial of this option would mean that there is a non-Absolute limit to knowledge, after all; in which case the DM-thesis that human knowledge is unlimited would have to be abandoned. It would also leave dialecticians with no way of knowing which of the allegedly irresolvable contradictions their theory throws up is an 'objective' feature of reality or merely a by-product of their own imperfect theory.

(2) Unfortunately, this tactic would introduce other intractable problems for dialecticians since it would remove the limit toward which they suppose human knowledge is progressing, and with that would go the idea that there is an 'objective' reality (out there) for us to know (even if we never fully attain to it).

Naturally, these observations take into account the fact that the universe might be 'infinite' (a view held true by only some DM-theorists) and constantly changing. None of these factors affect the idea that there must now be a set of truths (possibly infinite) about reality toward which human knowledge is asymptotically converging (even if that set itself somehow grows over time), if Engels were correct when he said:

"'Fundamentally, we can know only the infinite.' In fact all real exhaustive knowledge consists solely in raising the individual thing in thought from individuality into particularity and from this into universality, in seeking and establishing the infinite in the finite, the eternal in the transitory…. All true knowledge of nature is knowledge of the eternal, the infinite, and essentially absolute…. The cognition of the infinite…can only take place in an infinite asymptotic progress." [Engels (1954), pp.234-35.]

"The identity of thinking and being, to use Hegelian language, everywhere coincides with your example of the circle and the polygon. Or the two of them (sic), the concept of a thing and its reality, run side by side like two asymptotes, always approaching each other but never meeting. This difference between the two is the very difference which prevents the concept from being directly and immediately reality and reality from being immediately its own concept. Because a concept has the essential nature of the concept (sic) and does not therefore prima facie directly coincide with reality, from which it had to be abstracted in the first place, it is nevertheless more than a fiction, unless you declare that all the results of thought are fictions because reality corresponds to them only very circuitously, and even then approaching it only asymptotically." [Engels to Schmidt (12/3/1895), in Marx and Engels (1975b), p.457.]

Of course, if there is no such set, then Engels's metaphor is defective.

However, in this regard, Woods and Grant quote a revealing passage from Engels's DN:

"The fact that our subjective thought and the objective world are subject to the same laws, and that consequently too in the final analysis they cannot be in contradiction to one another in their results, but must coincide, governs absolutely our whole theoretical thought. It is the unconscious and unconditional premise for theoretical thought." [Woods and Grant (1995), p.349; quoting this source.]

To be sure, the above passage was not included in the 'official' version of AD, but it certainly shows that Engels believed that the 'objective' world should be free from contradictions (or at least free from contradiction with/in subjective thought --, which view, it must be admitted, is impossible to distinguish from the former).

So, if any randomly-selected dialectician were to think that, say, motion is 'contradictory' then that subjective thought cannot be in contradiction with 'objective' reality (and thus with 'objective' thought, one presumes, even if this blesses state is never attained).

Naturally, that does not commit Engels to the view that reality is in the limit a contradiction-free zone, but if science can only advance by resolving contradictions in subjective theory (so that it becomes progressively more 'objective'), the conclusion (given above) seems inescapable: that in the limit, human knowledge of the world must see nature as totally free from contradictions.

However, in the absence of any clear indication from Engels that he believed this, little more can be asserted here with any confidence.

One suspects that because the DM-classics are silent on this, modern-day dialecticians themselves would not be able to decide anything here without being called 'Revisionists', sparking perhaps yet another dialectical split.

[In the limit, perhaps, this might mean that future dialectically-knobbled Marxist parties should have a maximum of one member each. At that ideal point, the splits and expulsions will stop, one supposes -- unless, of course, that other DM-thesis (that everything is a UO) induces each lonely comrade to expel herself! Maybe this is the real cunning of reason?]

[AD = Anti-Dühring; UO = Unity of Opposites.]

34. As noted above, it is entirely possible that this is not what DM-fans really mean by "contradictory" forces; but then again it is equally doubtful whether they have ever subjected their own theory to this level of scrutiny, so that they could confirm or deny this fact. Hence, it would probably be pointless asking a DM-adept for an answer to this question, as things now stand.

35. It is worth repeating here that these assertions are aimed neither at affirming nor denying the truth of DM-theorists' claims about the Totality, or its supposedly 'contradictory' parts, since both options are metaphysical. [The reasons for saying this will take up most of Essay Twelve Part One, Essay Eleven Part One and Two.] As was pointed out earlier, the intention here is simply to make patent the latent non-sense they contain.

Moreover, an appeal to 'relative knowledge' would be of little help, either; surprising as this might seem, that notion was torpedoed by Lenin. On this, see here.

36. As we saw earlier, these relate to questions about whether it's a force's effects, or the relative motion between objects, or the interrelationship between bodies, which are 'contradictory'.

37. This is so on Hegelian/Aristotelian grounds (although, here, as with other things, one would be well-advised to stick to the latter's account, since the former seems to have committed his 'thoughts' to paper in a dialect not of this planet -, or while permanently drunk).

So, even though male and female, hot and cold are 'opposites', a male dog is not the opposite of a female flower, and a hot forehead is not the opposite of a cold furnace (indeed, they could both be at 39oC). Such contrasts can only work as opposites if they have the same substantival term to back them up. Hence, a male dog is the opposite of a female dog, a hot furnace the opposite of a cold one, and so on. On substantivals, see here.

Naturally, this undermines much of what dialecticians themselves say about UOs; but since this ground was covered in Essay Seven, no more will be said about it here.

38. Here we appear to have another ironic "dialectical inversion"; in this case, the said forces would not 'contradict', they'd augment, one another -- even though they are still 'opposites'. Perhaps then we should call such ensembles "dialectical tautologies"?

On this basis, therefore, we might be able to construct a whole (and it must be said, wholly insincere) theory of universal harmony, using the fact that forces naturally combine to form resultants and opposites more often than not attract (on this, see Note 40), both of which in turn 'encourage' motion and change. As a result of such an 'inversion' -- putting DM back on its heels, as it were -- change could then be seen as an expression of cooperation, not conflict. And we could even re-introduce the idea of an 'imminent deity' (a suitable -- but equally obscure -- analogue of the DM-'Totality') to give this novel theory the unity it needs, claiming all the while that these ideas have not been imposed on nature, merely read from it.

Since this 'theory' is based on a more realistic appraisal of the interplay between forces, who could object? We could even call this 'theory' "Anihalectics" (since it eliminates dialectics). Subsequent 'contradictions' implied by this 'theory' could, of course, be Nixoned away, in classic DM-fashion.

[We could even declare, with equal pomposity, that anyone who disagrees does not "understand" Anihalectics, ending all discussion.]

On the positive side, this 'theory' enjoys much more evidential support than the average DM-thesis does (given that resultant forces govern every example of change in motion in nature).

On the negative side, however, this 'theory' means that class collaboration/harmony will usher in the 'revolution' (we saw that that was an implication of DM, anyway; here and here), since it is not needed anyway (in such a harmonious world...).

Anyone critical of the above (wholly insincere and fancifully) dotty 'theory', should now take an equally sceptical view of the consistent (but less scientifically-accurate) dottiness of 'Materialist Dialectics'.

39. Even so, and once again, howsoever it is that forces actually do manage to combine, change is not initiated by contradictory forces, but by those annoyingly 'harmonious' resultants.

40. Engels himself regarded the two poles of a magnet as an example of the unity of AR-opposites in nature (something else he lifted from Hegel, and which has been parroted down the ages by countless uninventive DM-authors). [Cf., Engels (1954), p.72. Hegel for example, here.]

The alleged 'unity' in this case appears to revolve around the fact that the north and south poles of a magnet cannot exist independently of each other, and their 'opposite' nature is shown by the effect they have on bodies and upon each other.

However, upon closer examination it is clear that the poles of a magnet are in fact examples of AA- or RR-, and not AR-opposites. This is because in this case it is non-opposites that repel each other (i.e., two norths or two souths); hence, like poles repel. On the other hand, opposites attract (i.e., a north and a south). Consequently, in the way that their poles inter-relate, magnets are in fact AA- or RR-forces. A moment's thought will further confirm this -- since when do magnets attract and repel one another, at the same time?

So, it now turns out that the magnet is hardly a paradigm example of an AR-force -- united in opposition --, as DM-lore would have us believe.

Mysteriously, DM-theorists en masse have failed to notice this serious flaw in one of their key examples. So much for the claim that DM-theses have been read from -- but not projected onto -- the facts.

[Incidentally, the same comments apply to electrical and thus sub-atomic phenomena. This means that much of the dialectical guff in, say, Woods and Grant (1995) is gloriously wrong. More on this in Essay Seven, Part Two (when it is published).]

It could be objected to this that, while it might be true that two unlike poles are examples of an AA-force type, their continued motion toward one another will be prevented at some point by structural forces within the magnets themselves, and these force couples would operate in an AR-manner. In that case, R-forces operating between approaching nuclei of the material from which the magnets are made will prevent opposite poles closing in on one another, counteracting the A-forces that had brought them together. This therefore implies that the relation between the poles of a magnet is indeed that of an AR-couple -- or so an objector might claim.

Even so, this means that, as magnetic opposites, these poles would still not be AR-UOs. To be sure, other forces might come into play, but that does not affect that salient point. In that case, they would not be opposites of the same Aristotelian/Hegelian type (as noted above).

Despite this, the above objection would reduce the oppositional relationship between the forces originating in these magnets to the effect that these poles had on motion (since the latter manifestly do not affect each other, only the relative motion of the matter in each magnet). Hence, the two poles would not be inter-related directly to each other as opposite AR-forces; they would just oppose any motion that either or both of them had induced in the system. We have already had occasion to dismiss this view as inimical to DM.

In which case, the inter-atomic forces governing the operation of AA-, RR-, or even AR-couples, actually oppose or limit whatever motion is already present in the system -- or they restrict the freedom of bodies to move once set in motion. But, they still do not seem to oppose each other as force upon force. Again, this is probably one reason why Engels toyed with a positivistic re-interpretation of forces (in DN, as pointed out above in Note 4), since no physical sense can be given to any such relation between forces (as also noted earlier) -- that is, over and above seeing it as an obscure way of depicting relative motion between bodies.

Of course, it could be argued that the force field of each pole does in fact affect that of the other; so the above claims are incorrect. But these force fields are merely the expression of the motion of, or that induced in, instruments (or, indeed, in scattered iron filings) placed near the said poles, so the above claims are not incorrect. Such forces are, as Engels said, a shorthand for relative motion.

On the other hand, if by "force fields" we mean the mathematical objects of theory, they cannot affect one another, for they are not material. [This was discussed in more detail in Note 25, and will be in even more, below.]

Anyway, the nature of the UO here clearly depends on what is meant by the terms "opposite" and "unity". North and South poles are not united in the sense that they are one (as DM-theorists would be the first to point out), they are connected in the sense that they 'depend' on each other. But, this 'dependence' is causal not logical; magnetic properties are the result of the vector configuration of the 'motion' and 'spin' of certain electrons. There is nothing in nature that logically forces this interrelation on these poles. Indeed, the idea that such a configuration represents a UO is empty, since the 'forces' involved are the consequence of a vector field. And, as we have already seen, it is not easy to see how vectors can be regarded as 'contradictions' (or as UOs).

Indeed, in ferromagnetic substances, the magnetic field is built up by the cooperative alignment of individual magnetic moments (perhaps illustrating the fundamentally cooperative nature of reality again, created by those helpful 'dialectical tautologies' we met earlier(!)).

Certainly, given Engels's use of the term "force" (whether interpreted realistically, or positivistically as a "useful fiction"), this is a rather poor example of a UO, anyway; it is consequent upon a particular sort of mathematical analysis (i.e., it is based on the alignment of electrons, which orient the vector field that determines the direction of the magnetic field). Calling this a UO would be to substitute an obscure metaphor for a clear mathematical description for no extra explanatory gain.

[Of course, there is no UO here anyway, since the field in question is the result of one sort of particle, the electron, which is a single charged elementary object (or wave?) that is not itself a UO. This has already been commented upon here.]

Naturally, this deflationary approach will satisfy few DM-fans since it depends on a non-standard view of the nature of mathematical 'objects' (such as, vectors, matrices, manifolds, dimensions, abstract spaces, etc.). In opposition to this, it could be argued that mathematics in fact represents what is really out there in the world, since it has been abstracted from nature by human beings as part of their practical activity. This means that mathematics presents us with an 'abstract' reflection of reality.

[Chapter 16 of Woods and Grant (1995) contains a classic (but nonetheless confused) version of this idea. Because if its influence, I will be devoting a special Essay to this book, which will be posted at this site (as Essay Seven Part Two) in the next year or so.]

However, this interpretation of mathematics is badly mistaken. Mathematics cannot be a description of the world (nor an 'abstraction' from it) for reasons rehearsed in Essay Three Parts One and Two, and in Essay Thirteen. Mathematics is based on systems of concepts that are not causally linked. Nor do the concepts that mathematicians construct exercise any sort of causal influence on material bodies (nor do they 'correspond' to anything in reality that could conceivably so behave) -- unlike other material bodies. [On that, see here, and here.]

Mathematical propositions and theorems yield neither an abstract nor a concrete picture of reality. This is because they express rules for the manipulation of symbols that licence inferences we make about objects and processes in nature. At best, they set up complex analogies that assist in our understanding of objects, events and processes in the material world.

The development of Field Theory since Maxwell's day does not alter this picture in any way. Vector and scalar fields are mathematical structures that not only enable scientists to model nature, they assist in the derivation and interpretation of the empirical consequences of their hypotheses. To imagine otherwise (i.e., to suppose that mathematics is an abstract description of the world) would reduce its structures to absurdity. For example, it would imply that, say, a vector field -- in re -- is actually composed of a set of infinitely thin and infinitely strong wire-like curves, or curve segments (of mysterious composition and provenance). Or, that a scalar field is actually an invisible array of real numbers 'floating' in (abstract?) space -- or, worse still, that it is an infinite n-dimensional set of dimensionless connected, dense but disjoint points --, and so on.

On Maxwell, cf., Buchwald (1985); on mathematics as it features in Physics, see Morrison (2000), pp.62-108. In addition, the last chapter of Harré and Madden (1976) is relevant here.

Other literature on this topic was listed here. More will be said about the nature of mathematics in later Essays (for example, here).

41. This could be regarded as a serious interpretive error -- given the fact that change is central to DM. But, the point being made in the text is specifically targeted at the DM-notion that all change is a consequence of the interplay between polar opposites. Clearly, if these allegedly polar opposites can combine in some way to augment one another, the term "opposite" can't fail to lose most of its dialectical bite. If change can occur as a result of 'opposites' that do not really work as 'opposites' (still less as "polar" opposites) then this particular dialectical 'law' stands in some danger of violating the dialectical equivalent of Metaphysical Trades Description Act.

If this picture is now extended to take in HM, and if, for example, we consider the operation of "opposing" forces in the class struggle, it is not easy to see how, say, one social force could switch around in the way that forces in nature can. Is it possible, therefore, for Capitalists to swap sides in the class struggle (as a class force -- and not as individuals) to augment workers' battles in the latter's interests and on their terms? Admittedly, the detailed structure of -- and processes within -- the class war are complex; elements from each side may detach themselves (or be detached), and can work against their own (misperceived) class interests (on a temporary or even semi-permanent basis), but that is not something revolutionaries can or should rely on -- still less ought they to trust in its outcome. If they did, it would clearly encourage reformism and centrism (let alone court defeat). Even at the margin (where whole class forces are not involved), switches are sporadic.

But, such things occur all the time in nature. Hence, this crude analogy relating opposite forces to 'contradictions' lifted from DM is useless, at best, when applied in HM.

42. It is worth recalling here how Stalinists used to justify the frequent changes in tactics in the 1930's on the basis that this was a 'dialectical' requirement (nay, virtue). Hence, a 'dialectical' pact with Hitler made eminent good sense. Not only that, but anyone who disagreed with this randomly applied, chaotic logic clearly showed they "did not understand dialectics". The treaty so forged was as good an example of a UO as one could wish to find. Who could complain -- except those with "bourgeois" prejudices motivated by an antiquated reliance on FL?

[Well, perhaps only those without an excessive "tenderness" against pacts with Nazis!]

Moreover, this theory is so contradictory, it can sanction any conclusion whatsoever, no matter how contradictory. Hence, it is of great use to opportunists and sectarians alike. [Details can be found in Essay Nine Part Two  and Essay Ten Part One.]

43. Is this a second 'dialectical tautology'?

44. This insurmountable obstacle indeed blocks the path of all forms of Metaphysical Realism; it is not just a problem for DM-theorists. More on this in Essay Twelve (summary here).

45. Admittedly, this could be a complete distortion of DM, but, as we have seen on numerous occasions already, over the last hundred years or so, DM-theorists have been so preoccupied with the simple repetition (and almost word-for-word) of the theses that have been handed down to them that they have neglected to think about their import with any obvious care, or with any clarity whatsoever. There is in fact very little in DM-texts to help prevent distortion -- or even to assist dialecticians in its detection.

Once again, DM-apologists are welcome to produce their own clear account of this part of their 'theory' -- making the 'Materialist Dialectics' of forces perspicuous for the very first time in history.

46. Of course, this attempt is unclear itself. We should normally want to distinguish the opposition between force P1 and P2 from that between events E1 and E2, or indeed any combination of all four. These sorts of complications will be examined in what follows (in fact, some of them were analysed earlier).

47. Admittedly, this qualification runs foul of the idea that everything in the Totality is interrelated, but we can avoid that by modifying the stated condition to "relative independence". Naturally, this would mean that several other comments in the text (originally aimed at trying to make this part of dialectics clear) would become even vaguer by default. However, as will readily be appreciated, a 'theory' like this -- beset as it is by an internally generated fog, aggravated further by its supporters who insist on lobbing yet more metaphysical smoke bombs at it -- will always resist attempts to dispel the Stygian gloom that permanently engulfs it.

48. It is worth recalling, once again, that in FL two contradictory propositions cannot both be true and cannot both be false at once. One implication of this is that the claim that two allegedly contradictory states of affairs could both exist at the same time (expressed by two supposedly true contradictory propositions) must rest either on a mis-description of reality, or on an un-discharged ambiguity --, and, indeed, on the projection of logical categories onto nature. This was analysed in more detail in an earlier section, in Essay Five, and will be examined again in Note 67, below.

49. However, it could be claimed that the disjunction of the effects of P1 and P2 (as in "E1 or E2") distorts the picture somewhat. Indeed, it could be argued that what is missing here is an account of how P2 interacts with E1, which interaction could be dialectical. [One variation of this theme will be considered presently in the main body of this Essay, others later on (for example, in Note 55).]

But, plainly, what has not been taken account is the fact that the alterations induced in E1 mean that this theory (i.e., that change comes about through contradictions modelled by material forces) could still succeed in gaining some sort of grip.

Hence, it could be argued that the contradiction between P1 and P2 alters E1 so that it becomes, say, E1a. In that case, we would have here real terms for the 'contradiction' to model, and thus we would have a concrete example of change through 'internal contradiction'. Or, so it could be maintained.

But, plainly, this would only be so because these forces have already been described as "contradictory", when it has not yet been established yet whether or not this is an accurate, or even an appropriate, way to depict the relationship between them.

Nevertheless, and ignoring even this point, as has been underlined already, what actually happens here is that the resultant of these two forces produces the said change. In that case, and on the contrary, calling this a change motivated by a 'dialectical tautology' would be more accurate. [This option and others are considered again below.]

Moreover, even if the objection volunteered above was correct in some way -- wherein P1 and P2 alter E1 so that it becomes E1a --, it would be of little use to dialecticians, for in this case E1 itself will have been altered externally, and so change in this case would not have been the result of its own 'internal contradictions'.

Worse still, if this is to be the model for all DM-change, then no change at all could be 'internally-generated'.

We saw this problem recur throughout Part One of this Essay, where no matter how we tried to slice things up, the result was always the same: if all things are "self-moving", then the universe is populated either by eternally changeless 'particles' or by non-interacting systems. On the other hand, if systems of forces change the objects in that system, then those objects cannot be "self-moving". The volunteered response above simply reproduces this very problem in a more abstract form.

Anyway, this 'difficulty' will be tackled presently in the main body of this Essay, and in more detail below (once again, in Note 55).

50. It could be objected that forces actually make things happen, as opposed to preventing them. But even then, such things would happen because one force 'wins out': the resultant. And making something happen is even less easy to interpret as a 'contradiction' than opposing or preventing something would be. In that case, once more, calling this a "tautology" would be more appropriate.

51. The terminology used here is not what I should prefer, but tinkering with it will not make the conclusion any clearer. The following is, perhaps, a little more 'correct':

F16a: Anything that is prevented from occurring does not happen.

But, F16a is just a discursive tautology (although I should prefer to call it a "grammatical remark", since it expresses a linguistic convention).

52. It needs pointing out (once again!) that this 'new' account of the connection between forces and contradictions (given in the text) is only offered tentatively since DM-theorists are hopelessly unclear in this area.

53. The phrasing of F24 might be considered prejudicial -- F24a perhaps being preferable:

F24:  P1 contradicts P2 only if it counterbalances P2.

F24a: P1 contradicts P2 if it counterbalances P2.

This option will be considered presently, in the text (as F27).

54. We saw in the passages listed at the beginning of this Essay that several DM-authors regard disequilibria in nature and society as important as corresponding equilibria, and in need of explanation.

54a. To see this, compare it with the following:

S1: NN will win the chess game over MM if she uses the XYZ opening.

But as a sufficient condition, S1 does not rule out S2:

S2: NN will win the chess game over MM in so far as she employs the PQR opening.

Since there are many different ways to win a chess game -- even though none of them might be necessary, but all could be sufficient --, none of them are uniquely so.

55. However, some may still object and claim that if a force prevents something coming into being/happening, it must have contradicted it.

Let us say, therefore, that:

T1: if event Ei at time t (and belonging to process A), is prevented from becoming  Ei' at t' by force P (where t' > t), then  Ei at will have been contradicted by P.

Hence, it could be argued that in this sense it is clear that forces prevent the effects of other forces from being realised by contradicting certain events, stopping them from occurring.

But, even here, forces do not 'contradict' one another (as force on force), they merely affect the events 'controlled' by other forces. So this cannot help us understand how forces can be said to contradict each other.

Nevertheless, let us examine this objection in more detail, so that every possibility is catered for.

Consider then the following:

T2: Let there be an event set E, consisting of sub-events E1-En, which would all take place, or would all have taken place, had force P not stopped things at the Ei stage.

T3: Had these events carried on as 'normal', Ei would have led into Ei+1, but as things turned out, Ei+1 failed to occur because P prevented it.

T3: Hence, P contradicted Ei+1.

However, since Ei+1 never existed, it could not have been contradicted by P (unless, once more, we assume that forces can contradict non-existent objects, events and processes).

We thus hit the same brick wall.

Even if we now try to argue as follows:

T4: P contradicted Ei by stopping it producing Ei+1,

this will do no good.

This is because events are not like eggs which produce things; so they can hardly be prevented from producing other events if they don't produce them in the first place.

In that case, perhaps the following revision will do:

T4: P contradicted Ei by stopping Ei+1 from following on from Ei.

But, yet again, the alleged 'contradiction' amounts to the prevention of something that does not now exist. If forces can only be 'contradicted' by preventing non-existent objects/process/events from taking place, then all the above problems re-emerge.

At this point it could be objected that this entire approach to 'events' and 'forces' atomises them, and puts them in rigid categories, compartmentalising reality. Dialectics, in comparison, deals with the unity and fluid nature of reality, and thus it depicts such interactions in a totally different, albeit contradictory, light. Hence the above analyses are completely wrong-headed.

But, unless and until DM-apologists tell us what they intend -- or what, for example, the 'fluid' nature of reality is (or worse, what this odd metaphor could possibly mean) --, then that objection is itself devoid of content (since it contains several empty phrases). Anyway, this objection is neutralised here.

Once again, there is a simple solution staring us in the face here: dialecticians should tell us what, if anything, they mean by their odd use of (such Hermetic) language.

56. This is, once more, to use dialectical-terminology (of dubious content, and even more suspect provenance); it does not imply I accept that any of it makes the slightest bit of sense.

57. Of course, in an analysis of situations where the smallest angle between these two forces lies between 0° and  90°, or between 90° and 180°, the components of these forces would be put into the required relation.

Unfortunately, the prospects for a realist/metaphysical account of forces (given such an analysis) do not look at all promising. Hence, it is worth asking: Are the components of such forces in effect merely 'shadow forces', mathematical fictions, or are they genuine forces, or what? And how could we tell these apart?  [This was discussed in more detail in Notes 24, 2527, and 30.]

58. Hegelians might not object too much at this point, since they are by now somewhat used to Word Magic -- their master having created 'Nothing' out of 'Being', and then 'Becoming' out of both (i.e., miraculously out of a reified verb) --, but genuine materialists might want to pause here, and see this 'derivation' for what it is: empty word-juggling.

Even so, this latest twist brings into question the 'ontological' status of forces, and whether 'resultant forces' actually exist. On this, see the comments and links in Note 57 above.

59. How did revolutionaries manage to miss this third force for so long?

It might, however, be felt that this view of forces is overly simplistic; in HM, social forces are far too complex to be represented as vectors, which means that the criticisms aired here are once again completely misguided.

In response to this, it is worth recalling that the analysis in the main body of this Essay was forced upon us (forgive the unintended pun) because DM-theorists have so far failed to say what they mean (if anything) when they try to explain the nature of 'dialectical contradictions' (in nature or society) by an appeal to forces.

Nevertheless, dialecticians, in abeyance of such an account (and thus acting almost totally in the dark), are themselves quite happy to declare that such 'contradictory' forces occur everywhere in HM (and, indeed, throughout the universe). Is this not yet another case of foisting dialectics on the facts?

[It is worth reminding the reader here that the existence of forces in HM is not being questioned by the present author (nor will it be), just the assumption that they are 'contradictory'; but see Note 61, below.]

Clearly, DM-theorists employ the phrase "contradictory forces" in order to provide their theory with a scientific-looking façade, linking it in with Physics, perhaps. Otherwise, why use it?

If this allegation is correct, it would be disingenuous of DM-supporters to complain that the analogy given in the text does not apply to social forces. If the word "force" wasn't meant to be taken in its usual scientific sense as a vector, such an analysis would, it is true, be inapt -- but in that case the import of this word (i.e., "force" as it is used in DM) would be unclear, too. If it is not being employed in DM in a way that can be modelled by the use of vectors, what other scientific way is there of doing it?

Anyway, as far as the complexity issue is concerned, this counter-argument itself fails to address the problem of the identification of forces with 'contradictions' in nature and society. If it is impossible to give a clear sense to an avowedly simplified picture of them (i.e., as they operate in nature), a more complex one stands no chance.

As has been pointed on many occasions in this study, if DM-advocates object to any of the comments made in this Essay, there is a simple remedy: they should say clearly for the first time ever what it is they mean when they try to link forces with 'contradictions'.

59a. Anyway, we have been considering real material forces since the beginning of this Essay. After all, what are gravity, magnetism and other fundamental forces if not real and material? [What we haven't done fully yet (but see here) is consider forces at work in class society, but that is all.]

59b. Here are a few examples; 1, 2, 3, 4, 5; with a particularly crass list of alleged instances, here (which link will take the reader to a site called "Dialectics For Kids" (poor sods), so it can be forgiven somewhat). Several more were given earlier.

Here is another recent example:

"The current debate over stem cells provides a very good illustration of the contradictions inherent within capitalism. On the one hand it is capable of generating amazing new technologies.

"However, the amount of money flowing into stem cell research is still miniscule compared to that being used for developing new ways to kill people.

"A recent report concluded that while stem cell research was pioneered in this country, lack of funding was compromising the ability of British scientists to keep things moving forward in this area.

"Meanwhile, as the leader of the richest country on earth talks about the sanctity of a ball of cells, in Iraq the most sophisticated weapon systems are being used to murder real, living human beings." [Parrington (2007), p.9.]

On the contrary, this illustrates the fact that dialecticians (like John here) regularly confuse 'contradictions' with paradoxical, irrational or unexpected events, as I alleged in Essay Five.

Even in DM-terms, this makes no sense. Does either 'half' of the above 'contradiction' struggle against the other? Does the one turn into the other (which they should do, according to the dialectical classics)? Is George W Bush and/or the rest of his class about to morph into a bunch of under-funded scientists/new equipment?

If not, where is the 'dialectical contradiction'?

60. Several more examples of alleged 'real material forces' and/or 'contradictions' (such as those between the forces and relations of production, and between use and exchange value) will be considered below, in Note 70.

61. If this notion is to assume a viable role in HM, it must be understood analogically. The details of my own interpretation of such a key concept within HM will have to wait on another occasion.

In the main body of this Essay, however, I am simply questioning the literal and metaphorical application of the word "contradiction" to situations that occur in HM and DM.

62. The negation of "wealth" might appear to be "poverty", but this is so in only a loose or figurative sort of sense. Recall that something could fail to be "wealth" without automatically becoming a cause of, or being identical with, "poverty". Naturally, this is because the two words have a complex set of application conditions. So, for example, £10,000 ($20,000) does not constitute "wealth" in and of itself, and the lack of it does not automatically amount to "poverty", either. Both options obviously depend on the surrounding circumstances (historical and social). Of course, in Marxist economic theory, wealth is associated with "use-values". This is not being denied here. [Nevertheless, it is unclear whether the introduction of this technicality would alter things in any noticeable way. On this, see Note 70.]

Some might want to interject that the contradiction is between the forces that create wealth and those that produce poverty -- or, perhaps, the contradiction inherent in the processes that do this. Furthermore, these social forces are inextricably inter-linked, and work in opposite directions.

But, why call these "contradictions"? The only reason seems to be that this word has been imported from Hegel, who in turn based his use of this word on some highly dubious 'logic'. [More on that below.]

However, this is covered more thoroughly, here and here.

63. We encountered similar problems over the simplistic interpretation of schematic letters (such as "A" and "not A") earlier, in connection with Trotsky's criticism of the LOI (i.e., in Essay Six), and in an extended analysis of DL and FL (in Essay Four). There, it is demonstrated that the logic of even these apparently simple-looking schematic letters can be rather complex.

It is also worth adding that it is only the sloppy way these letters have been used by dialecticians (beginning with Hegel) that has allowed dialectics to get off the ground. More on that here.

[LOI = Law of Identity; DL = Dialectical Logic; FL = Formal Logic.]

64. Unfortunately, F52 requires the use of somewhat stilted language if it is to remain literal. The "poverty" reading will, anyway, be adopted presently in connection with F56.

A detailed analysis of the alleged 'contradiction' between use-value and exchange-value can be found in Note 70, below. See also here.

65. F52a has to be interpreted this way otherwise it might suggest that Capitalism had in fact made the very same person (or groups of people) wealthy and not wealthy at the same time.

66. Someone might object that these are rather trite examples, and not the sort of contradictions with which dialecticians are concerned. Maybe so, but since the nature of the 'contradictions' they study is left terminally vague, they will have to do until they manage to say what on earth they mean.

However, on this, see here, and Note 70 below.

67. This would be of no help to DM-apologists, anyway. That is because (once more) linguistic tinkering of this sort simply creates 'contradictions' by fiat when what is required was an example of a real material contradiction -- not a reified linguistic expression for one, hastily cobbled-together just to save the theory.

Nevertheless, the claim advanced in the main body of this Essay might seem rather bold (i.e., that contradictions would normally be regarded as figurative or ambiguous, if held 'true'), but it is based on how we would respond now when faced with a contradiction in ordinary material language.

[There is a partial explanation of the background to this approach (derived from Wittgenstein) here.]

Naturally, this means that the observation in the text is not just the result of the present author having been 'corrupted' by Analytic Philosophy; on the contrary it is occasioned by the way workers themselves speak, and how anyone not suffering from 'dialectics' talks when operating in the material world. Indeed, it is based on the way DM-theorists actually have to speak to make themselves understood in every day life.

Nevertheless, the following comments will test the patience of any dialecticians who have made it this far; they will no doubt regard the examples of contradictions given below as discursive, but not dialectical, contradictions. That worry will be allayed presently, when examples of just such 'contradictions' (advanced by DM-theorists themselves) will be considered.

In that case, in order to illustrate how we would handle such 'contradictions' now, consider, how worker NN would respond if she has been faced with the following:

C1: Boss: "NN, you are being paid £7.50 an hour and not being paid £7.50 an hour."

[Of course, no one speaks like this, but it is not easy to find examples where ordinary human beings use 'true contradictions'; not even bosses do anything so crass!]

At first sight, C1 would (possibly) be interpreted as a joke of some sort, a slip of the tongue, or a mistake. If the boss insisted that none of these were the case, then the only way to proceed would be to ask what on earth C1 meant.

In that event, the explication of C1 might involve interpreting the word "paid" in one of three ways; it could:

(1) indicate what NN was going to earn, regardless of whether he or she will ever receive the money. Hence, in a round-about sort of way, C1 could be referring to the effect of taxation and other deductions on NN's pay. It could even refer to the boss's intention to pay the worker in 'kind';

(2) mean that although the money had been earned, it would not actually be paid to NN for some reason. It might be being withheld as a part of the boss's attempt to victimise her for helping to lead a successful strike, for example;

(3) mean that although NN will be paid at the stated rate, the true value of her contribution to production could not be measured in cash terms. Hence, it might suggest that the boss intends to reward NN with more than mere money (or maybe with none at all) -- but, with his/her 'highest esteem', etc. A clue to this way of viewing C1 would be the inflection in the boss's voice -- a note of sarcasm, perhaps.

However, 'contradictions' like these would never be regarded as literally true, for as soon as NN here was actually paid the said money the second half of C1 would become false (a fact which all ordinary workers are well aware of in advance of being paid). Hence, such a conjunction of a falsehood with a truth could never become literally true (short of altering the meaning of the words used to assert that it was true -- or, of course, without altering the meaning of "literal"). We would not be able to make sense of anyone who thought that this sort of eventuality could arise (save in the ways indicated above, etc.). Certainly, without the alternatives outlined here (and perhaps others), no worker (or anyone else) would be able to understand C1.

This brings us back to a difficulty DM-theorists must always face if they persist in regarding "contradictions" as true, or they continue to use the word "contradiction" in the loose way they have done for generations (where they sort of half mean the word in its ordinary (or even its FL) sense, half with its new and unexplained DL connotations). When we bring this word back to its ordinary (material) sense, any propositions containing this word -- if they are still regarded as true -- could only ever be understood in a non-standard way, and then disambiguated.

If, on the other hand, the word "contradiction" is meant to be taken in a special or technical (but as yet unspecified) sense, then DM-theorists risk being misunderstood at every turn (or their ideas will fail to communicate anything determinate) -- especially if they hope to depict the sorts of situations in material reality familiar to ordinary people/workers. And that risk will remain until DM-apologists make it clear (and for the first time ever) what they mean by their use of this word in such non-standard contexts.

This means that in practice, when faced with sentences like C1, DM-theorists would also interpret the alleged "contradictions" they contain in the standard way, in line with the vast majority of ordinary human beings (and hence paraphrase them away). Thus, and despite dialectics, few DM-fans would understand the words attributed to the fictional boss in C1 (above) as literally true. In fact, only the most useless trade union rep. in history would allow such a boss to get away with the nonsense reported in C1. Representing and/or defending the material interests of the working-class certainly does not mean that we let bosses off the hook by adopting ways of speaking that were invented by Idealists -- supporters and members of the boss-class itself.

However, socialists who are normally alert to the dangers of class collaboration when they surface elsewhere seem only too willing to allow material language to suffer from class contamination of this sort when it comes to Philosophy.

Even if the word "contradiction" were intended to be taken literally, DM-theorists themselves would not be able to say what in nature or society a 'true contradiction' could depict (without helping themselves to yet more figurative language). If (per impossible) this could be done, then the word "literal" would have to be taken non-literally!

In Essay Five, we saw attempts to eliminate the confusions that plague Engels's account of motion continually fail. It turned out that it was impossible to understand what Engels could conceivably have meant by what he actually said if his words were taken literally.

So, it is small wonder then that DM-theorists have remained unclear and equivocal about core DM-theses (like this one) for over a hundred years -- there is in fact nothing that anyone could say, or could have said, to make the incomprehensible comprehensible. Like the mysteries of transubstantiation, DM-theses resist all attempts at materialist explication.

At this point, DM-apologists might be tempted to complain about the continual use of contradictions drawn from FL to make points against the use of "dialectical contradictions" in DM. The obvious response to this is (once again) to request a clear explanation of what a "dialectical contradiction" itself amounts to so that those making this complaint could themselves convince sceptics that dialecticians actually mean something (anything?) by the phrase "dialectical contradiction", as opposed to their having used an empty phrase generation upon generation.

Until then, the above volunteered objection would itself be devoid of meaning since it contains a senseless phrase -- i.e., "dialectical contradiction".

The claim that there are literally true contradictions (advanced by philosophers like Graham Priest) will be examined in a later Essay. [However, it is a moot point whether the paradoxes he considers are, or ever could be, dialectical.]

Well, What Are 'Dialectical Contradictions'?

The Best Article i have Ever Read

However, easily the best account of 'dialectical contradictions' I have come across in my trawl through the wastelands of 'dialectical logic' is to be found in Lawler (1982). Having said that, I should immediately qualify it by adding that Lawler's essay is the best of the worst, for his analysis of this terminally obscure piece of Hegelian jargon is no better than was his analysis of Bertrand Russell's criticism of Hegel for confusing the "is" of identity with that of predication, discussed in Essay Three Part One.

In fact, there are so many logical errors in Lawler's article that any conclusions he draws are not really worth the paper they were printed on. [Anyone wanting to by-pass this long and detailed preamble, can skip to the main part, here.]

First of all, running through the entire article is the Hegelian confusion of logic with the 'science of thought', which Lawler nowhere tries to defend, and upon which he does not even comment. Indeed, he quotes Engels in support of this very idea:

"Modern materialism is essentially dialectical.... What independently survives of all former philosophy is the science of thought and its laws -- formal logic and dialectics." [Engels (1976), p.31, quoted in Lawler (1982), p.14; Lawler's added italic emphasis here.]

Lawler then adds:

"In view of this passage, in which the distinction between formal logic and dialectics could hardly have been made more clearly, it is difficult to see how Marx and Engels could have confused elsewhere undoubtedly, formal logic with dialectics or, more seriously, rejected formal logic altogether." [Lawler (1982), p.14.]

However, the passage from Engels seems to identify formal and dialectical logic (indeed, he lumps them together as "the science of thought and its laws -- formal logic and dialectics"). In that case, far from making the said distinction so plain that it could not have been clearer, had Engels actually said they were distinct, that would have been clearer.

Hence, it is obvious from the beginning that Lawler's aim is to defend a view consonant with tradition, rather than read even Engels with any accuracy.

As noted in Essay Two, when it comes to Philosophy, dialecticians are as studiously traditional as they are demonstrably conservative. Indeed, they are happy to recapitulate all the errors committed by aristocratic Greek (and now modern-day Hermetic) thinkers, and spin their a priori webs of Jabberwocky-lore with obscure jargon they struggle even now to explain to the rest of us.

[How they do this is the subject of Essay Three Parts One and Two, and Essay Twelve Part One. Why they do it is outlined in Essay Nine Part Two and Essay Fourteen (summary here).]

Sure, we have no evidence that Marx himself was similarly confused about the nature of logic, but there is enough in Engels's writing to indicate that he was no clearer than Hegel  -- indeed, Hegel was less clear than Aristotle (who tended to confuse logical with psychological and ontological issues far less than did this modern-day, Hermetically-confused 'genius') --, which makes the logical views of both these dialecticians totally worthless.

And, as we have already seen (in Essay Four), Logic cannot be counted as a science of thought, for if it were, logicians would perform brain scans, psychometric testing and surveys (etc.), and not waste their time with all those useless definitions, rules of inference and proofs.

Nevertheless, we should not let these relatively minor errors detract from the worse ones to come.

Another Syntactic Mess

Lawler now tackles this topic with a consideration of Hegel's criticism of the LOI, which he regards as central to understanding the nature of 'dialectical contradictions'. But, as we have seen (and will see later), Hegel's criticism of the LOI is worthless, since he confused predication with the relation of identity, which then 'allowed' him to conjure his Ideal universe out of a reconfiguration of the diminutive verb "to be", a stunning trick even David Blaine could not match.

[LOI = Law of Identity, which Lawler calls "the principle of Identity".]

[Lawler's own misguided attempt to have the charges of logical ineptitude against Hegel dropped were ruled out of court in Essay Three Part One.]

We have also seen that Trotsky's attack on the LOI was even more inept, and while Hegel cannot be implicated with the latter's misconceptions, these two shared enough confusion in this area to make it difficult for us to tell which one of these two jokers was the Stan Laurel and which the Oliver Hardy of Logic.

[However, since Hegel got us into this mess, I reckon he's Stan.]

Be that as it may, if we turn to more substantive issues, we find Lawler is just as slip-shod in his use of 'logical' terms as other dialecticians are. Indeed, this is the only way he and they can make Hegel's 'logic' seem to work.

First of all, as we have already seen with respect to other DM-fans, Lawler is decidedly unclear about the denotation of the letter "A"s he uses.

For example, on pages 18-19, in reference to Hegel's discussion of Identity, Lawler has this to say:

"Hegel's critique of formal-logical principles begins with consideration of the principle of identity, A = A, or a thing or a concept is itself." [Ibid., pp.18-19. Italic emphasis in the original.]

We have already shown that this is a thoroughly inadequate way to characterise identity (either in logic or in ordinary language), but the point at issue here is the fact that Lawler views these "A"s as the names of objects and concepts, or perhaps even as those entities themselves, three different kinds of 'things'.

[LEM = Law of Excluded Middle.]

But then in the very same paragraph he goes on to say:

"The other principles follow from this basic one. The principle of noncontradiction, Hegel argues, is the principle [of Identity, RL] stated negatively. 'A is A' implies 'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false. The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid., p.19. Italic emphasis in the original; quotation marks in all the passages taken from Lawler have been altered to conform to the conventions adopted here. The middle set of quotation marks here (around the LEM) are missing in the original.]

As we will soon see, the principle of identity does not imply what Hegel says it does (or even what Lawler himself says it does -- since he nowhere corrects Hegel), but that is not of immediate concern here. However, when Lawler qualifies what he takes Hegel to mean, he clearly views these "A"s as propositions:

"'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false." [Ibid.]

So, they are no longer the names of objects or concepts, they are (the names of, or proxy letters for) propositions. That's now four different 'kinds' of things.

Of course it could be argued that Lawler is merely saying that such things cannot be asserted (etc.) of A, making A an object, or perhaps its name (but that is hardly likely; Lawler and/or Hegel were not bothered to discover alleged truths about names, one supposes). But even if this were so, in the above passage, "A" itself would be an object and what can be asserted of an object (i.e., a predicate expression, say). So, this response would be at once to defend Lawler and convict him.

Despite that, his wording does not support this contention. Lawler pointedly says:

"…one cannot assert something to be true and at the same time, and in the same respect, assert it to be false." [Ibid.]

As opposed to:

"…one cannot assert something to be true of A and at the same time, and in the same respect, assert it to be false of A."

If Lawler had meant his "A"s to be named objects, say, then he would have used the latter phrasing.

[Anyway, as we shall soon see, later on in Lawler's Essay these accommodating letters are unambiguously propositions.]

In addition, as pointed out above, it is worth noting that these "A"s (or at least, these "not-A"s) appear to be properties, or predicates (perhaps?); that's now six different 'kinds' of things:

"The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid.]

Of course, it could be that Lawler is merely adopting a tradition in ancient/early modern logic that treats all logical expressions equally sloppily (which, as it turns out, is the tradition that presided over the creation of the bowdlerised version of AFL that Hegel was taught at University (the kind of sloppy 'formalism' one finds in Kant's Logic, for example), and which he then put to no good), which seems to be the most likely explanation for Lawler's confusion here, given the other things we are about to discover (and to which we have already drawn attention, in Essay Three Part One, and Essay Four).

[AFL = Aristotelian Formal Logic.]

Nevertheless, it is this slip-shod approach to logic that 'allowed' Hegel (and now Lawler) to construct some rather 'innovative' metaphysics. Indeed, as Bertrand Russell noted:

"This illustrates an important truth, namely, that the worse your logic, the more interesting the consequences to which it gives rise." [Russell (1961), p.715.]

And this is somewhat reminiscent of the sort of word-juggling which allowed, say, St Anselm to concoct his famous 'proof' of the existence of 'God'.

[For more on Hegel's confused logic, the reader should consult Rosenthal (1998), pp.111-36, and Rosenthal (2001).]

This is all so quintessentially traditional as it is thoroughly confused.

But, after another flip, on page 21, Lawler now says:

"Putting the concept of identity into practical application, as it is interpreted by abstract understanding. We are compelled to say that a cow is a cow, a man is a man, white is white, spirit is spirit, etc. In attempting to express the principle of identity according to the spirit of abstract understanding, we end up paradoxically speaking of an endless number of different things." [Ibid., p21. Italic emphasis in the original.]

Although Lawler does not mention those "A"s here, they have now clearly become "things" once again. However, on page 22, they quickly transmogrify into "entities":

"'A is A' implies that A is not some other entity which is not-A." [Ibid., p.22. Italic emphases in the original.]

And, in the same paragraph, they soon morph into "beings":

"…in the abstract, undialectical understanding of identity, the relation of A to not-A (beings that are not A as well as A's own nonbeing) seems to 'vanish.'" [Ibid., p.22. Italic emphasis in the original.]

Here, not only has one of these "A"s been confused with a "being", "not-A" becomes its "non-being" (in fact, and to be more precise, it seems that these "A"s might also be predicates, once more, or even the subjects to which "being" is attributed; who can say?). At any rate, so far this makes the letters eight different kinds of 'things'.

[The reader should now convince herself that if someone says "Bush is not Bush" or even "Blair is not Bush", this does not imply Bush no longer exists. Anti-imperialists would surely have consigned one or both of these war-mongers and mass murderers to 'non-being' had their sticky end been quite so easy to engineer. To be sure, in the quirky world of Hermetic Hegelianism, negation might indeed be the same as 'non-being', but in the material world, one has to do much more to one's enemies than merely wish them away -- or simply glue a "non" or a "not" onto their names.]

On page 24, these chameleonic "A"s now change into "terms", and perhaps even propositions again:

"The point we have argued is that Hegel is attempting to establish identity, not destroy it. A term 'to be itself,' requires a negative relation to another term…. Does Colletti [an Italian Marxist, who Lawler is criticising in this article, RL]  deny Hegel's point that asserting 'A' is equivalent to saying 'not-not-A'" [Ibid., p.24. Italic emphases in the original.]

If something is capable of being asserted, it must be an indicative sentence, or a clause, at the very least (and thus perhaps a proposition). To be sure, predicates can be asserted of named individuals (etc.) -- or perhaps better: true or false sentences can be formed if predicative expressions are completed with names, or with other singular terms (or indeed with the linguistic equivalents of the bound variables of quantifiers). As should seem obvious to any language-user, it is not possible just to assert a bald "term", predicate or concept. Uttering "ξ is a cat" (or " a cat", or even "is a cat") is to assert nothing (i.e., it is to make no assertion) -- and the same is true of merely uttering the word "cat".

Of course, one can point at an animal and utter this word, but that is the equivalent of saying "That is a cat". Without the pointing gesture, the use of that word would be to assert nothing. And one can utter the phrase "a cat" in answer to a question, such as, say,  "What animal seems to know more logic than Hegel?"

To be sure, Hegel appears to think that objects/'concepts' can be true:

"In common life the terms truth and correctness are often treated as synonymous: we speak of the truth of a content, when we are only thinking of its correctness. Correctness, generally speaking, concerns only the formal coincidence between our conception and its content, whatever the constitution of this content may be. Truth, on the contrary, lies in the coincidence of the object with itself, that is, with its notion. That a person is sick, or that some one has committed a theft, may certainly be correct. But the content is untrue. A sick body is not in harmony with the notion of body, and there is a want of congruity between theft and the notion of human conduct. These instances may show that an immediate judgment in which an abstract quality is predicated of an immediately individual thing, however correct it may be, cannot contain truth. The subject and predicate of it do not stand to each other in the relation of reality and notion." [Hegel (1975), p.237, §172.]

Unfortunately, detailed consideration of the above will take us into areas that will be discussed in Essay Twelve (when it is finally published); suffice it to say here that Hegel's confusions on this score have clearly arisen out of his conflation of predicate expressions with singular terms, compounded by the adoption of the Medieval Identity Theory of Predication. [More on that here.]

The conflation of "terms" with "things", and then with linguistic expressions that can be asserted of named individuals (or once again perhaps better: the formation of true or false sentences by the completion of predicative expressions with names, or with other singular terms (or indeed with the linguistic equivalents of the bound variables of quantifiers, etc., etc.)), 'allows' Lawler (just as it 'allowed' Hegel) to derive the sort of "interesting" results we have come to know and loathe.

So, that is nine sorts of things that these "A"s are.

On page 26, these impressively Heraclitean (if not worryingly Cratylean) letter "A"s now morph into relations (as far as can be ascertained, that is), or perhaps named relational expressions(!):

"Hegel's main objective is to show an integral connection between A and not-A, or, in categorical terms, between 'identity' and what is supposed to be the contradictory of identity, 'difference.'" [Ibid., p.20.]

"In view of the criticisms made of Hegel, it is quite significant that Hegel recognises the force of logical contradiction as a weapon of criticism of his philosophical opponents. First they say, Hegel maintains, that identity has nothing to do with difference. Then they say that identity is different. They assert 'A' and then 'not A'" [Ibid., p.26.]

The only way to understand these passages is to read the "A" above as standing for "identity" and the "not-A" for "difference" (i.e., "not-identity", one presumes). Of course, this could be to misread what Lawler says --, but then he simply invites it.

That is now ten, or possibly eleven, different denotations for these semantically-dithering letters.

And it will not do to say that Lawler is merely reporting what Hegel's opponents might say, since he nowhere tries to pull these miscreants up for their syntactical sins.

At the very least these morphoholic letter "A"s now stand for propositions again, since here Lawler says they can be asserted once more. This interpretation is confirmed in the next-but-one paragraph:

"The contradiction is not any kind of contradiction. For example, first they [the said critics, RL] affirm that all swans are white and then they deny that all swans are white." [Ibid., p.26.]

Well, if two hundred years ago Hegel was indeed faced with such simple-minded opponents, then no wonder he got away with so many logical howlers. But even so: What is so contradictory about someone changing his/her mind (if that is what one of these 'simpletons' did)?

[In fact, this is the only way to read this example that does not treat Hegel's opponents as sub-literate morons.]

Nevertheless, Lawler's "A"s have been transmuted once more into either propositions or predicates -- or perhaps even into properties(?) --, or maybe all three(?).

On the very next page (but in the same paragraph), it becomes a little clearer that these plastic "A"s are indeed relations, or nominalised relational expressions (or maybe nominalised relational phrases(?)); in fact it is quite plain that this is indeed what they are:

"The law of noncontradiction holds, for if 'identity held aloof from difference' (A) is false, then the contradictory 'not identity held aloof from difference' (not-A) is true." [Ibid., p.27. Italic emphases in the original.]

Since phrases can neither be true nor false, Lawler's reasoning is, shall we say, 'innovative'. Nevertheless, these busy little "A"s have plainly had yet another denotational make-over, and now stand for "identity held aloof from difference".

[The phrase "identity held aloof from difference" might appear to make sense to some, but that is only because they too have become inured to this odd way of talking -- perhaps as a result of reading far more Hegel, or "systematic dialectics", than is good for any denizen of this planet --, a use which pretends that relational expressions can be named and still remain relational. (This ancient ploy was exposed for what it is in Essay Three Part One.)]

The mercurial career of these infamous "A"s continues apace; on page 28 they metamorphose into indexical or token-reflexive terms(!):

"Hegel's statement is made in response to Zeno's famous paradox. Zeno's paradox, according to Hegel, is that since motion involves both A and not-A, and since this violates the principle of noncontradiction, it follows that motion is impossible. What should probably be called 'Hegel's paradox' is the assertion that since motion occurs, there must in some sense both the A and not-A of Zeno's position. It is clear that this assertion cannot be taken in the sense of a strict contradiction. Not-A in a purely formal sense means only the denial of A, and is compatible with saying that the object is both 'here' and 'anywhere else,' perhaps also on the moon. Not-A can also mean the simple denial of 'here' -– an assertion that clearly leaves us nowhere….

"…Hegel's line of thought here is similar to his approach to the problem of 'abstract identity' or 'identity held aloof from difference.' The paradox arises if we begin with an abstract notion of place, a 'here' which is totally discrete and unrelated to any other place. The common-sense definition of motion as 'change of place' or as a passage of an object through a succession of places runs into insuperable intellectual difficulties if 'place' is understood in this manner. For one thing 'place' is defined as 'fixed place,' i.e., as motionless place. Can motion be explained in terms of a concept which excluded motion? On the other hand, it does not seem possible to eliminate some notion of definite place from our concept of motion, but such a notion must be that of a 'relative place,' a place which is both 'here' and 'there' or, paradoxically, 'here' and 'not-here." [Ibid., pp.28-29. Italic emphases in the original.]

In this passage, Lawler's "A"s and "not-A"s now plainly stand for "here" and "not-here", respectively. A change of identity perhaps, but no less an example of lamentably poor logic for all that.

That is now at least thirteen different identities for these impressively fluid letters!

However, we saw in Essay Five that the above 'analysis' of motion had more holes in it than a lorry load of Polo Mints. There is no 'common sense definition' of the items Lawler mentions; ordinary language (let alone 'common sense') easily allows for the sorts of motion in the material world that Idealists like Hegel ignored --, and both of these (i.e., the vernacular and 'common sense') do this with relative ease, too.

Nevertheless, on page 32, these change-oholic "A"s go into morphological hyper-drive as they become parts (or perhaps 'reflected' parts) of one another:

"One might readily grant that the definition of A includes A's relating to something that is not A (some non-A which is not-A). This does not mean that non-A or what is not-A is a part of A or part of A's identity….

"It is necessary to ask, first of all, whether and in what sense the fact that A necessarily relates to what is not-A permits us to insert not-A in A….

"…it seems reasonable to look for some 'imprint' of this 'other' in A, so that in some sense not-A is internally constitutive of A." [Ibid., p.32. Italic emphases in the original.]

These denotationally-profligate letter "A"s, it seems, can take on any form whatsoever in order to make this Hermetic Hodgepodge seem to work. I have been able to identify at least fourteen different denotations for them in this article. This means that Lawler is a verbal-trickmeister to rank with some of the best.

In the Summary of Essay Two, the following was baldly asserted:

"For over two thousand years traditional Philosophers have been playing on themselves and their audiences what can only be described as a series of complex verbal tricks. Since Greek times, metaphysicians have occupied themselves with deriving a priori theses solely from the meaning of a few specially chosen (and suitably doctored) words. These philosophical gems have then been peddled to the rest of humanity, dressed-up as profound truths about fundamental aspects of reality, peremptorily imposed on nature -- often without the benefit of a single supporting experiment….

"Even before the first dialecticians put pen to misuse, they found themselves surrounded on all sides by ideas drawn from this ancient tradition. Clearly, they faced a serious problem: if they imposed their ideas on nature in like manner, they could easily be accused of constructing a comparable form of Idealism. On the other hand, if they didn't do this, they wouldn't have a 'philosophical' theory of their own to lend weight to, and provide a bedrock for, their claim to lead the revolution. Confronted thus by traditional styles-of-thought (which they had no hand in creating, but which they were only too happy to appropriate), DM-theorists found there was no easy way out of this traditional minefield -- or at least none that managed to keep their theory the right side of immaterialism.

"Their solution was simple and effective: ignore the problem.

"This is not to deny that dialecticians are aware of the Idealism implicit in traditional thought; on the contrary, but their excuse for ignoring its pernicious influence on their own ideas is that the materialist flip they allegedly inflicted on Hegel was capable of changing such theoretical dirt into philosophical gold. However, flip or no flip, their own thought is still thoroughly traditional in style: it is dogmatic, a priori, and couched in jargon lifted straight from the Philosophers' Phrase Book. Even though few DM-theorists deny that traditional Philosophy is largely Idealist, not a single one has avoided copying its conservative approach to a priori knowledge.

"So, despite the fact that dialecticians constantly claim that DM has not been forced on nature -- for that would surely brand their theory "Idealist" -- they all invariably end up doing exactly that, imposing their theory on reality. In so doing, they merely underline the fact that traditional thought has found a new batch of converts among erstwhile radicals."

We are now (partly) in a position to see why this was asserted quite so forcefully back then. Lawler's defence of Hegel depends solely on such a sloppy use of words, where predicate expressions are turned into names, objects, terms, indexicals and possibly relations themselves -- and which can thus stand in some relation to other similarly deformed linguistic expressions, or suitably processed objects.

Indeed, this is the only way that those spooky Hegelian "internal relations" can be generated (as Bertrand Russell correctly noted), which "relations" to this day still defy scientific detection. [Not that anyone in the dialectical fraternity (or beyond) is searching for them with much urgency.]

But, without this 'innovative' use of language, Lawler's explanation of 'dialectical contradictions' falls completely flat, as we will see.

Now it could be argued that these syntactical niggles are not really all that important; after all, it is quite clear what Hegel and Lawler meant. Anyway, it might prove possible to repair both accounts so that they pass such 'pedantic' hurdles with ease.

That, of course, remains to be seen. But since Lawler's article is by far and away the best defence of this incomprehensible Hegelian notion (i.e., 'dialectical contradiction') I have so far seen, this should indicate to the reader just how bad things are in this back-water of traditional myth-making. In that case, a dialectical rescue is highly unlikely from this wing of Idealism. Even academic dialecticians regularly make serious errors of this sort, and worse -- and they all fail to notice them, let alone acknowledge them, even after they have been exposed. That is how logically purblind this ruling-class gobbledygook has rendered them.

[This was the outcome with respect to Rosenthal (1998, 2001), which also fell upon deaf dialectical ears. The above allegations, however, will be substantiated in Essay Twelve, where Hegel's work in this area (along with that of his 'Marxist' groupies) will be taken apart.]

Naturally, I exclude Graham Priest's work from these impertinent indictments since it is far from clear whether the 'contradictions' he considers are 'dialectical' to begin with (even if we could tell!), or even contradictions to at all -- and he is generally very careful with his syntax. Nevertheless, as far as I am aware, he has not yet noticed the logical blunders I have exposed in this Essay.

Rosa's Pedantry?

However, to those who think that this sort "pedantry" can be ignored it is worth pointing out that that would be the only way they could excuse their own sloppy thinking, and the only way they could make their ideas appear to work.

This sort of attitude would not be tolerated for one second in the sciences, or in any other branch of genuine knowledge. Can you imagine the fuss if someone were to argue that it does not matter what the Magna Carta said, or when the Battle of the Nile was fought, or what the Declaration of Independence actually contained, or what the exact wording of Newton's Second Law was, or whether "G", the Gravitational Constant, was 6.6742 x 10-11 or 6.7642 x 10-11 Mm2kg-2, or indeed something else? Would we accept this sort of excuse from someone who said it did not matter what the precise wording of a contract in law happened to be? Or, that it did not really matter what Marx meant by "variable capital", or that he "pedantically" distinguished use-value from exchange-value -- or more pointedly, the "relative form" from the "equivalent form" of value --, we should be able to make do with anyone's guess? And how would we react if someone said, "Who cares if there are serious mistakes in that policeman's evidence against those strikers"? Or if someone else retorted "Big deal if there are a few errors in this or that e-mail address/web page URL, or in that mathematical proof! And who cares whether there is a difference between rest mass and inertial mass in Physics! What are you, some kind of pedant?"

You can be sure such 'anti-pedants' will be examining these Essays with well-focussed magnifying glasses, nit-picking with the best, having turned their selectively pedantic eyes on all I have written in order to locate the tiniest of assumed errors --, all the while refusing to examine anything in the DM-Grimoire with a tiny fraction of such attention to detail. [In fact, they already have.]

With such a sloppy regard for logic and fondness for Mickey Mouse Science, is it any wonder that genuine ruling-class theorists regard Dialectical Marxists with undisguised contempt, and workers in their billions ignore Marxism?

Hegel Screws Up Big Time

Nevertheless, in order to consider every option open to Dialectical Mystics to say what they mean by 'dialectical contradictions', Lawler's argument will be considered on its own merits, and his syntactical sins will be put to one side for now -- that is, where they can.

Notwithstanding this, Lawler tries to revamp Hegel's criticism of the LOI by arguing thus:

"Hegel's critique of formal-logical principles begins with consideration of the principle of identity, A = A, or a thing or a concept is itself." [Ibid., pp.18-19. Italic emphasis in the original.]

"A thing or concept is itself"? Is this meant to be serious!? Not only is it a caricature of the LOI, it ropes in "concepts" which are not objects, and so cannot be related to themselves. We saw the difficulties traditional thinkers got themselves into over precisely this in Essay Three Part One, and Essay Four.

[LOI = Law of Identity; FL = Formal Logic.]

To be sure, Hegel was writing at a time when little work had been done on this 'law', but Lawler isn't. And yet he refers his readers to no modern work in this area; had he done so Hegel's 'definition' would have been seen for the mystical joke that it is. [On this, see here, and here.]

Again, putting this to one side, Lawler now goes on to argue as follows:

"The other principles follow from this basic one. The principle of noncontradiction, Hegel argues, is the principle [of Identity, RL] stated negatively. 'A is A' implies 'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false. The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid., p.19. Italic emphasis in the original; middle set of quotation marks (around the LEM) missing in the original.]

This is so full of errors it is difficult to know where to begin. Lawler (following Hegel) tells us that the other principles of FL follow from the LOI, or rather from it being stated "negatively". The latter principles comprise the LOC and the LEM –- but notice once again the common error dialecticians make (exposed in Essay Four) of thinking that FL has just three fundamental principles.

It seems in this regard therefore that academic Marxists (HCDs) are just as benighted as their more lowly LCD brethren were shown to be (here). Naturally this sorry state of affairs is itself not unconnected with the fact that both wings of Dialectical Darkness think that, to a greater or lesser extent, sane and sober sections of humanity can learn something useful from Hegel.

[LOC = Law of Noncontradiction; LEM = Law of Excluded Middle; HCD = High Church Dialectician; LCD = Low Church Dialectician. MFL = Modern Formal Logic.]

Hegel (and now Lawler) offers no proof of this 'inference', nor could he (they). The LOI concerns the relation that is supposed to hold between an object and itself (or perhaps between its names, depending on how one reads this 'law'); it is not about the truth-functional properties of propositions, which is what concerns these other 'laws'.

Lawler thus reports the following:

"The principle of noncontradiction, Hegel argues, is the principle [of Identity, RL] stated negatively. 'A is A' implies 'A cannot at the same time be A and not be A,' or one cannot assert something to be true and at the same time, and in the same respect, assert it to be false." [Ibid.]

But this 'derivation' only works because of the aforementioned confusion over the denotation of these letter "A"s (which explains why I went into all that 'pedantic' detail making this very point!).

Now, in relation to the LOC, if these letters refer to propositions, no problem. The above would at least be a passable 'definition' of the LOC; but under no stretch of the imagination can these letters refer to propositions when they appear in the LOI. That 'law' is not about the identity of a proposition with itself (which means that, with respect to propositions, the LOI is not a tautology), but even if it were, that would have no implications for the LOC. The LOC does not rule out propositions being non-identical (but see below), since it doesn't concern the identity of propositions to begin with. So, it neither rules them in nor rules them out. Indeed, if a proposition lacked identity it would not be a proposition in the first place. And if it possessed identity it would be an object, not a proposition.

To be sure, we can speak about two propositions saying the same thing, but that would not be to relate them, but to predicate something of one or both. Any attempt to go further than this stands in danger of confusing a propositional sign (i.e., the physical marks on the page, or the sounds involved when it is spoken) with what a proposition expresses. [On this, see below.]

We have already seen (here, here and here) that the LOI cannot be about the alleged identity between concepts, or even between predicates (since if it were, the latter would be objects too, and cease to be predicative), so the LOI can only apply to objects (or perhaps to their names), if it applies anywhere. This means that identity statements are at best 'necessary truths' (although I should want to call them "grammatical propositions"), not tautologies.

This is partly because they are not molecular --, that is, they relate objects to themselves, and so they do not contain sub-clauses, or simpler propositions. (On this, see Glock (1996), pp.164-69.) And even in predicative sentences, tautologies (at a discursive level) merely "say the same thing", or involve the use of synonyms. They do not involve identity statements, since the latter are not predicative, but relational. At best, a proposition expressing identity contains a relational expression which is both symmetrical and reflexive (among other things).

In short, identity statements cannot be tautological (in the sense of "saying the same thing") because both halves do not "say the same thing" (since they do not say anything at all). "A", "A", in "A = A", if it is a name, or other singular term, does not say the same thing as  since "A", if it is a name (etc.), says nothing. Only clauses, propositions or sentences can be used to do that. And if "A" is a proposition, or clause, it cannot be put into a relation with itself, since it is not an object.

[MFL = Modern Formal Logic; wff = well formed formula -- pronounced "woof".]

Discursively, an example of a tautology would be something like "A vixen is a female fox", which expresses a rule of language, and so cannot be true or false (this was argued at length in Essay Twelve Part One). On the other hand, "A vixen is a vixen" is not a rule of language. However, if it is taken predicatively, "ξ is a vixen" cannot be saying the same thing as "A vixen", for the latter is plainly not of the form "ξ is a vixen". Moreover "A vixen" is not saying anything determinate, so "A vixen is a vixen" cannot be saying 'the same thing'. And ""ξ is a vixen" is a vixen" is not a tautology.

Of course, it could be objected here that the above would mean that "A vixen is a female fox" is not a tautology since "A vixen" and "ξ is a female fox" are not 'saying the same thing' (in the strict sense meant in the previous paragraph), which is absurd.

Indeed, and that is why this sentence was called a rule, since it expresses a pattern for replacing synonymous terms in English, so that anyone who used "a vixen" in a sentence" would be saying the same as anyone using "a female fox" (in non-opaque contexts).

[MFL = Modern Formal Logic; wff (pronounced "woof") = well formed formula .]

It could be argued that an identity statement is predicative, or could be put into predicative form; for example "ξ is identical with ξ", which always gives the value true for any substitution instance. Maybe so, and in that sense, it would be a tautology in MFL (if that is defined as any wff that always maps onto the true). But this is not a necessary adjunct to logic, as Wittgenstein showed. In a properly constructed formal language, identity would be expressed by the use of the same sign, so we do not in fact need this formal relation. [More on this, here.]

And it is certainly not what Hegel and Lawler were talking about.

Anyway, even as predicative propositions, they would still not be tautologies in the discursive sense Lawler and Hegel need (i.e., in the sense of "saying the same thing"). This is because the predicate here would be a two-place linguistic function "ζ is identical with ξ" (it cannot be "ξ is identical with ξ", for that prejudges the substitutional instances allowed), which is in no way tautological. [Once more, " identical with ξ" does not "say the same thing" as "ζ is identical with...".]

[The term "linguistic function" is explained in Geach (1961). Basically, such functions are analogous to mathematical functions, except in this case, they map linguistic expressions (of a certain sort) onto linguistic expressions (of another sort) -- although, in Frege's sense, they map such expressions onto the "True" or the "False". (The latter sense is not intended here.)]

But, even if the predicate were "ξ is identical with ξ", this would be no use, either, for " identical with ξ" does not "say the same thing" as "ξ is identical with...".

The Law Of Identity Mis-Identified

But, even if we were to concede that the LOI were the following:

L1a: p = p

[Where "p" denotes a proposition, statement or spoken token indicative sentence, (etc.), depending on one's philosophy of logic.]

or perhaps:

L1b: (x) [Fx = Fx]

[where "(ξ)" is the universal quantifier, and "F(ξ)" a one-place, first-level predicate expression], neither of these would have any bearing on the relation they are supposed to have with their alleged negative/'opposite', as might be the case with the following:

L2: p cannot at the same time be p and not be p.

Nor would either have anything to do with so-called "assertibility conditions":

L3: One cannot assert that p is true and at the same time, and in the same respect, assert that p is false.

This is because there are no rules for deriving either L2 or L3 from L1a or L1b (or from the less formal versions of these two), or indeed from anything analogous. And it is not hard to see why. [More on this presently.]

[Of course, L3 could itself be correct (I will pass no opinion on it here), but L2 and L3 certainly do not follow from L1a or L1b, or from their alleged negative versiosn (or from the less formal versions of these two).]

Now, if L2 had been:

L2a: p cannot at the same time be identical with p and not be identical with p,

the problems associated with Hegel's 'derivation' would have been a little easier to see. Quantifying across propositions (if that were possible, and if we could make sense of the use of an "=" sign between propositional variables/tokens), we might be able to obtain this:

L4: (p) [(p = p) ® ¬(p ≠ p)].

If not, then perhaps just this:

L4a: [(p = p) ® ¬(p ≠ p)].

But, exactly how this implies the LOC is still rather obscure.

Perhaps the following will work? From L4a we can obtain:

L5: ¬(p = p) v ¬(p ≠ p),

and thus (by De Morgan's rules):

L6: ¬[(p = p) & (p ≠ p)],

and if we now replace "(p = p)" with "Γ" and "(p ≠ p)" with "¬Γ" we could derive the following from L6:

L7: ¬(Γ & ¬Γ).

But, we have as yet no rules for parsing the identity sign in the required manner, i.e., so that (p ≠ p) º ¬(p = p). Until we do, this derivation cannot work.

[On the rules we do have, see Bostock (1997), pp.323-33, Lemmon (1993), pp.159-67, and Quine (1974), pp.221-26.]

Even if we did have such rules, in order to obtain L7, the alleged LOI (i.e., "p = p") had to be combined with its supposed Hegelian 'other' (i.e., "¬(p = p)") [or is it "(p ≠ p)"?]), and then with its double negation (i.e., "¬(p ≠ p)") in a conditional. But, as we have seen, it is not too clear how L7 can be derived from "p = p" on its own, or even from its alleged negative form.

However, it is worth pointing out again that if a proposition is not 'identical with itself', it cannot be a proposition (at least, not one with a determinate content). In that case, nothing could follow from it. And if it is 'identical with itself', it would be an object -- and, plainly, nothing follows from an object.

Either way, we hit another brick wall.

Nevertheless, it could be argued that in stencils like, say: 

L9: (x) [Fx = Fx]


L10: (x)(y)((F)(Fx º Fy) ® (x = y))

there is an unambiguous identity sign between propositions, or at least between their signs. So the earlier claims cannot be correct.

But, logicians who use either the equal or the equivalence sign between propositional tokens do not imagine that these physical objects on the page are identical. They do have eyes! They variously interpret them as expressing a truth-functional relationship between the results of applying F(ξ), for example, to names or to objects (depending on the philosophy of logic to which they adhere), yielding an identity (or as expressing an equivalence relation) of some sort between abstract objects (i.e., sets, courses of values, graphs, ranges, classes, and the like), or between the truth values of the interpreted sentences that finally emerge as a result, and so on.

So, these signs in effect express rules that are applicable to other signs/symbols; they do not express an identity between lifeless marks on the page, or between propositions that exist in an ethereal realm somewhere.

[To be sure, some philosophers have held this view, but they too confused propositions with objects.]

Indeed, the second of the above (L10) shows that this is so by implicitly interpreting the equivalence sign as one expressing an identity between objects of some sort. In that case, stencils like L9 and L10 do not contradict what was maintained earlier, which was that where the sign for identity (etc.) is used, it expresses a relation between objects (or an object and itself -- or between its names), not between concepts, predicates or propositions.

Moreover, in L10, the "=" sign appears between quantified variables (the interpretation of which will depend on the domain of quantification, so this might not even be an example of the use of that sign between propositional tokens).

Now, whether this employment of signs captures the full range of meanings available in scientific contexts, or even in ordinary language, I will leave to one side for the present (but, it is worth adding here that Essay Six delivers a negative judgement in this regard).

[Of course, in stencils like L9, the "=" sign would be replaced by an "º", that is, by a biconditional sign. This is because "=" is a sign for two-place predicate/linguistic function (i.e., "ξ = ζ"), which can only take names or singular terms as arguments.]

Nevertheless, one thing is clear: MFL and ordinary language succeed in capturing the full range of words we have for identity (etc.) far better than the syntactical mess we find in DL. In fact, as Essays Three through Seven show, DL cannot handle the simplest of ideas/objects (such as a bag of sugar!), let alone anything more complicated.

[DL = Dialectical Logic.]

Hence, once more, the suggested Hegelian 'derivation' of the LOC (i.e., the one expounded by Lawler) cannot work if these "A"s are read as objects (since objects cannot be true or false), nor, indeed, if propositions are viewed as objects (and, for the same reason).

This is why it is so important to be clear about the denotation of these letters, and (once more!) why such a fuss was made earlier.

Alas, there is not much that can be done with this:

"The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid.]

Here, the letter "A" oscillates between predicative and naming roles (it seems), and if so, the LEM as stated above cannot be correct. [Even Aristotle saw through that one!]

[Nevertheless, as with most topics in logic, things are not quite so simple. We need to distinguish between sentential negation (i.e., "not p"), predicate negation (i.e., "not F") and predicate-term negation (i.e., "not-F" or "non-F"). It is unclear which form Lawler intends to use in the above passage (but his indiscriminate employment of "not A" and "not-A" suggests he is either unaware of this distinction, or he considers it unimportant -- the same unfortunately seems to be true of Hegel and his many groupies), so I have not dwelt on this difference in this Essay (nor on its alleged double negated form --, as in "non-non-F"). This topic will, however, loom large in Essay Twelve, where the deleterious effects of suicidally sloppy syntax like this will be exposed.

More details on this distinction can be found in Horn (1989) and Wansing (2001).]

This (new) third version of the LOC (repeated below) fares no better. What exactly this 'law' has to do with what an object can or cannot be is entirely unclear, since that 'law' (in its simplest form) merely concerns the truth-functional connection between a proposition and its negation.

If the "A" in the above passage were a predicate expression or property token (as the latter part of the last sentence in the quoted passage reproduced below clearly indicates) this version of the LOC could only be interpreted, for example, as "…is red" cannot be "…is non-red" (if viewed traditionally --, but as "ξ is red" cannot be "ξ is non-red", otherwise).

"The principle of excluded middle is that something must either be A or not be A: there is no third possibility. By extension, the law of noncontradiction implies that 'A cannot be non-A', where 'non-A' is something that is not A, or some part or property of A." [Ibid. Bold emphasis added.]

As we saw earlier, this would only be 'true' if these expressions were interpreted as names (or objects?), and not as predicate expressions or properties -- or, perhaps, as the names of whatever predicates allegedly designate.

And in that case, Lawler's "A cannot be non-A" would yield "C cannot be D". This is because Lawler clearly sees these "A"s here as the names of properties (and if these are expressed as predicate expressions, then the latter will become names once more). So using "C" for the name of whatever " red" is supposed to stand for, and "D" for whatever " non-red" is supposed to designate, we obtain "C cannot be D". And that is because, " red" must name something different from " non-red".

Of course, this will be so unless "…is red" is viewed as the same name (say "E") as "…is non-red" (also "E"). If so, Lawler's 'definition' would become "E cannot be E"!

Either way, we hit yet another brick wall, hence it is impossible to make sense of what Lawler is trying to say here.

[This is because Lawler's 'definition' tried to relate a term to its negated 'other', but his own (sloppy) syntax prevents this. The reader will note that at the beginning of this passage, "A" is a predicate letter, but by the end it has become a name! That is clear from Lawler's own paraphrase: "where 'non-A' is something that is not A, or some part or property of A." This is the confusion I have tried to highlight above.]

Now, there might be a way of reading these predicate expressions that allows them to be grafted into the LEM in the way Lawler imagines; I cannot say since he does not say. [And no one else has.]

Moreover, when Lawler says that "non-A is something that is not A", it is unclear what he means. It seems it might be either:

P1: Non-A is not A,


P2: Non-A is B which is not A.

Where B is the "something" that is not A. But Lawler immediately qualifies this by saying that "non-A" is "something that is not A, or some part or property of A". In which case he might mean:

P3: Non-A is not some part or property of A,

or perhaps:

P4: Non-A is some part or property of A.

It is impossible to decide which of these represents his view. And this lack of clarity is, once again, a direct result of the impoverished conceptual and logical tools Hegel passed on to the unfortunates who look to him for inspiration.

So, as things stand, this 'logical' sow's ear cannot be made even into a plastic purse, whatever is done with it.

More Dark Sayings From Hegel's Dialectical Dungeon

Now Lawler moves on to consider several other dark sayings he rescued from Hegel's Manichean Mausoleum:

"Recognition that the principle of noncontradiction is the principle of identity stated negatively, or is implied in the principle of identity, is central to Hegel's dialectical analysis." [Ibid., p.19.]

If so, Hegel's analysis is a non-starter, since it can only 'work' if propositions, predicates and objects are confused one with another, as we have seen. This means that we can only make sense of 'dialectical contradictions' if we pretend that the denotation of words and letters does not matter. In which case, we should openly remove the word "logic" from its already precarious presence in Hegel's corpus, and rename it perhaps "Dialectical Licence".

However, Lawler continues:

"Hegel's main objective is to show an integral connection between A and not-A, or, in categorical terms, between 'identity' and what is supposed to be the contradictory of identity, 'difference.' Hegel approaches this objective by considering the claim that 'identity' is 'held aloof from difference.' This is the claim that 'identity' is a concept that stands by itself and does not require its opposite or contradictory, 'difference,' in order to acquire its meaning." [Ibid., p.20. Italic emphases in the original.]

But why do we need to refer to "difference" in order to speak of, or give meaning to, "identity"? More to the point, why do we have to nominalise relational expressions in the first place?

As we saw in Essay Three Part One, this was an inept trick the ancient Greeks tried to pull: nominalise anything and everything in sight. In fact, they had to do this to try to make their a priori 'theories' work (and this in turn was prosecuted for ideological reasons, explored in Essay Twelve (summary here)).

The problem is that this move changes propositions into lists, which destroys their capacity to say anything at all. [Why that is so is demonstrated here.] Any 'contradiction', or, indeed, conclusion that 'follows' from this Stone Age segue is thus entirely bogus, since nothing can legitimately follow from a named abstract object like "identity". [Conclusions can only follow from propositions, or clauses.]

Well, perhaps Hegel meant that the practice of referring to identity statements tended to exclude those that expressed difference; in other words, he was merely speaking elliptically about one or both.

If so, this still won't work since there is no such thing as Identity (i.e., it is not an object, but a relation), and yet it is quite plain that both Hegel and Lawler need this 'abstraction' to be an object so that it can serve as the denotation of those annoyingly plastic letter "A"s we met earlier. However, if identity isn't an object (abstract or otherwise), then neither of these two can extract a contradiction from even their idiosyncratic version of the LOI:

"Hegel's main objective is to show an integral connection between A and not-A, or, in categorical terms, between 'identity' and what is supposed to be the contradictory of identity, 'difference.'" [Ibid.]

Here, plainly, "A" stands for "identity" and "not-A" for "difference". But, once again, we see that it is only sloppy syntax that allows this argument to gain even so much as a pretend toehold. If so, and without it, no contradiction can follow, as we have seen.

The problems this now creates for Lawler's interpretation of Hegel become clearer if we consider the latter half of the passage quoted earlier, along with what follows:

"Hegel approaches this objective by considering the claim that 'identity' is 'held aloof from difference.' This is the claim that 'identity' is a concept that stands by itself and does not require its opposite or contradictory, 'difference,' in order to acquire its meaning. This is also the claim that the identity of something can be determined without contrast to something that is not the thing we wish to define." [Ibid, p.20.]

Here identity is many things all at once: a property (as in "identity of something"), a concept (as in "'identity' is a concept"), a word (as in "in order to acquire its meaning") as well as an object (as in "'identity' is 'held aloof…'"). So it is no wonder that Hegel can derive all sorts of 'interesting' results from logical goulash of this (in)consistency. But there is more:

"According to this 'philosophy of abstract identity,' meanings and objects (including processes, relations, etc.) are independently identifiable, standing on their own, atomistically. Against this claim, Hegel argues that it is impossible to say what one means by identity without bringing into the definition what it as supposed to exclude, namely difference." [Ibid., p.20.]

However, if this is correct, and if Hegel were the genius we have been led to believe, he should have pointed out what seems obvious to his straw opponents: 'abstract identity' can only be conjured into existence if relational expressions are changed into names (in a way that is analogous to the linguistic atomism found in the theories of those he was criticising).

How could he possibly have missed this obvious response?

[Hint: Hegel was a logical incompetent.]

Insults aside, can any sense be made of this?

Not much, it seems, since the whole topic (indeed, the whole of Hegel's work) is a direct result of a crass misuse of language, on a grand scale, and nothing less.

And, of course, it is possible to identify something (in the sense of the LOI) without having to involve "difference". Consider the following:

[1] (x)(y)((x = y) º (Fx ® Fy)).

[2] (x)(y)((F)(Fx º Fy) ® (x = y)).

[3] j(y) º [(x)((x = y) & j(x))].

[4] (x)(y)[(x = y) º (j)(j(x) º j(y))].

[These symbols were explained in Essay Six.]

To be sure, different signs are used here, but many are equated.

Of course, someone could argue that all four of the above nonetheless involve "difference", but that would be to misread what they actually say.

[1] says: "Any two objects are identical if and only if they share the same properties", -- or, "…whatever is true of one is true of the other". No mention, or hint, of "difference" (and what they say is hypothetical): it sets conditions on objects being the same, not different. The same applies to the others (they were all translated here).

Moreover, it is worth noting that here Hegel (and perhaps Lawler) slides between two uses of the word "identity/identify" -- that is, between (1) this word when it is used to provide an empty (or perhaps significant) identity statement for any given object, and (2) when it is used in relation the capacity most of us have of being able to identify (in the sense of being able to pick out, or to recognise perhaps) a person, property, process or object.

If, say, squaddie NN is asked whether or not he can identify Osama bin Laden in a line-up, and he replies, "Osama is identical to Osama", he would risk being put on a charge. On the other hand, if he pointed to one of the suspects and said, "That's him!", he would not.

Naturally, the latter use could in some circumstances involve the capacity to differentiate among objects, but this is not necessarily so in every case (as was pointed out here).

By conflating these two senses, Hegel demonstrated he was even more confused than this dim squaddie. Lawler might well be advised, therefore, to resign as his defence counsel.

[Admittedly, there are three uses of this word (indeed, in ordinary language, there are countless -- on this see here), the third being found in more 'philosophical' contexts, connected with an attempt to provide a comprehensive description of a substance, a là Leibniz.]

Of course, to do the former (i.e., (1) above) we do not need to refer, or allude to --, or even so much as vaguely hint at --, 'difference'. However, in order to do the latter (i.e., (2) above), an ability to tell one object/human being from another clearly helps. But the two skills (if such they may be called) are not at all the same (irony intended).

So, it looks like this Hegelian wild-goose chase can only get started if we are prepared to become linguistic philistines, or if we confuse our capacity to construct empty (or significant) identity statements with our ability to identify friends, relatives and/or suspects.

Surely this is philosophy for absolute idiots, not just Idealists!

Lawler now inflicts more of the same on his readers:

"In fact, Hegel replies, when we want to identify something we assert in the predicate something different from what is in the subject. The subject of a proposition is in itself something (relatively) undifferentiated or unspecific and real thinking does not consist in simply repeating this." [Ibid., p.20. Italic emphasis in the original.]

We have already seen that since 'subjects' (I assume Lawler means names here, or some other singular designating expression) assert nothing (and neither can we assert anything merely with a name, or other singular term), then the use of predicates can assert nothing different from the use of names (or other singular terms). There can be no difference in assertibility protocols if only one of these is capable of asserting anything, or of being used in this way. [All this was argued in detail in Essay Three Part One.]

Of course, and by default, it could be argued that this does in fact represent a 'difference': one of these can be used to assert something while the other cannot -- so, there is a difference.

This is undeniable, but it is not Hegel's argument. And even if it were, it would have nothing to do with the alleged identity between a predicate and a subject term. The latter was based on the identity and difference that supposedly exists between the two halves of a proposition ('subject' and 'predicate'), which are said both to assert the same thing and also something different from each other. But, since, only one is capable of asserting anything, we cannot even derive an 'identity' here, never mind a 'difference'.

It is hard to credit this to a leading Philosopher (one whom many regard as among the greatest ever), but if Hegel's argument did indeed depend on the supposed physical or phenomenological differences between subject and predicate terms, it would plainly have been based on the rather crass confusion noted above -- in that it would have run together identity with being able to identify, and difference (i.e., lack of identity) and difference (being distinguishable from). These are not at all the same, and do not always depend upon each other, as noted above. [More on this in Essay Six.]

We also saw earlier, that predicates need not be physically different from 'subjects' (nor even temporally divorced from them); so this 'argument' is hopeless from beginning to end.

Once again, it is quite clear that it is only by blurring the distinction between subject and predicate expressions that this slip-shod logic is allowed even to limp badly along.

'Difference' Rendered Unrecognisable

Unfortunately, there is still more:

"Moreover, the defense of the theory of abstract unrelated identity leads proponents of such a theory unwittingly to assert the contrary of their original position. They must say that identity and difference are…different. Or, Hegel dialectically goads his opponents: identity is different…from difference. In this proposition identity has been 'identified' with difference, or difference is regarded as a property of identity. So much for 'identity held aloof from difference,' Hegel concludes." [Ibid., p.20.]

But, Lawler should have pointed out that this dialectically-benighted Hegelian riposte only works if the identity relation is nominalised, and turned into the name of an abstract particular (and the alleged contrast (or comparison) with "difference" is modelled on that which might or might not exist between two objects).

Now, even though Lawler (and as far as I can determine, Hegel) did not identify (no irony intended) the 'simpletons' criticised here, it is quite easy to see what 'they' should have said in return, to prove they were more than a match for both:

"Mock all you like, Herr Hegel/Lawler, your 'argument' only works because you talk as if you think identity is not a relation, but an object, or a name of an object. Now, this is about as crass as thinking that if someone were to say, '99 is nearly the same as 100' and '999, 999 is nearly the same as 1,000, 000', and that since 'nearly the same' names the same object in both cases (i.e., 'nearly the sameness', or perhaps 'approximate identity') '99 is thus nearly the same as 1,000, 000'. If the relational term 'nearly the same' names the same abstract entity each time (as it must, given your crazy 'theory'), then we would be able to argue that any two numbers you care to mention (no matter how far apart they were on the number line) are nearly the same!"

As seems plain, this dialectically-annoying riposte is effective only because it makes hay of Hegel's dim-witted confusion of relational terms with singular designating expressions, or, indeed, with abstract particulars, and/or the names thereof --, a trick, of course, he learnt from Ancient Greek mystics.

In fact, this manoeuvre does not just relate to, but helped create the empty Idealist flap over 'Subject/Object identity', which was the main problematic of German Idealism. In that case, if names and predicates are both objects (or they designate them), then their identity (or lack of it) naturally becomes a 'problem'. But, if it is only names that actually name things --, whereas predicates merely describe the objects so named --, then the many centuries devoted to solving this bogus 'problem' can be seen for what they are: a monumental waste of time. Naturally, this consigns several thousand works (and tens of thousands of commentaries on such works) to the dustbin of history'; and good riddance, too.

Indeed, we will see later (in Essay Twelve Part Six) that this doctrine originated in ancient Greek ideas concerning 'non-propositional' thought (in Aristotle and Plotinus, for example), and the relation of the mystical knower to the Hermetic unknown. It is this ancient doctrine that lies behind all the nominalisations we have seen, and the Identity Theory of Predication Hegel was taught and which he needed to make his 'theory' work.

[On the Greek end of this sorry tale, see the Owen (1966) -- particularly, pp.207-11 (i.e., of the 1986 version) --, Sorabji (2005), pp.90-93, Sorabji (1982), and Alfino (1988). On the Identity Theory of Predication, see here.]

So much empty philosophical verbiage extracted from such a seemingly insignificant syntactical error, and by supposedly intelligent theorists!

[A deep and wide puddle of Metaphysics condensed from a cloudy use of grammar, to paraphrase Wittgenstein.]

In that case, Marx did not go far enough: ruling ideas do not just rule such minds, they ruin them.

Hence, Lawler's conclusion:

"Irrespective of the validity of this argument (sic), it is clear that Hegel maintains that the defenders of the concept of abstract identity, or identity unrelated to difference, become prey to a logical self-contradiction, by affirming difference of identity, while at the same time trying to deny this." [Ibid., p.20. Italic emphasis in the original.]

is so wide of the mark it is lodged in the next star system.

Now, Hegel (or one of his groupies) can maintain the above doctrines until the cows evolve, for all the good it will do him (them). Only those stupid enough to fall for the systematic nominalisation of relational expressions will be embarrassed by the 'simpleton's' response, recorded earlier.

This sorry tale continues:

"Hegel points to another inconsistency to which defenders of the position of abstract identity are subject. Putting the concept of identity into practical application, as it is interpreted by abstract understanding, we are compelled to say that a cow is a cow, a man is man, white is white, spirit is spirit, etc. In attempting to express the principle of identity according to the spirit of abstract understanding, we end up paradoxically speaking of an endless number of different things. The category of difference asserts its right to exist despite the intent to banish it -- which Hegel attributes to his opponents -- and the two categories appear in a peculiar relationship in the cognate category of 'diversity.'" [Ibid., pp.20-21. Italic emphasis in the original.]

This is no better; if anything, it is worse. Exactly who would want to "banish" difference is unclear (how they would manage to pull this trick off is even less obvious  -- take out a court order, perhaps?).

Nevertheless, such conveniently fictional characters need not bother us for now. What is more worrying is the uncritical way in which Lawler accepts this lamentable 'argument'. Quite apart from the odd examples of identity Lawler quotes (for instance, his "white is white" can only work once more by nominalising the predicate "ξ is white", so that "white" is treated as the name of an abstract particular), the alleged diversity involved is no argument for the existence of the other nominalised entity in this mutant couplet, "difference" --, which is a creature of Hegel's own fevered imagination.

The most that can be concluded from this latest example of devilishly Diabolical Logic is that the five examples given above are all different from one another. How "difference" (i.e., this abstract particular) can be conjured out of that banal observation, Lawler (and still less Hegel) neglected to say.

[As noted in Essay Six (more specifically here) it looks like modern logicians are at last taking a hard look at the complexities in our use of words like "diverse", "same but distinct", "identical but not the same". (Examples of these were given in that Essay). On this see Sanford (2005). One thing is reasonably clear, few, if any, will be consulting Hegel's badly misnamed books on this subject in order to learn anything in this regard -- except, perhaps, how not to approach the entire subject.]

But, let us assume that an abstract 'entity' -- named by the word "difference" --, does indeed exist. If so, it must be a particular of some sort, which means that the word in question cannot be a general term, but a singular designating expression. In that case, it can tell us nothing about the many and diverse relations that exist in the material world. So, even if Hegel were right, we would not need to appeal to this 'entity' (indeed, we would be wise to ignore it) in order to understand how to make identity statements, if ever we do.

So, we hit the same annoying, material/syntactical brick wall every time. Once particularised (a là traditional logic/metaphysics), words like "Identity" and "Difference" lose all contact with their original meanings, and thus cease to have a meaning (since they no longer function as relational expressions).

The Fog Thickens

From here, Lawler's attempt to clarify the meaning of the fog-bound phrase 'dialectical contradictions' only succeeds in lobbing a few more smoke bombs at it:

"'A is A' implies that A is not some other entity which is not-A. Thus a peculiar negative relation to not-A is implicitly asserted in the principle of identity and in the expression 'A is A.' It is easy enough to say that this is only a negative relation and to interpret the concept of negative relation as meaning no relation at all. If, however, it is a relation without which it it (sic; "is"? RL) impossible to establish the identity of A (any definite being or concept at all), then it cannot be 'nothing at all.' 'Abstract understanding' does not probe seriously into this problem, and in the abstract, undialectical understanding of identity, the relation of A to not-A (beings that are not A as well as A's own nonbeing) seems to 'vanish.'" [Ibid. p.22. Italic emphases in the original.]

As we have seen, if this is an implication, then the required relation can only be forged out of it if the propositions involved it are nominalised. But, once that is done, no inference is possible; objects do not and cannot imply other objects, and neither can nominalised expressions.

But, is it really the case that "'A is A' implies that A is not some other entity which is not-A" as Lawler says? Well, "A is A" does not in fact imply that A not also not-A; hence it could be the case that even while "A is A", A could also be B (which is not-A).

Taking an example of Lawler's: while it is true that "a cow is a cow" -- "A is A" -- ii is also true that "a cow is brown" -- "A is B" --, even while it is also true that "brown is not a cow" -- "B is not-A".

Now, it is little use dialecticians objecting to the syntactic 'looseness' of this counter-example, for the "A"s they use are subject to no little dialectical double-dealing of their own. Hence, dialecticians have no more right to complain about sloppy syntax when it used against them that George W Bush has a right to moan about "terrism". Consequently, if this counter-example is to be ruled out on syntactic grounds, then much of Lawler's (and hence Hegel's) argument must go with it.

In that case, if it is indeed true that "abstract understanding" ignores this 'problem', it would be well-advised to continue doing so -- for there isn't one.

More-or-less the same comment applies to this example of casuistry:

"Looking one step further into this matter, Hegel suggests that the relation of A to not-A is doubly negative. Identity is established (not immediately given) through a negative relation to not-A. A is itself in not being not-A. But this negative relation to not-A is itself negated. That is, the identity of A does not consist solely in its being not-A, there is a 'return' to A again -- which Hegel calls 'reflection.' Thus 'A is A' is not a tautologous (sic) repetition of A (as 'abstract understanding' would have it) but an affirmation that has been made possible only through a doubly negative movement, a 'negation of the negation.'" [Ibid., p.22. Italic emphases in the original.]

Once more, these 'inferences' only work if they are expressed propositionally, whereas the relations they express only apply if they are not.

However, as we have just seen, there is no "negative relation" of A to not-A, and that means that it is not the case that "A is itself in not being not-A". The whole passage is thus about a genuine as one of George Brown's smiles.

In that case, the NON here is just as fabulous a beast as the Jabberwocky ever was. Hence, if the NON works, it cannot apply to negation, and if it applies to negation, it cannot work.

[NON = Negation of the Negation.]

Zeno -- No Help At All

We are now in a position to see just how Lawler employs the results of thee above examples of reconstructive linguistic-surgery, as he turns to Hegel's use of contradictions, beginning with a consideration of Zeno's paradox of motion:

"Hegel's statement is made in response to Zeno's famous paradox. Zeno's paradox, according to Hegel, is that since motion involves both A and not-A, and since this violates the principle of noncontradiction, it follows that motion is impossible. What should probably be called 'Hegel's paradox' is the assertion that since motion occurs, there must in some sense both the A and not-A of Zeno's position. It is clear that this assertion cannot be taken in the sense of a strict contradiction. Not-A in a purely formal sense means only the denial of A, and is compatible with saying that the object is both 'here' and 'anywhere else,' perhaps also on the moon. Not-A can also mean the simple denial of 'here' -– an assertion that clearly leaves us nowhere….

"…Hegel's line of thought here is similar to his approach to the problem of 'abstract identity' or 'identity held aloof from difference.' The paradox arises if we begin with an abstract notion of place, a 'here' which is totally discrete and unrelated to any other place. The common-sense definition of motion as 'change of place' or as a passage of an object through a succession of places runs into insuperable intellectual difficulties if 'place' is understood in this manner. For one thing 'place' is defined as 'fixed place,' i.e., as motionless place. Can motion be explained in terms of a concept which excluded motion? On the other hand, it does not seem possible to eliminate some notion of definite place from our concept of motion, but such a notion must be that of a 'relative place,' a place which is both 'here' and 'there' or, paradoxically, 'here' and 'not-here.'" [Ibid., pp.28-29. Italic emphases in the original.]

But, this is of no use at all in helping anyone understand the term "dialectical contradiction" since Zeno's 'paradox' is no paradox, as we saw in Essay Five (or, rather, it is only a paradox for those Idealists who are determined to think and speak like linguistic Philistines).

Perhaps this is too hasty?

"The solution to the paradox, which is expressed in the form of a logical contradiction, is the 'dialectical contradiction.' Thus in the case of motion the logical contradiction arises for the 'natural' mode of thought, based on common sense…, that argues 'either continuity or discontinuity.' Since place is classified as an instance of discontinuity, while movement implies continuity, the notion of motion as 'change of place' leads to a logical contradiction and to Zeno's paradox. The dialectical solution involves the recognition of the relative nature of the basic categories involved in thinking about motion as 'change of place.' Motion must be understood as involving a 'unity of opposites,' 'discontinuity' which is relative to 'continuity' (or, perhaps, space that is relative to time)." [Ibid., p.29.]

Here, the terminally unclear (i.e., "dialectical contradiction") is explained by means of the hopelessly obscure (i.e., "unity of opposites").

Nevertheless, at the risk of further annoying those who are even now content to stumble about in this Hermetic Haze, this alleged 'unity' can only be cobbled-together if the predicates "ξ is continuous" and "ξ is discontinuous" are nominalised once more into "continuity" and "discontinuity". Only then can these abstract particulars be put in any sort of relation with one another. But as soon as that is done, these 'terms' either cease to be predicates, or they are no longer general (depending, of course, on how this Hegelian fairy tale is finally unwound -- that is, whether it is interpreted as applying to 'things' or to the names of 'things').

[It is worth pointing out here that I am not arguing that nothing should be nominalised, only that once this has been done, the logic of such terms changes dramatically. Traditional theorists in general ignored this glaringly obvious fact.]

As we noted in Essay Three Part One, this remarkable a priori 'truth' is such solely because Hegel's system depends on a methodology derived from an ancient ruling-class tradition, one which mangles ordinary material language in order to concoct such 'interesting' results. [On this, see here.]

Lawler then notes that Hegel's analysis of 'dialectical contradictions' begins from the 'commonsense' view of motion and place, and proceeds from there. He adds that it is not relevant to argue that modern definitions of motion are more precise -- or rather, that this would be an effective response if it could be shown that:

"(1)…there was no valid use of the common-sense categories of place and motion from which the paradox arises; and (2) that no new paradoxes arise from the categories involved in more advanced mathematical interpretations of motion." [Ibid., p.30.]

But, (1) above does not apply, since ordinary language does not collapse into paradox -– that is, not unless it is twisted out of shape, a là Hegel, or a là Zeno -- as we saw was the case in Essay Five. And (2) only applies if the terminology that mathematicians use is twisted in like manner, and functional expressions are transmogrified, for example, into the names of 'categories', i.e., abstract particulars once more.

Now, as we approach the seemingly impossible goal -- that of trying to find some sense in the phrase "dialectical contradiction" -- Lawler confronts those who think that Hegel:

"…illicitly passed from the fact that an object relates to some other object, and the consequent need to include this relation to another object in either the definition or the description of the first object, to a theory that the being of the first object includes the being of the second. And if the second is something that is not-A, the definition of the relating being should be expressed in the logically contradictory form, 'A and not-A.'" [Ibid., p.32. Italic emphases in the original.]

Well, how does Lawler answer the query about this non-contradiction?

[Indeed, that is what "A and not-A" is -- a non-contradiction --, unless, that is, "A" is no longer an object, or name of an object, but a proposition, and as such is in no relation to anything, since propositions are not objects, nor yet the names of objects.]

He does so as follows:

"One might readily grant that the definition of A includes A's relating to something that is not A (some non-A which is not-A). This does not mean that non-A or what is not-A is a part of A or part of A's identity. Such a position would lead to regarding all interacting beings as constituting essentially one being. Only the relation of non-A (not-A) seems to be a property of A -- not non-A or not-A itself. Hegel clearly wants to claim more than this…. Despite Hegel's detailed critique of this category, critics commonly persist in interpreting dialectical contradiction as the assertion of the undialectical identity of A and not-A." [Ibid., p.32. Italic emphases in the original.]

We note once again that none of this works without the Hegelian/traditional confusion of relations, properties, names, predicates and propositions.

[And, while we are at it, what exactly is the difference between "not A" and "not-A" (or even "non-A")? If the first "not" is (or stands for) a sentence forming operator (which maps a sentence onto its 'negation'), we are surely on firmer ground. But, that cannot be the case with "not-A", which Lawler clearly sees as an object of some sort --, an "entity" --, but which "entity" he also regards somehow as the same as "not A". This unfortunately now means that the latter "not" cannot be a sentence forming operator as was supposed. In fact, and to be honest, one suspects that Lawler has confused a sentential use of these letter "A"s with a phrasal (or predicate term) operator -- or worse, he sees no problem with sliding effortlessly between the two. However, on this see here.]

Unity Of Opposites?

Now, Lawler rejects the open insertion of "not-A" for "A" (which, if correct, as we saw in Essay Four (here), would in fact be bad news for Diabolical Logicians) with an obscure quotation from Hegel that seems devoid of earthly sense (omitted here, to help conserve the reader's sanity), but he then goes on to say:

"If we grant that A's identity involves its necessary relation to what is not-A, and that this not-A is 'its own other' -- a definite other being and not any being whatsoever -- and that this relation to some definite other is necessary for the existence of A or is essential to the constitution of A (A's identity) it seems reasonable to look for some 'imprint' of this 'other' in A, so that in some sense not-A is internally constitutive of A. The internal structure of an entity should be investigated, according to this schema, not as something that stands alone, in isolation, but as 'reflecting' in various forms its necessary relations to its environment. In other words, to understand the internal nature of A it is necessary to study the determinate not-A not only as a necessary external condition but as 'reflected' in A. This is not to say that one should expect to find in A some direct or immediate duplication of not-A. The direct identity of A and not-A would constitute the annihilation of the beings involved. Short of this 'abstract identity.' However, the dialectical theory of the unity of identity and difference suggests a different general schema for understanding things in their necessary relations. A is not to be conceived of as already formed, but as coming into being through its relation to not-A. The necessary relation of A to not-A is thus 'internal' to the constitution of A and should be regarded as necessarily reflected in A's identity." [Ibid., pp.32-33. Italic emphases in the original.]

Even so, is there any evidence that nature itself sees things this way? Lawler thinks there is:

"...At any rate, it seems obvious that living beings, which are normally contrasted with nonliving beings, are nevertheless internally composed of non-living elements, transform nonliving sources of energy into living forms and break down ultimately into nonliving components." [Ibid., p.33.]

Now, as we saw in Essay Seven, this example of homespun neo-Romantic pseudo-science won't work; there is no intrinsic difference between living and non-living matter, so the alleged contrast is bogus. In fact, the above is more an expression of the obscure ideas found in mystical vitalism (which was current in Hegel's day) than it is an accurate reflection of living things themselves.

And what should we say of lifeless matter as it was before life evolved? Then there was nothing with which it could be 'contrasted'. Did that mean lifeless matter had no 'identity'? Did it gain an 'identity' only when the first living things evolved? In that case, was life bound to evolve, just to help identify, or provide an 'identity' for, non-living things? Indeed, does this classic example of a priori superscience mean that life in the universe cannot (logically cannot) ever cease --, otherwise lifeless matter will once again lose its 'identity'?

Taking this a step further, should we not now postulate the existence of non-material beings (spirits) to help identify material beings? Surely, on this view, 'spirit matter' must exist somewhere if all things, including matter, are to have an 'identity' only in and because of an "other"? Have we not now found a perfect argument for the existence of 'God'?

And we had better not ask what the "other" of the universe is. [To be sure, Hegel thought he had an answer to this, but the hot air will be let out of that metaphysical balloon in Essay Twelve.]

Perhaps we need to understand 'dialectical negation' a little better, so that the above materialist impertinences can be ruled out? Lawler is ready to help:

"The crucial issue does not seem to be how necessary relations to specific entities involve some form of 'reflection' of the 'other' in the relating entity. It is the problem of understanding this necessary relation and internal constituting activity as one involving negativity. This is the respect in which 'interaction' becomes 'contradiction.'" [Ibid. p.35.]

At last we are beginning to see a little less darkness at the end of the stygian tunnel, for now we are in a position to understand how "negativity" and "interaction" relate to those elusive 'dialectical contradictions':

"It is one thing to say that to understand organic processes one must understand their systematic connection with and 'internalization' of inorganic processes, and another thing to argue that this relationship involves opposition or 'contradiction.' Starting with a picture of the world as consisting of 'diversity' -- the juxtaposition of A and indifferent non-A's -- Hegel attempts to arrive at a view of interconnecting beings in which the negativity reflected in our mental distinctions, contrasts and comparisons is regarded as a real feature of the entities themselves." [Ibid., p.35. Italic emphases in the original.]

Maybe so, but it would have been an even better idea if Hegel had made a more concerted attempt to review how we actually speak about medium sized dry goods and the like (indeed, as he himself must have spoken about them in his day-to-day affairs), instead of imposing on 'thought' a form which is really only of interest to members of the ruling-class and their hangers-on.

Well, maybe not Hegel, but certainly Lawler should.

Except, had Hegel done this he would not have been able to spin any of his notoriously convoluted dialectical fairy tales, since ordinary speakers do not confuse predicate expressions with 'beings', sentences with objects, objects with relations, and "not" with 'negativity', in their everyday use of language.

And even if they did (but on this see here), that would have ontological implications only for Idealists.

The Magical Use Of 'Negation'

But, is this once again a little too hasty? We will soon find out:

"In the first place, negation cannot be understood in the formal sense, according to which the existence of some entity implies the nonexistence, pure and simple, of another." [Ibid., p.35.]

The ripe old fun we had at the expense of assorted LCDs (in Essay Four) was perhaps too hard only on them, for here we see an HCD like Lawler make all the same old sophomoric errors.

What the dialectics has "formal" negation got to do with any of this? Precisely which non-existence of what entities does the following imply: "Blair owns a copy of Hegel's Logic" and "Blair does not own a copy of Hegel's Logic"?

Would that it were that it was that easy to consign Hegel's confused book to logical limbo!

[LCD = Low Church Dialectician; HCD = High Church Dialectician.]

And even if two contradictory sentences could be found that did imply that something or other did not exist, what would that have to do with formal negation in general, as opposed to a particular instance of it?

Of course, actual negation is very complex -- on this see Horn (1989) -- but formal negation is the result either of the use of a sentence-forming or phrase-forming operator. That is it! Anything else ain't formal negation, howsoever much this 'anything else' might seem to allow this virulent strain of Hermetic Herpes to grow further in size.

Lawler continues:

"And yet intuitively we recognize in real life some entities do destroy others, or less radically, they 'clash,' collide or struggle. It is common to regard such practical negativity as external or accidental to the nature of the entity or entities involved.... To place negativity within the framework of necessarily related beings, however, it is necessary to conceptualise negativity differently and paradoxically. It is necessary to say that the negative or destructive tendency is not extrinsic to the connections that positively constitute the beings involved, but are (also) intrinsic to that constitution. The negativity is not an unfortunate by-product, which one might possible eliminate, of the positive relations necessary for the things development. It is intrinsic to that positive connection." [Ibid., pp.35-36.]

There are so many things here that Lawler just takes for granted he stands in danger of being indicted on a conceptual robbery charge.

What has a "clash" got to do with 'negativity', or even with negation? And what has 'intuition' got to do with recognising the destructive aspects of nature? And why do we have to agree that the latter aren't external (extrinsic), but are internal (intrinsic)? All are given here (by Lawler) are a few manufactured terms-of-art that he (following Hegel) says mean that objects are related to their significant "others" in a quirky sort of way. On examination, all this turns out to be based on a motley collection of transmogrified words with an ill-defined "not" attached to them, and nothing more. So, apart from an appeal to yet more sloppy logic, there is nothing to indicate that 'internal relations' are any more real than gryphons and harpies.

Perhaps because he recognises the bogus nature of this alleged 'necessity', Lawler now retreats into the subjunctive mood:

"However, such dialectical negation may nevertheless be real and the dialectical negativity characteristic of certain thought processes may also characterise extra-mental processes." [Ibid., p.36.]

But, the "dialectical negativity" of "certain thought processes" is a genuine as a thirteen dollar bill. So, unless the physical world is itself as logically-challenged as this passage clearly is, 'innovative' reasoning of this sort will find no correlate in nature. [Perhaps Lawler has access to the missing container-loads of data (that went 'walk-about' soon after Lenin made similar, but even more grandiose claims several generations ago) which 'support' such hyper-bold claims?]

Well, here it is; here is the missing 'evidence' -- and, surprise, surprise, it is just as watery-thin as the 'data' produced in support of the Mickey Mouse dialectical superscience we met in Essay Seven, scraped-together by the aforementioned, conceptually-benighted LCDs:

"Thus we intuit a negative side to the relation of living beings to he non-living environment. Gravitational, electromagnetic, geological, meteorological, solar, etc. forces constitute obstacles to the development of life as well as necessary conditions. The fact that certain optimal conditions of inorganic processes are required for life to evolve does not mean that the negative forces which otherwise would have prevented the appearance of life have simply ceased to exist. Rather, the optimal conditions permit them to be 'surmounted' or 'overcome,' but not eliminated. Moreover, this 'surmounting' of the negative life-destroying forces of the environment is intrinsic to the development of life. Life can only develop by 'repelling' the negative forces of its environment -- by 'negating its negation.'" [Ibid., p.36.]

We have already seen in this Essay that this way of depicting forces does not work, howsoever they are sliced, diced or re-heated. But, flowery language aside, the forces at work here are all manifestly external; there are no internal relations (except, of course, those conjured into existence by Hegelian Hocus Pocus, once more).

And, like it or not, life arose because of the operation of material/causal factors at work in nature, not logical principles inherent in Hegel's concepts.

But what, we might ask, has become of all that earlier talk about those eternally-plastic letter "A"s, which were said to have one and only one "other"?

"A's identity involves its necessary relation to what is not-A, and that this not-A is 'its own other' -- a definite other being and not any being whatsoever -- and that this relation to some definite other is necessary for the existence of A or is essential to the constitution of A (A's identity)…." [Ibid. p.32. Italic emphases in the original.]

But, here we are confronted by "forces" (plural) that oppose life. So life, it seems, is exempt from that earlier Hegelian caveat in that it appears to have hundreds, if not thousands of "others". Of course, this depends on how we count forces. [Is, for example, each molecule of, say, Carbon Monoxide, or Ozone an opposing force? Or do they work in gangs? (Perhaps they have a Union?)]

We must not expect answers to such questions; this is Mickey Mouse a priori superscience, after all.

But, Lawler has an answer:

"For the same reasons that we argued for the 'imprint' of the 'other' in an entity chosen for study, we should expect to find an imprint within the entity of this opposition that exists between entities. For example, the internal process of growth is opposed by excessive heat -- a physical or inorganic force. Growth must surmount this force which tends to inhibit or suppress growth. Extreme temperatures would prevent life altogether. At the same time, growth is dependent upon heat. Systems of temperature self-regulation develop whereby the negative effects of heat are, within limits, negated while the positive effects are absorbed." [Ibid. p.36.]

And yet, what has happened to those 'imprints' we met earlier? Where is heat itself (not its regulation) 'imprinted' in a cell? And, where are cells 'imprinted' in heat? Or does the 'imprinting' only work one way? And where is the 'cell regulation force' inside heat? And what happened to heat's own "other": cold?

Of course, heat is not a force; it is in such contexts merely a shorthand for the energy with which certain molecules have been accredited. Hence, it is even more difficult to see how the vibrational energy of, say, a Carbon-Carbon bond could be the "other" of anything at all.

However, cells have to regulate more than just heat; homeostasis is maintained inside cells by a variety of processes. In that case, we are forced to ask: Do cells have several (countless?) significant "others"? How might we tell?

Despite this, the processes Lawler describes are all causal; there are once again no Hegelian concepts here for Biophysicists to study.

Nevertheless, this might be to miss the point; indeed, perhaps it is:

"The expression 'tends to' has been used advisedly, since 'full' realisation of a dialectical negation would amount to the destruction of both external and internal conditions of existence, and hence total self-suppression. Dialectical negation is not abstract or formal negation of the 'other,' but is 'mediated' by the other itself." [Ibid., p.37.]

[There then follows a few hundred words of fluent Martian I have not the heart to inflict on the reader -- she has suffered enough.]

So, how does heat 'mediate' here? Unfortunately Lawler forgot to tell us.

No doubt, some day soon a Biophysics department somewhere will commission a PhD student to fill in the gaps...

To be sure, Hegel argued as follows:

"...[E]ach determination implies its opposite. Father is the other of son, and the son the other of father, and each only is as this other of the other; and at the same time, the one determination only is, in relation to the other; their being is a single subsistence. The father also has an existence of his own apart from the son-relationship; but then he is not father but simply man; just as above and below, right and left, are each also a reflection-into-self and are something apart from their relationship, but then only places in general." [Hegel (1999), p.441; §960.]

This paragraph brings out Hegel's warped and prejudicial thinking quite nicely. This is neatly summed up by Rosenthal:

"...[D]espite Hegel's obvious preference for patrilineal forms of descent -- 'father is the other of son,' he writes, 'and son the other of father, and each only is as this other of the other'... -- burdened with two biological sexes. Clearly, a father can still be a father, even if his 'other' happens to be a daughter, and a son cannot be a son without another 'other' besides his father." [Rosenthal (1998), p.218.]

And if a man were to reproduce with his daughter (surely a common occurrence, at least among royalty), then her son will also be her brother (and the child's mother will be his sister), as well as being son and grandson all at one go to the father.

Of course, the situation is even worse than this, for Hegel seemed to be fixated only on alleged binary relations. What about tripartite relations (like speed, distance and time, or mass, density and volume)? Or multivariate relations like the points on a compass?

Figure One: Hegel Loses His Bearings

And if this example is regarded as 'abstract' (those who think so should check out the next 'abstract compass' they use on a walk in the mountains, say, and it should seem pretty material), think of the same figure, but now representing people sat around a circular table. Each individual will be sat next to at least two contingent 'others' (who could change from time to time), and sat opposite many 'others'. And, worse still, none of these will 'pass over' into any of its 'others' (as Hegel imagined). If we now move into three dimensions, and consider objects placed around a globe, Hegel's 'logic' will begin to look even more ridiculous. [Of course, these can all be translated into Relational Algebra, so this is an apposite counter-example. This might be regarded as unfair, since the latter was invented after Hegel's day -- but that just shows once more what hopelessly limited the 'logic' Hegel used.]

And do not even begin to think about large finite relationships, such as "the millionth woman to give birth to a child", or "the ten thousandth man to visit the USA", who are only such because of the ordering relations we have among our numbers; each is only what he or she is because of the 999,999 or the 9999 individuals/'others' they are related to respectively as their predecessors.

And Hegel's other examples are no less bogus. Sure, in two dimensions, something can be to the right only if some 'other' is to the left, but what about a third object between the two? It would be between here because it has at least two 'others'. And if we move into three dimensions once more, something can be both to the right and left of an 'other', if it is on a globe.

As Wittgenstein noted, Metaphysics is a disease of the intellect brought on by an unbalanced diet of too few examples.

Hegel's Hermetic House Of Horrors

Before we reach the final part of this guided tour through Hegel's Hermetic House of Horrors, Lawler summarises the story so far:

"But perhaps it would be better to say that logical negation or the law of noncontradiction is an abstract representation of a certain limit of dialectical negations in reality. The ontological significance of the law of noncontradiction would be found in the nature of dialectical contradiction, with the impossibility of fully realising relative negations without the suppression of the entity that negates." [Ibid., p.37.]

Earlier we had this:

"…in the abstract, undialectical understanding of identity, the relation of A to not-A (beings that are not A as well as A's own nonbeing) seems to 'vanish.'" [Ibid., p.22. Italic emphasis in the original.]

And yet, while we are clear about the nature of contradictions (in FL at least), we are still in the dark as to what 'dialectical contradictions' are --, other than their merely being the products of Hegel's insecure grasp of the logic of his day, and (at least in his theoretical deliberations) of ordinary language -- balanced, of course, by its own "other": an all too secure grasp of mysticism.

Unfortunately for Lawler, and for Hegel, the LOC has no ontological implications (it is not about "non-being"): all it says (once more!), and in its simplest form, is that a proposition and its negation cannot both be true and cannot both be false. [This characterisation can even be found in Aristotle's famous "Square of Opposition".]  Nothing here about what must or must not exist, or about "non-being". Admittedly, some of the LOC's propositional instances might be 'about' existence, or what does or does not exist, but that is a separate matter.

However, even that is controversial. For example:

C1: Tony Blair exists and Tony Blair does not exist.

In many systems of logic, if Tony Blair does not exist, then "Tony Blair does not exist" is truth-valueless. On the other hand, "Tony Blair exists" would be a logical truth if he does exist! In such systems, C1 is not even a contradiction, since the first half lacks a truth value. In that case, even this 'contradiction' is not about "non-being", since it is not a contradiction. And even if it were a contradiction, as noted above, it would have no implications for the LOC in general. [More about this in Essay Twelve. Until then, see Williams (1981), and Miller (2002).]

To be sure, in certain forms of traditional logic, a non-empty universe must be assumed. But even there, the LOC is not about what exists, or about "non-being".

Now, it is true that there are many different characterisations of contradictions in MFL. For example, Grimm [in Grimm (2004), pp.51-55] lists 19 different definitions, and when he combines these with other factors, he tells us that there are at least 240 different ways of depicting contradictions [p.55]!

It is worth pointing out, however, that not only are most of the above definitions virtually indistinguishable, in many of them it is quite clear that their originators have confused contradictions with inconsistencies. Indeed, in his opening sentence, Grimm commits that very error himself!

Out of these, only a handful are described by Grimm as 'ontological':

"On an ontological outline, a contradiction would be neither a single statement nor a pair of statements, neither a proposition nor a pair of propositions, but a state of affairs. A contradictory state of affairs would be one in which something had a particular property and also an incompatible property, or in which something both had a particular property and lacked that property."

Even so, the only modern logicians Grimm references for this definition are Arthur Prior and the two Routleys (p.52) -- i.e., the late Richard and Val Routley, who later changed their names to Richard Sylvan and Val Plumwood. Their definition is as follows:

"A contradictory situation is one where both B and ¬B (it is not the case that B) hold for some B". [Quoted from Grimm (2004), p.52. I have used a different sign for negation here.]

This is not a happy definition, since it seems to treat the letter "B" as a substantival term/variable (i.e., capable of being quantified: in "some B"), and not as a proposition. Of course, if "B" is a predicate letter, then this definition relies on second order logic, and is thus controversial. [I won't try to defend or justify that assertion here.]

Putting this to one side, we would need to know what these two mean by "situation" before we could decide if this is indeed "ontological". For example, if "situation" means "formulae in the context of a theory", then it would not be "ontological". Unfortunately, the original article in which this appears was published in an obscure Colombian mathematics journal (Revista Colombiana de matemáticas) to which I do not have access, so I can't say much more. Anyway, even this unfortunate definition is not about "non-being".

However, the two Routleys were both radical activists, and Sylvan himself was also a Paraconsistent logician who collaborated with Graham Priest. In that case, it is not difficult to believe that Hegel's baleful influence lies behind their definition. This is indeed confirmed by Routley and Meyer (1976).

[On this, see Graham Priest and Dominic Hyde's brief biography of Sylvan in Hyde and Priest (2000), pp.1-3, (indeed, in Hyde and Priest (p.13), Sylvan pointedly recommends 'dialethic logic' (often spelt "dialetheic logic"), a family of non-standard logics which is heavily dependent on Hegel), and the many essays in Priest, Routley and Norman (1989). Background material can be found in Franklin (2003).]

Prior's 'ontological' definition goes as follows:

"The law of contradiction asserts that a statement and its direct denial cannot be true together ('not both p and not-p') or, as applied to terms, that nothing can both be and not be the same thing at the same time ('Nothing is at once A and not-A')" [Prior (1967). I have relied on the quotation found in Grimm, here --, p.50.]

This is an appallingly bad definition from a top logician (on a par with the lamentably poor 'dialectical definitions' we met in Essay Four Part One)! I will not try to defend it. Even so, there is nothing here about what must exist, or about "non-being", and Prior's 'definition' does not seem to conform to Grimm typology, anyway.

Now, I suspect Prior would have paraphrased this definition (maybe in a longer article) in terms of modern quantification, thus removing the apparent existential implications it seems to have. Indeed, this guess is partially confirmed by the other definition Grimm quotes from Prior (1967) (on p.51), which is far superior, and much closer to the one adopted here.

Grimm also quotes Aristotle's alleged 'ontological' definition (pp.49-50):

"For a principle which every one must have who understands anything that is, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect; we must presuppose, to guard against dialectical objections, any further qualifications which might be added. This, then, is the most certain of all principles, since it answers to the definition given above. For it is impossible for any one to believe the same thing to be and not to be, as some think Heraclitus says. For what a man says, he does not necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same subject (the usual qualifications must be presupposed in this premiss too), and if an opinion which contradicts another is contrary to it, obviously it is impossible for the same man at the same time to believe the same thing to be and not to be; for if a man were mistaken on this point he would have contrary opinions at the same time. It is for this reason that all who are carrying out a demonstration reduce it to this as an ultimate belief; for this is naturally the starting-point even for all the other axioms." [Aristotle (1984b), p.1588. In the internet version, this can be found in Book IV, at the end of section 3. Bold emphases added.]

This is not much better than Prior's attempt, and will not be defended here, either. The only thing that can be said in Aristotle's defence is that he was writing 2400 years ago, and attempting to create logic almost from scratch. The same excuses cannot be extended to Hegel and his many dialectical dupes. Even so, Aristotle's 'definition' does not mention "non-being", either. To be sure, Aristotle says: "For it is impossible for any one to believe the same thing to be and not to be", but this is far too vague to co-opt to Hegel's defence -- since Aristotle might have meant: "For it is impossible for any one to believe the same thing to be and not to be true/a man/a number...". This interpretation is confirmed by the next sentence in the above passage:

"For what a man says, he does not necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same subject...." [Ibid]

In that case, even if it were clear what 'dialectical contradictions' are, FL would need neither this notion nor dialectics to help explicate, or apply, the LOC.

After all, does Astronomy need Astrology?

At last we are nearing the dialectical denouement:

"For our purposes, this illustration is sufficient to show that while the term 'contradiction' as used here does not have the seemingly 'full' sense of logical contradiction, nevertheless it is not reducible to some 'clash' of externally related 'positives.' Nor is it equivalent to some 'tranquil' association of mutually exclusive logical contraries, such as odd and even numbers, male and female persons, or north and south poles of a magnet -- unless these are in fact understood dialectically…. It is necessary to understand the mutual relation and opposition that constitutes the inner dynamic of the terms in opposition. This opposition may contain the possibility of developing into 'full' contradiction, i.e., into real destruction. However, the real potentiality for the development of dialectical contradiction is not to be seen in this possibility of destruction, but in a potentiality for transformation where only the 'immediate forms' of opposing phenomena are suppressed -- while other, often more developed forms are realised through essential 'internal' interconnections."  [Ibid., pp.37-38.]

All this a priori jargon is standard fare in HCD texts, but that doesn't imply that it means anything. Indeed, it is a sure sign of the opposite.

But why is "full contradiction" equated with "real destruction"? Now, the LOC was (and still is) connected with all manner of things in the bad old logic (Lawler himself seems to think it has something to do with "cancelling out" -- although he does not use those words, as far as I can tell, but he does speak of negatives in mathematics cancelling; see below --, or as "self-nullifying", as he puts it on page 16). As we will see in Essay Twelve (and here), card-carrying HCDs do likewise.

However, neither the contradictions of FL nor those of ordinary language have anything to do with "cancelling out", or "nullifying". If a proposition "p" is true, its contradictory "not p" is false, not "cancelled out".

Look, it is still there on the page/screen, unharmed!

This odd idea is connected with the equally bizarre belief that 'negative' propositions are all false (or 'defective' in some other way). But, 'negative' propositions can be, and often are, true. For example, "Blair is not a socialist" is true, as is "Anyone who reads the Daily Mail, and doesn't reject much of what it says, is no Marxist."

And, not even the content of "not p" is "cancelled", for whatever "not p" says is still up for consideration, it is just false if "p" is true, true if "p" is false. Nor is it "nullified", for (once more) "not p" could one day become true and "p" itself false, or vice versa. For example, "Blair has not resigned" is the contradictory of "Blair has resigned"; the first is false, but hopefully it will become true one day -- it could not do that if it had been "cancelled", or "nullified". [Needless to say, this was written before Blair finally went!]

Moreover, every proposition is paired/pairable with its negation; does that mean that all propositions have been "cancelled"?

Anyway, what would count as the "nullification" of "Blair has not resigned"? One could try to nullify Blair's actual resignation (or its effects), but what could one do to nullify "Blair has not resigned"? Prevent this message getting out? Silence whoever might want to utter it? [If it is false, what it says has not happened, so nothing can nullify it, surely?] Even so, that proposition is still there, on your screen, annoyingly mocking any attempt to "nullify" it.

Those who talk this way have clearly confused FL-contradictions with contradictory orders or instructions, like "Open the door!" and "Close the door!", which, if acted upon, undo each other, etc. But the propositions of FL and ordinary language are neither instructions nor orders.

Lawler does, however, try to illustrate this sort of negation by appealing to negatives in mathematics (a common ploy used by, among others, Engels):

"From the thoughtless viewpoint of abstract understanding, A is conceived of as simply given, and the implicit relation to not-A does not get the trouble of a serious consideration. Just as in mathematics two negatives make a positive, in which they are thought of as cancelling out, here abstract understanding makes the journey from A to not-A and back again without noticing that any movement has taken place." [Ibid., p.22. Italic emphases in the original.]

For sure, Lawler sort of rejects this view (or, rather, he aims to transcend this formalist approach), but he does not repudiate the idea that it is correct to regard formal negation as a sort of "cancelling-out". He then uses this 'analysis -- beloved of the "abstract understanding" -- to develop a dialectical account of negation; so for Lawler, the latter is not just "cancelling-out", it has moved beyond it.

However, if formal negation is not and never has been a "cancelling-out", then the dialectical moves that allegedly follow from (or seek to transcend) this ploy cannot use it as a launch pad for this pointless 'logical' journey to nowhere.

Well, not even in mathematics -- if we adopt for the moment this primitive way of talking -- is it always true that two negatives give a positive. For example: -1 + -2 = -3. [No "cancelling-out" here!]

Exactly why Lawler considers only multiplication (or perhaps division) as a valid option to illustrate this obscure point is somewhat unclear, but even there the results are not always as he imagines: -i x -i = i = (-1)1/2 which is still negative!

Of course, it could be objected that (-1)1/2 is not negative (even though it contains a negative sign!), but what about -(i1/2)/-i = i-1/2; is that negative? Maybe so, maybe not. Well then what about -(a-b) x -1 = (b-a), where b>a? Or -a x -a = a, where a<0? Or, (x2 - 3x -1) x -1 = 1 + 3x - x2. Are any of these negative?

In that case, it seems clear that this quasi-Hegelian 'rule' is far too crude to use even in lower school mathematics. But, when we come to more complex areas (such as matrices and their inverses, groups or infinite series), the whole idea becomes ridiculous.

Anyway, negatives in mathematics do not "cancel-out"; what happens is that certain functions take negative numbers as arguments and yield positives as images (but, the domain set of negatives still exists -- it has not been "cancelled-out", or even "nullified").

In that case, there is no good reason to connect the "full" contradictions of FL with "destruction".

Well, not for us materialists there isn't.

Lawler continues:

"Real opposition must be understood as dialectical contradiction." [Ibid., p.38. Emphasis added.]

And that is it! A plain "must" after this long detour through this pre-Aristotelian wasteland.

The rest of the article is merely window-dressing. We are left with this counterfeit "must" here, backed neither by logic nor by fact. So why we "must" see these obscure creations of Hegel's Hermetic Hallucinations in this way is entirely mysterious.

To be sure, there is no problem with the phrase "real opposition". But, the phrase "dialectical contradiction" is still lost in the same dense fog Hegel left it in 200 years ago. Exactly why the word "contradiction" has to be super-glued to this other term is a mystery -- except that Lawler might have wanted some of the clarity of the former to rub off onto the latter.

[However, I offer a materialist explanation for this odd phenomenon in Essay Twelve (summary here), and a much more political one in Essay Nine Part Two.]

Lawler now quotes the following prime example of a priori superscience from Hegel:

"Neither in heaven nor in earth, neither in the world of mind nor nature, is there anywhere an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things with then lie in the want of correspondence between their immediate being and what they essentially are. Thus, in inorganic nature, the acid is implicitly at the same time the base: in other words its only being consists in its relation to its other. Hence the acid persists quietly in the contrast: it is always in effort to realize what it potentially is. Contradiction is the very moving principle of the world." [Ibid., p.38; quoting Hegel (1975), p.174. I have used a different edition from Lawler.]

If we consider this famous quotation from Hegel: either he wrote it or he did not. If either (but not both) of these is the case, then Hegel was wrong to say that there was nowhere just such an "either-or" --, for here there would be one.

Worse: in heaven, hell or high water, there is an "either-or" or there isn't. So, if Hegel was right (and there wasn't), he was wrong, since there would be (i.e., here!). And if he was wrong, then he was wrong anyway. Either way, he was wrong.

The rest of what he says should now be consigned to one of Hume's bonfires. I'll get the can of petrol...

How did Lawler miss this obvious inference? Has the bad old logic "nullified" his brain? Has Hermetic Hype "cancelled" his ability to use/understand a simple "or"?

Acid Corrodes Hegel's 'Logic'

The acid example is none-too-clever either. Lawler comments on it as follows:

"…the acid is only an acid through its implicit relation to what negates it…." [Ibid., p.38.]

But acids burn the skin not because a base exists (which negates nothing, since it is not a sentential/phrasal operator) -- which would counteract it if they came into contact --, but because of its corrosive properties. And, if there were no bases anywhere in existence, acids would still do what acids do.

Of course, modern definitions of acids do not mention bases. The Brønsted-Lowry definition says that acids are proton donators, while the Lewisian definition tells us that an acid is an electron-pair acceptor. To be sure, bases are still defined as the 'opposite' of each of these, but acids and alkali's are no longer defined in terms of each other, but in terms of a third item (or a third and a fourth, if we lump the lot together).

So, it seems that Chemistry has taken a decidedly reactionary turn since Hegel attempted to pontificate on the subject.

But, this is a specially-chosen example. It won't work in cases that DM-fans conveniently ignore. Many of these were listed in Essay Seven, some have been above. Here are several new examples: voltage, current and resistance are all interlinked, but no single one has its 'being' defined in terms of any one "other" (but two "others"); and this is true also of pressure, volume and temperature in an ideal gas, just as it is true of the items found in the traditional square of opposition (where implications, contraries, subcontraries and contradictories are interdefined among four "others"). Lest these be rejected as 'abstract' (a fine accusation to have levelled at one by a Hegel-Honcho!) consider this: in the Periodic Table, none of the Halides (Chlorine, Bromine, Fluorine, Iodine, etc.,) is defined in terms of a significant "other", and neither are salts, proteins, enzymes, catalysts, alcohols, Aldehydes… 

And what are we to say of "buffer solutions", which can be both acid and alkaline? 

Furthermore, this entire topic is mixed up with Hegel's mystical fugue on "finitude" and "infinity"; Lawler quotes him thus:

"Thus essentially relative to another, [something -- Lawler's addition, RL] is virtually against it: and since what is passed into is quite the same as what passes over, since both have one and the same attribute, viz., to be another, it follows that something in its passage into other only joins with itself. To be thus self-related in the passage, in the other, is the genuine Infinity." [Ibid., p.39, quoting Hegel (1975), p.139; Lawler's italics. Here, I have referenced a different edition from that used by Lawler.]

Well, that certainly clears things up!

But, how is self-relation "the genuine Infinity"? Lawler just accepts this mystical missive, and does not explain it -- except he expands on it with yet more jargon:

"…in speaking of the chemical relation of an acid and an alkali, where he notes that 'the negation of the negation is not a neutralization: the infinite is the affirmative, and it is only the finite that is absorbed' (quoting Hegel here). The 'absorption' of finite objects consists in the transition implicit in the 'want of correspondence between their immediate being and what they essentially are,' which leads to the realization of that essential being of to the 'genuine Infinite' which Hegel calls being 'self-related in the passage' into the other. In other words, since the other is essential to the original being, there is a form of relating to that other which is not a relation to something 'alien' but a 'self-relation' -- a relation in which the being, at first seemingly self-sufficient, finds its 'self' in and through the other (its other, some definite other)." [Ibid., p.39.]

I think I  have made enough derogatory remarks about verbal bindweed like this, but what is a materialist like Lawler (I am assuming, of course, that he is one!) doing assisting the spread of this Idealist pest, as if it helps resolve a single thing?

We seem, therefore, to be going backwards in  our "passage" away from the clarity found in FL (and, potentially, in ordinary language), but toward infinite nonsense.

However, we now get a flash of sense (or do we?); for Engels relates this 'infinity' to "law":

"In fact all real exhaustive knowledge consists solely in raising the individual thing in thought from individuality into particularity and from this into universality, in seeking and establishing the infinite in the finite, the eternal in the transitory. The form of universality is the form of completeness, hence of the infinite. We know that chlorine and hydrogen, within certain limits of temperature and pressure and under the influence of light, combine with an explosion to form hydrochloric acid gas, and as soon as we know this, we know also that this takes place everywhere and at all times where the above conditions are present....The form of universality in nature is law." [Engels (1954), pp.234; quoted in Lawler, p.39-40. Italic emphases in the original.]

Lawler comments on this as follows:

"While rejecting Hegel's ultimately idealist interpretation of 'self-relation' or 'reflection' in the other as 'ideality,' Engels' treatment of 'infinite' as law-governed process, 'absorbing' finite moments into itself, is faithful to Hegel." [Lawler (1982), p.40.]

At the risk of repeating myself, how is it possible to translate the word "infinite" as "law-governed process"? Are the rest of us using the wrong Gobbledygook to English dictionary?

Now Engels tries to equate these two, but, for those still in command of their reason, neither an "always" nor an "at all times" is an "infinite".

[In a later Essay, we will see that this view of scientific law is a carry-over from ancient animistic ideas about nature, and so it is no surprise to find this doctrine re-surface here, in such Hermetically hobbled company. On this see here and here; the first is Swartz (2006), the second Swartz (2003).]

As noted in Essay Three Part One, from simple sentences like "John is a man" (and now in Lawler's case "Socrates is mortal") we could -- if we were so minded, and with just enough Hegel-hubris --, 'derive' the thesis that the world is a law-governed "Totality", and that knowledge is an infinite asymptotic journey into oblivion. As Lawler now explains:

"It is clear from these passages that 'ideality' is not derived by Hegel from the simple suppression of distinct phenomena but from the interaction and dialectically negative interpenetrations which result in their law-governed transformations. The explosive combination of hydrogen and chlorine is more than the 'clash' of two externally related beings. It is the negation of their 'immediate' form as self-subsistent 'free' entities, and the realization of their inner or essential connectedness with each other (under the necessary conditions). The result is not their mutual annihilation, but their transformation." [Ibid., p.40.]

But, this poetic description of a chemical reaction is far from being even metaphorically 'true'. Since when has Chlorine been a 'free' being? At the very least, as a gas, under normal temperature and pressure, it exists as a diatomic molecule, and nowhere in nature does it subsist as a 'pure' element -- so far as we know.

And, we note once more that the semi-religious typology of the "other" has now been dropped, since Chlorine reacts with practically everything. In fact, it has more "others" than Blair has excuses.

By way of contrast, if we choose a far less 'dialectically-accommodating' element -- say one of the 'Noble gases' (Helium, Neon, Krypton, etc.) which seem in comparison to be rather stand-offish, loners, as it were, with no "others" to speak of -- the above comments become all the more apposite. This is because, except under the most extreme conditions, these gases react with nothing at all, and have to be dragged, kicking and screaming down the "passage". So, this 'logical' object, this "other", has to be forced into adopting its designated Hermetic role, in this case.

But even if this dialectical fairytale about the formation of HCL were correct, how this is an internally-driven process is somewhat unclear. Surely, Chlorine is not to be regarded as not-Hydrogen? If it were, then everything in the universe that is not Hydrogen (or not-Hydrogen) would be Chlorine! Or, conversely, everything that is not-Chlorine would be Hydrogen. [In which case, dear reader, you are Hydrogen!]

Of course, that is why the significant "other" myth was spun earlier (to block this very objection), but as we noted above, Chlorine reacts with so many things we would have to use a veritable via negativa to 'identify' it (e.g., Chlorine is not-this, not- that, not-...); indeed, in the limit, it would be not-anything. In this Hermetic Hell-hole, Chlorine should disappear like the Cheshire Cat's smile!

The same is true (only more so) of Fluorine --, and even more so of Hydrofluoric Acid.

And, as we saw in Essay Eight Part One, these 'internal relations' turn out to be 'external relations', only mis-described. It is thus no wonder that we need Super-duper logic -- courtesy of Hegel -- to assist us here; ordinary language, FL, and good old-fashioned matter are most uncooperative.

And now we encounter this:

"However, if their identity is narrowly or abstractly defined by the superficial features of their original phenomenal form, the result appears to be annihilation. And this annihilation seems to 'realize' a formal contradiction: for example, 'hydrogen exists independently of chlorine' and 'hydrogen does not exist independently of chlorine.' Following the law of noncontradiction, both of these statements can only be true if we distinguish the 'different respects' in which independence of chlorine can be asserted and then denied of hydrogen. Thus, in the original free state hydrogen is independent of chlorine, while in the chemical reaction or in the hydrochloric acid gas it is not. The logical contradiction in the original crude statements seems to be resolved by qualification of the different respects or conditions in which the seemingly contradictory assertions hold." [Ibid., p.40.]

Well, Lawler's 'contradiction' isn't one if the word "exist" is a quantifier, and the first (i.e., "Hydrogen exists independently of chlorine") is of the form:

L11: E(x)E(y)[(Hx & Cy) & Fxy].

Or perhaps:

L12: (x)(y)[(Hx & Cy) ® Fxy].

L13: (x)E(y)[(Hx & Cy) ® Fxy].

[Where "E" is the existential quantifier, "" is the universal quantifier; "®" is the implication arrow; "H(ξ)" and "C(ξ)" are one-place, first level predicate expressions, standing for "ξ is Hydrogen" and "ξ is Chlorine", respectively; and "F(ξζ)" is a first level, two-place predicate (in this case, a binary relation), standing for "ξ is independent of ζ"; "x" and "y" are bound variables, ranging over elements, in these examples.]

L11 roughly reads: "There are two elements, Hydrogen and Chlorine, which are independent of each other". In that event, its contradictory would be: "No two elements, which are Hydrogen and Chlorine, are independent of each other". L12 translates out approximately as: "Take any two elements, if they are Hydrogen and Chlorine, then they are independent of each other". If so, the contradictory would be something like: "For any element there is some other element, which, if the first is Hydrogen and the second is Chlorine, then there is at least one example where the latter is not independent of the former." L13 is roughly "For any element, if the first is Hydrogen, and there is a second which is Chlorine, then they are independent of each other". The contradictory here would be something like: "For any element there is no other element, which, if the first is Hydrogen and the second is Chlorine, the latter is independent of the former."

If, on the other, hand Lawler's example were of the following form:

L14: E(x)E(y)[(Hx & Cy) & Fxy].

where "F(ξζ)" is a first-level two-place predicate, standing for "ξ exists independently of ζ", not much would be different.

Of course, this method of analysing propositions could be rejected; there is nothing that forces us to adopt this way of looking at language, or logic, or both (except perhaps the fact that it prevents this sort of a priori Idealism and superscience from establishing even a slender toe-hold in our brains, as was pointed out in Essay Three Part One, here and here). Anyway, if this 'modern method' is rejected, then Lawler's example would be a contradiction only if someone asserted both conjuncts, and held both to be true at once, and who denied both could be false at once. But who would want to do that?

[In all that talk about "respects", I suspect Lawler realised this, but seemed to want to ignore it.]

In that case, this example is a dud too.

Two Senses Of "Independent" Confused

Well, perhaps not -- for Lawler continues:

"We should first of all note that the above reformulation of the apparent contradiction implicitly depends on the general proposition, formulated according to the law of noncontradiction, that something, at any one time or in one respect, is either independent or not independent (dependent). But for something which is independent to become dependent, it must have within it the potential to become dependent. It was therefore relatively, not absolutely independent. The potentiality for the chemical reaction was present in the hydrogen in its free state. To follow Hegel's form of expression, in its free state hydrogen was all the while 'repelling' or negating possible reactions with other elements with which it was nevertheless related. Its 'independence' was maintained in its state of interdependence under certain conditions where this was possible." [Ibid., pp.40-41.]

There are several highly dubious moves in the above argument. The original claim that "Hydrogen is independent of Chlorine" has now morphed into "Hydrogen is independent, period" -- that is, it is independent of everything. Moreover, the meaning of the word "independent" has altered, too. From "independent" implying "not linked to" (or "isolated from"), it has become "does not depend on", and this is what allows the potential for the one to depend on the other to be smuggled in while no one is looking.

But, it is surely possible for Hydrogen to exist totally isolated from Chlorine (this is in the first sense of "independent"), but still for it to be capable of reacting with it if and when this state is altered.

Indeed, scientists invent new compounds all the time (about which they might know very little), that are in fact isolated from other compounds (some of which they will never encounter), but with which they would react if given the chance (and if we but knew it).

Let us assume, therefore, that one day a group of scientists create a new compound called "Hegelase" (a new form of poison -- apparently it blocks the 'passages', and cripples its victim's powers of reason, before brain death finally sets in), which they keep isolated from everything as best they can -- for obvious reasons. However, let us imagine that some of it escapes and kills a dialectician (who, for the sake of mischief, we will call "Lawless").

Now, did Hegelase have the potential to kill Lawless before it reached him? Was this poor schmuck Hegelase's significant "other"? Well, in the sense that this poison will kill him if it reaches him, it most certainly has this potential. That is why it had to be isolated (but not just from Lawless). On the other hand, in the 'logical' sense that Lawler (not Lawless) needs, the answer must be, no it does not. If it did, then we must argue that Hegelase has over 6 billion "others" out there, who it has the potential to kill 'programmed' into it. And if we now assume that Hegelase is able to kill all living things, then that 6 billion "others" would amount to a mere blip in comparison.

Does this one chemical have so much 'programmed' into it? So many significant "others"?

To those who look upon "potentialities" as "actualities" in disguise --, or, at least, as very well hidden "actualities" --, the above example presents serious problems. Every time a new life comes into the world, Hegelase will gain a new "potentiality", for free, without moving a muscle. Such unearned income should be taxed, one feels.

Let us now say that a new strain of bacterium comes into existence (which, for the sake of further mischief, we will christen "Grantococcus Woodsonii B#2", or "GWB2", for short), by whatever means such cells have of reproducing/evolving. Let us further suppose that Hegelase can (i.e., has the potential to) kill GWB2. When GWB2 comes into existence, Hegelase will thus gain a new potential to kill GWB2 (say, "PGWB2", for short). But, to do so it must have had the potential to develop this potential (or it would not have happened, given this traditional way of looking at things). So, before PGWB2 came into existence, Hegelase must have had a potential to develop PGWB2, say, "PPGWB2". But, once more, in order to develop that it must have had a further potential to develop PPGWB2, say "PPPGWB2". Well, it does not take very much Diabolical Logic to see where this is going if we insist on regarding potentialities as the disguised properties of bodies (governed by ill-defined 'negations'), and not just our way of making sense of what they do, or can do.

We have to say this, or imagine that Hegelase has an (actual?) potential to kill things that do not exist. But what kind of 'potential' is that? How is it able to kill things that do not exist?

But, even if this is rejected for some reason (perhaps, by the use of a complex counterfactual), what is all this "repelling" that Hegel thinks things engage in?

"To follow Hegel's form of expression, in its free state hydrogen was all the while 'repelling' or negating possible reactions with other elements with which it was nevertheless related. Its 'independence' was maintained in its state of interdependence under certain conditions where this was possible." [Ibid.]

It is worth noting that in the highlighted sentence Lawler implicitly admits that Hydrogen, for example, has no significant 'other'. With that Hegel's account of change "repels" even his own logic, and collapses under the weight of its own 'internal contradictions'. A rather fitting fate for such a useless 'theory'

But, despite this, is Hydrogen that intelligent and focussed? Can it "repel" each and every "possible" reaction -- even those on the far side of the universe? [This powerful atom is clearly master of all it cannot survey.] But, apart from sounding profound, what sense can be made of any of this?

Perhaps this:

"Within this analysis, the concept of independence and nonindependence as mutually exclusive states applies primarily or most adequately to the surface distinction between the phenomenal states of hydrogen (classification of phenomena) but does not apply, at least with the same ease, to the law of hydrogen's development and its internal structure. In this deeper analysis it is necessary to see 'independence' as a form of interdependence ('nonindependence'). The conception of the categories 'independence' and 'dependence' as mutually exclusive and so not applicable to the same thing -- in the same respect -- is more difficult to defend." [Ibid., p.41.]

But, this only works because of the ambiguous way that the words "independence" and "dependence" have been used (as noted above: one minute the first is understood to mean "isolated", or "free and unconnected", the next it means "not dependent on").

Lawler then goes on to discuss more technical notions connected with "form" and "essence", which add little to the above -- except, perhaps, this:

"Although 'essence' and 'form' are mutually exclusive categories there is no possibility of adequately separating the phenomenal 'respect' from the essential 'respect' -- so as to permit one to say, unproblematically, that hydrogen in its phenomenal form is independent while in its essential properties it is not independent. Such a distinction of respects superficially applies to the two phenomenal states of hydrogen ('superficially' in the sense that it is necessary to go on from the distinction to understanding the law relating to the phases of hydrogen's transformations). But in understanding the essential nature of hydrogen there can be no comparable distinguishing of 'respects' -- except as an abstract or formal approximation of the dialectical unity of opposites." [Ibid., pp.41-42. Italic emphasis in the original.]

What exactly the "unity of opposites" amounts to here is left tantalisingly vague, and so the whole passage is as clear as dialectical mud.

A Few Threads Left

Mercifully, we are near the end; Lawler now tries to draw several disconnected threads together:

"Thus the process of chemical reaction demonstrates the inner connectedness as well as relative opposition of hydrogen and chlorine which must be taken into account and explained in a scientific theory of the law of chemical reactions and in an understanding of the particular properties of these elements. The 'finitude' that is suppressed is the particular state of the element as 'free.' as existing (relatively) independently of other elements while being essentially related to them." [Ibid., p.42.]

However, all that Lawler has done here is connect these elements (Hydrogen and Chlorine) with talk about potentialities, those that cannot be regarded as physically real, but perhaps can be thought of as a poetical sort of way of depicting their capacity to react. And all of this is based on the earlier word-juggling of a few letter "A"s, themselves of a somewhat 'mercurial' disposition (or, indeed, "potential").

As far as the laws governing nature are concerned, these cannot be seen as decrees written into matter, which all things have to obey (as it seems this line of thought implies). For sure, Hegel could accept such an animistic idea, but no materialist should -- unless, that is, they subscribe to the non-materialist doctrine that the universe is governed by a cosmic will of some sort. [Again, on this see here and here.] Lawler almost admits as much in his final paragraph:

"It seems that the main reason why Hegel terms the essential relatedness of one element to another and their lawful connectedness as their 'ideality' is that Hegel regards matter as inherently incapable of such relations and transformations. Matter is conceived of as the embodiment of the principles of abstract understanding. In other words, Hegel accepts the mechanistic or atomistic theory of matter, and so any discovery nonmechanistic, nonatomistic properties of reality is interpreted as evidence of the operation of a nonmaterial force -- the Idea." [Ibid., p.42.]

And there we have it in a nutshell; Hegel's Idealism prevented him from seeing the material world as it is, sufficient to itself, and capable of doing all the things Idealists deny it is capable of doing unaided (since that would not be 'rational'). This alone explains all the desperate word-magic and symbol-juggling, aimed at re-enchanting nature in order to make it in effect the development of Idea, since plain, common-or-garden, boring old matter is not good enough on its own.

But, how does Lawler square all this with Marxist materialism?

"But the fact that Hegel sees in natural laws a manifestation of this Idea makes possible materialistic interpretations which reverse this scheme -- interpreting the 'idea' as the subjective image of the material law. This reinterpretation requires a rejection of the mechanistic form of materialism and the development of a more advanced theory of matter." [Ibid., p.42.]

And yet, how can this work if the belief that there are laws in nature is itself based on an Ideal view of reality? We have seen how the quirky logic Hegel used helped conjure these mythical beasts (these "laws") into existence; merely reversing our perspective in no way changes these bogus moves into a valid alternative. If it did, we should have to start believing that the Brothers Grimm were first-rate scientists. Without an Ideal backdrop, these allegedly materialist 'laws' would have no ontological basis, except perhaps, in a more deflationary sense, as part of the way we make sense of nature -- a materialist sort of Positivism.

[This (i.e., Hegel's) anthropomorphic way at looking at nature is traced back to its roots (as part of 'Divine'/ruling-class law, etc.) in Essay Twelve (summary here).]

What A Dialectical Dog's Dinner!

That is it! This is the best defence I have read in over 25 years of researching the logical ruins in this Dialectical Disaster Area!

Read it again dear reader and scratch your rather 'inadequate' material head.

WTF is a 'dialectical contradiction'?

Are you any the wiser? If you are, please help me out, for I am, if anything, even more in the dark!

Now, in many places throughout this work I have advanced the claim that the slur that dialectical mystics often throw in the faces of genuine materialists (i.e., that they "do not understand dialectics") also applies in reverse to those very mystics, since they clearly do not understand it, and have been quite incapable of explaining a single dialectical concept in over 150 years of not trying very hard.

Perhaps readers can now see why I have been saying this.

Finally: reading through papers and books (like Lawler's essay), written by Marxists who still think we can learn anything from Hegel, one is struck by the similarity between their approach to truth and that adopted by, say, Roman Catholic Philosophers who nearly a thousand years ago began the process of trying to make Aristotle consistent with Christianity, and then later with science -- and who are still endeavouring to do it --, or who even now attempt to defend Papal Infallibility in the face of the countless Pontifical screw-ups we have witnessed over the centuries.

The 'logical' contortions these comrades have to inflict on language is somewhat similar to the linguistic gyrations perfected by the above theologians and casuists. Indeed, the somersaults these comrades perform (in this area) merit some sort of International Gymnastics award. Dialectically double-jointed comrades should, in my view, receive Gold every time.

Lawler is no exception. In order to make Hegel's jargon work, he has to twist language way beyond even the knotted pretzel stage, just like the aforementioned RC contortionists.

Now, I do not expect dialecticians to accept the above criticisms since they are still wedded to the ancient idea that human discourse, at some level, contains within the key to the inner secrets of 'Being'. Given that view of language, all that these philosophical alchemists have to do is find the right formula -- the right key --, and linguistic dirt can be turned into theoretical Gold, the whole transformation achievable without having to leave one's non-dialectical armchair.

Such theorists are indeed the philosophical equivalent of those whom Marx called revolutionary alchemists; only here the right verbal formula is capable of unlocking the mysteries of 'Being', allowing these dialectical magi to invent an the ideal world to suite themselves. Up to now they have plainly not transformed the class structure of this world, but they have made up for that by withdrawing into an Ideal world, where they can juggle with 'reality' to their class-compromised heart's content, and ignore all criticism and political failure.

And this is partly why they cling to this mystical theory for dear life -- and resist all attempts to prize their fingers loose. Indeed, they do so for reasons Feuerbach exposed 160 years ago. This theory allows them to see the world as the opposite of what it really is, which fact explains the powerful hold it has on these dialectical dupes -- consolation from convolution.

There is no arguing with faith like this. Changing the material conditions that gave rise to such alienated thought-forms is the only thing that will finally bring Dialectical Day-Dreaming to an end. RL stands no chance!

Dialectical mystics are just going to have to rely on the material force of the working class to save them from themselves and from this virus of the mind.

[More on this in Essay Nine Part Two. My comments on Lawler's other significant contributions to this topic were posted here, and here.]

68. But, are opposites always contradictory? At this moment I am sat in front of my computer looking at the house opposite. Is my house therefore in some sort of 'struggle' with that house? Or, indeed, am I in struggle with it?

Unfair? Perhaps so. Dialecticians will be the first to point out that the sorts of opposites they regard as contradictory are those that are involved in a dialectical union of some sort (as UOs). Since my house and that opposite are not so linked (and neither am I), they are not therefore in 'struggle'.

Well, how do we know? Clearly we do not. Nature often surprises us. [And isn't everything interconnected in DM, anyway?]

See the previous Note on this.

However, consider the opposite sides of a polygon (one that have been drawn on paper, so this is not an abstract example). An equilateral triangle has two opposite sides; are they both battling against the third side, and/or with one another? Here, these sides are physically and logically linked; but this won't suffice since they are not dialectically-logically linked.

It seems then that only certain logical connections in reality are allowed to be, or the create, DM-UOs, which means that objects and processes that are merely empirically- or formally-connected, cannot be so categorised.

Perhaps too: since no house has yet been observed to be engaged in a life-and-death struggle with another across the way, they can be ruled-out as UOs? Who can say? But who has ever actually witnessed a posse of use values slugging it out with a gang of exchange values? So, such empirical niceties cannot be crucially important here. We are thus still in the dark.

In that case, it seems that only certain sorts of opposites are implicated, here. [But Hegelian opposites look pretty banal, anyway, and do not work, even on their own terms.]

Oddly enough, and by sheer coincidence, I am sure, these 'opposites' turn out to be (by-and-large) the kind of 'opposites' dreamt-up by Idealist Philosophers thousands of years ago. Now, since this doctrine is central to Hermeticism, that would seem to malign it sufficiently enough in the eyes of anyone who is at all concerned to remain consistent with atheistical materialism. [That is won't do so in the eyes of dialectical mystics confirms much of what I allege about them in Essay Nine Part Two.]

To test this claim, readers should now try to spot the difference (that is, beyond a few superficial details) between these:

"CHAPTER X POLARITY Everything is dual; everything has poles; everything has its pair of opposites; like and unlike are the same; opposites are identical in nature, but different in degree; extremes meet; all truths are but half-truths; all paradoxes may be reconciled." -- The Kybalion.

"The great Fourth Hermetic Principle-the Principle of Polarity-embodies the truth that all manifested things have 'two sides'; 'two aspects'; 'two poles'; a 'pair of opposites,' with manifold degrees between the two extremes. The old paradoxes, which have ever perplexed the mind of men, are explained by an understanding of this Principle. Man has always recognized something akin to this Principle, and has endeavoured to express it by such sayings, maxims and aphorisms as the following: 'Everything is and isn't, at the same time'; 'all truths are but half-truths'; 'every truth is half-false'; 'there are two sides to everything'; 'there is a reverse side to every shield,' etc., etc. The Hermetic Teachings are to the effect that the difference between things seemingly diametrically opposed to each is merely a matter of degree. It teaches that 'the pairs of opposites may be reconciled,' and that 'thesis and antithesis are identical in nature, but different in degree''; and that the ''universal reconciliation of opposites' is effected by a recognition of this Principle of Polarity. The teachers claim that illustrations of this Principle may be had on every hand, and from an examination into the real nature of anything....

"Light and Darkness are poles of the same thing, with many degrees between them. The musical scale is the same-starting with 'C' you moved upward until you reach another 'C,' and so on, the differences between the two ends of the board being the same, with many degrees between the two extremes. The scale of color is the same-higher and lower vibrations being the only difference between high violet and low red. Large and Small are relative. So are Noise and Quiet; Hard and Soft follow the rule. Likewise Sharp and Dull. Positive and Negative are two poles of the same thing, with countless degrees between them....

"CHAPTER IX VIBRATION 'Nothing rests; everything moves; everything vibrates.' -- The Kybalion.

"The great Third Hermetic Principle-the Principle of Vibration-embodies the truth that Motion is manifest in everything in the Universe-that nothing is at rest-that everything moves, vibrates, and circles. This Hermetic Principle was recognized by some of the early Greek philosophers who embodied it in their systems. But, then, for centuries it was lost sight of by the thinkers outside of the Hermetic ranks. But in the Nineteenth Century physical science re-discovered the truth and the Twentieth Century scientific discoveries have added additional proof of the correctness and truth of this centuries-old Hermetic doctrine.

"The Hermetic Teachings are that not only is everything in constant movement and vibration, but that the 'differences' between the various manifestations of the universal power are due entirely to the varying rate and mode of vibrations. Not only this, but that even THE ALL, in itself, manifests a constant vibration of such an infinite degree of intensity and rapid motion that it may be practically considered as at rest, the teachers directing the attention of the students to the fact that even on the physical plane a rapidly moving object (such as a revolving wheel) seems to be at rest. The Teachings are to the effect that Spirit is at one end of the Pole of Vibration, the other Pole being certain extremely gross forms of Matter. Between these two poles are millions upon millions of different rates and modes of vibration.

"Modern Science has proven that all that we call Matter and Energy are but 'modes of vibratory motion,' and some of the more advanced scientists are rapidly moving toward the positions of the occultists who hold that the phenomena of Mind are likewise modes of vibration or motion. Let us see what science has to say regarding the question of vibrations in matter and energy.

"In the first place, science teaches that all matter manifests, in some degree, the vibrations arising from temperature or heat. Be an object cold or hot-both being but degrees of the same things-it manifests certain heat vibrations, and in that sense is in motion and vibration. Then all particles of Matter are in circular movement, from corpuscle to suns. The planets revolve around suns, and many of them turn on their axes. The suns move around greater central points, and these are believed to move around still greater, and so on, ad infinitum. The molecules of which the particular kinds of Matter are composed are in a state of constant vibration and movement around each other and against each other. The molecules are composed of Atoms, which, likewise, are in a state of constant movement and vibration. The atoms are composed of Corpuscles, sometimes called 'electrons,' 'ions,' etc., which also are in a state of rapid motion, revolving around each other, and which manifest a very rapid state and mode of vibration. And, so we see that all forms of Matter manifest Vibration, in accordance with the Hermetic Principle of Vibration." [Anonymous (2005), pp.59-62, 55-58. The first is posted here; the second here.]

Compare that with this:

"The Unity and Interpenetration of Opposites

"Everywhere we look in nature, we see the dynamic co-existence of opposing tendencies. This creative tension is what gives life and motion. That was already understood by Heraclitus (c. 500 B.C.) two and a half thousand years ago. It is even present in embryo in certain Oriental religions, as in the idea of the ying and yang in China, and in Buddhism. Dialectics appears here in a mystified form, which nonetheless reflects an intuition of the workings of nature. The Hindu religion contains the germ of a dialectical idea, when it poses the three phases of creation (Brahma), maintenance or order (Vishnu) and destruction or disorder (Shiva). In his interesting book on the mathematics of chaos, Ian Stewart points out that the difference between the gods Shiva, 'the Untamed,' and Vishnu is not the antagonism between good and evil, but that the two principles of harmony and discord together underlie the whole of existence....

"In Heraclitus, all this was in the nature of an inspired guess. Now this hypothesis has been confirmed by a huge amount of examples. The unity of opposites lies at the heart of the atom, and the entire universe is made up of molecules, atoms, and subatomic particles. The matter was very well put by R. P. Feynman: 'All things, even ourselves, are made of fine-grained, enormously strongly interacting plus and minus parts, all neatly balanced out....'

"The question is: how does it happen that a plus and a minus are 'neatly balanced out?' This is a contradictory idea! In elementary mathematics, a plus and a minus do not 'balance out.' They negate each other. Modern physics has uncovered the tremendous forces which lie at the heart of the atom. Why do the contradictory forces of electrons and protons not cancel each other out? Why do atoms not merely fly apart? The current explanation refers to the 'strong force' which holds the atom together. But the fact remains that the unity of opposites lies at the basis of all reality.

"Within the nucleus of an atom, there are two opposing forces, attraction and repulsion. On the one hand, there are electrical repulsions which, if unrestrained, would violently tear the nucleus apart. On the other hand, there are powerful forces of attraction which bind the nuclear particles to each other. This force of attraction, however, has its limits, beyond which it is unable to hold things together. The forces of attraction, unlike repulsion, have a very short reach. In a small nucleus they can keep the forces of disruption in check. But in a large nucleus, the forces of repulsion cannot be easily dominated....

"Nature seems to work in pairs. We have the 'strong' and the 'weak' forces at the subatomic level; attraction and repulsion; north and south in magnetism; positive and negative in electricity; matter and anti-matter; male and female in biology; odd and even in mathematics; even the concept of 'left and right handedness' in relation to the spin of subatomic particles. There is a certain symmetry, in which contradictory tendencies, to quote Feynman, 'balance themselves out,' or, to use the more poetical expression of Heraclitus, 'agree with each other by differing like the opposing tensions of the strings and bow of a musical instrument.' There are two kinds of matter, which can be called positive and negative. Like kinds repel and unlike attract....

"Moreover, everything is in a permanent relation with other things. Even over vast distances, we are affected by light, radiation, gravity. Undetected by our senses, there is a process of interaction, which causes a continual series of changes. Ultra-violet light is able to 'evaporate' electrons from metal surfaces in much the same way as the sun’s rays evaporate water from the ocean. Banesh Hoffmann states: 'It is still a strange and awe-inspiring thought, that you and I are thus rhythmically exchanging particles with one another, and with the earth and the beasts of the earth, and the sun and the moon and the stars, to the uttermost galaxy....'

"The phenomenon of oppositeness exists in physics, where, for example, every particle has its anti-particle (electron and positron, proton and anti-proton, etc.). These are not merely different, but opposites in the most literal sense of the word, being identical in every respect, except one: they have opposite electrical charges—positive and negative. Incidentally, it is a matter of indifference which one is characterised as negative and which positive. The important thing is the relationship between them....

"This universal phenomenon of the unity of opposites is, in reality, the motor-force of all motion and development in nature. It is the reason why it is not necessary to introduce the concept of external impulse to explain movement and change—the fundamental weakness of all mechanistic theories. Movement, which itself involves a contradiction, is only possible as a result of the conflicting tendencies and inner tensions which lie at the heart of all forms of matter.

"The opposing tendencies can exist in a state of uneasy equilibrium for long periods of time, until some change, even a small quantitative change, destroys the equilibrium and gives rise to a critical state which can produce a qualitative transformation. In 1936, Bohr compared the structure of the nucleus to a drop of liquid, for example, a raindrop hanging from a leaf. Here the force of gravity struggles with that of surface tension striving to keep the water molecules together. The addition of just a few more molecules to the liquid renders it unstable. The enlarged droplet begins to shudder, the surface tension is no longer able to hold the mass to the leaf and the whole thing falls." [Woods and Grant (1995), pp.64-68; posted here.]

"'Everything Flows'

"Everything is in a constant state of motion, from neutrinos to super-clusters. The earth itself is constantly moving, rotating around the sun once a year, and rotating on its own axis once a day. The sun, in turn, revolves on its axis once in 26 days and, together with all the other stars in our galaxy, travels once around the galaxy in 230 million years. It is probable that still larger structures (clusters of galaxies) also have some kind of overall rotational motion. This seems to be a characteristic of matter right down to the atomic level, where the atoms which make up molecules rotate about each other at varying rates. Inside the atom, electrons rotate around the nucleus at enormous speeds....

"The essential point of dialectical thought is not that it is based on the idea of change and motion but that it views motion and change as phenomena based upon contradiction. Whereas traditional formal logic seeks to banish contradiction, dialectical thought embraces it. Contradiction is an essential feature of all being. It lies at the heart of matter itself. It is the source of all motion, change, life and development. The dialectical law which expresses this idea is the law of the unity and interpenetration of opposites...." [Ibid, pp.45-47; posted here. Quotation marks altered to conform to the conventions adopted here.]

Attentive readers will note that the same sort of Mickey Mouse Science appears in both the Hermetic tract and the super-fine dialectical hymnal sung to us by comrades Woods and Grant.

[However, the reader should check that I have not actually switched these two quotations around!]

But, still no indication of what it could possibly mean to suggest that opposites could contradict one another (for example, who taught them to speak?). [There is more on this in Essay Seven, here.]

69. The following might be regarded as a more viable alternative:

A1: Capitalism has the potential to offer wealth to all but delivers wealth and poverty, where wealth and poverty are opposites.

[F49a: Capitalism develops D, but actually delivers B and C, where B and C are opposites.]

In fact, this alternative was considered in the text: it is just a variant on F49a. An unrealised potential cannot contradict anything since it does not exist as an actualised option. So, even if true, A1 would be of no help in understanding what DM-theorists mean by their equation of forces with "contradictions" in HM.

Someone could argue that the fact that there will be a sea battle tomorrow is contradicted by the fact that there won't (to use Aristotle's example). Neither of these events are actual, but that does not stop them from contradicting one another.

Maybe not, but DM-enthusiasts regard their 'contradictions' as real material forces, and the latter can only 'contradict' whatever they can materially interact with (and such items plainly have to exist), ruling out the above as an effective response.

70. Contradictions In Das Kapital?

If, say, an abundance of money in one pocket (or even a large horde of "use values" in, for example, a lock-up somewhere) did in fact manage to 'contradict' another empty (lock-up), locally or remotely, this would make no sense even in DM terms. Presumably such lifeless objects would have no effect on one another; they could bring about no changes of themselves, nor could they morph into each other (as other DM-contradictions and UOs are all allegedly supposed to do).

So, even in DM terms it is unclear what sense it makes to say that such things are "contradictory".

However, Scott Meikle argues that there is indeed some sort of sense to be made of this. Meikle's case revolves around a short and relatively clear account of the alleged 'contradiction' between use-value and exchange-value, or more pointedly, between the "relative form" and the "equivalent form" of value, which Marx discusses in Chapter One, Volume One, of Das Kapital.

Now I do not want to enter into whether or not Meikle's interpretation of Marx is accurate; my concern is merely to see if his analysis can show us how and why these are indeed good examples of "dialectical contradictions". Here is what he says:

"All the contradictions of capitalist commodity-production have at their heart the contradiction between use-value and exchange-value. Marx reveals this contradiction to lie at the heart of the commodity-form as such, even in its simplest and most primitive form....

"The simple form of value itself contains the polar opposition between, and the union of, use-value and exchange-value.... [Marx writes that] 'the relative form of value and the equivalent form are two inseparable moments, which belong to and mutually condition each other...but at the same time they are mutually exclusive and opposed extremes.' Concerning the first he observes that the value of linen cannot be expressed in linen; 20 yards of linen = 20 yards of linen is not an expression of value. 'The value of linen can therefore only be expressed relatively, that is in another commodity. The relative form of the value of the linen therefore presupposes that some other commodity confronts it in the equivalent form.' Concerning the second: 'on the other hand, this other commodity which figures as the equivalent, cannot simultaneously be in the relative form of value... The same commodity cannot, therefore, simultaneously appear in both forms in the same expression of value. These forms rather exclude each other as polar opposites.'

"This polar opposition within the simple form is an 'internal opposition' which as yet remains hidden within the individual commodity in its simple form: 'The internal opposition between use-value and exchange-value, hidden within the commodity, is therefore represented on the surface by an external opposition,' that is the relation between two commodities such that one (the equivalent form) counts only as a use-value, while the other (the relative form) counts only as an exchange-value. 'Hence, the simple form of value of the commodity is the simple form of the opposition between use-value and value which is contained in the commodity.'" [Meikle (1979), pp.16-17. Italic emphases in the original.]

But, what evidence and/or argument is there to show that that these are indeed "polar opposites", let alone 'dialectically-united' opposites? And why call this a "contradiction"? We have already seen that this way of talking is based solely on Hegel's own egregious misconstrual of the LOI. So, what has Meikle to offer that stands some chance of repairing this tattered 'theory'?

Apparently, only this:

"Marx's absolutely fundamental (Hegelian) idea [is] that the two poles united in an opposition necessitate one another ('belong to and mutually condition each other').... [Ibid., p.19.]

But, what precisely is the source of this necessitation? Well, after a brief discussion of Quine's ill-considered views on logical 'necessity' (which analysis confuses the latter notion with extremely well-confirmed empirical truths), Meikle rejects the idea that the source of this 'necessity' can be found in logic.

"So, 'logical necessity' does not promise to account for the necessity that unites opposites within a contradiction. The unity of use-value and exchange-value within the commodity is certainly not something which, despite all necessitation between the two poles, may be abrogated (on Quine's conventionalist account). Not, that is, without 'abrogating' the commodity itself; for the commodity is precisely the unity of use-value and exchange-value. Use-value can exist alone. But exchange-value cannot; it presupposes use-value because only what has use-value can have exchange-value. What has exchange-value, a commodity, is, thus, necessarily use-value  and exchange-value brought into a unity. The commodity-form of the product of labour has as its essence the unity of the two. That is what it is. Their conjunction or unity constitutes its essence." [Ibid., p.22. Italic emphases in the original.]

But, why is this not just a de dicto (a merely verbal) necessity?

Fortunately, Meikle has that particular base covered:

"Use-value and exchange-value are, therefore, not 'merely' abstractions arrived at in thought about reality; they are constituents of reality in partaking in the essence of the commodity. And the opposition or contradiction between the two poles is a constituent of reality also, (although in the simple commodity or value-form it appears only primitively in the fact that the same commodity cannot act simultaneously as relative and as equivalent form of value)." [Ibid., p.22. Italic emphasis in the original.]

And yet, whatever else is true of these value-forms, how can they 'contradict' one another if one of them cannot exist at the same time as the other? If these items "mutually exclude" one another, how can they both exist at the same time? On the other hand, if they both exist at the same time, so that they can indeed 'contradict' one another, how can one possibly "mutually exclude" the other?

[We have already seen this insurmountable barrier stymie earlier attempts to make this sort of depiction of 'dialectical contradictions' work.]

Putting this serious problem to one side, why is 'necessity' not merely a spin-off of a determination to use a few words in a certain way? Why is this not just a de dicto necessity?

[Indeed, it is rather cheeky of Meikle to use Quine to criticise logical necessity, when he would have taken an even dimmer view of such de re (real world) necessities. (On Quine's ideas, see the references listed at the end of this Note).]

Of course, this has become a hot topic ever since Saul Kripke upset the de dicto apple cart a generation or so ago. [Kripke (1977, 1980).] And it is thus no surprise to see Meikle appeal to Kripke's work to argue that these are not merely de dicto, but are in fact de re necessities.

Unfortunately, Kripke's arguments are not quite as sound as Meikle appears to believe. [On this see, Ebersole (1982) and (Hallett (1991), Hanna and Harrison (2004), pp.278-88. See also an entertaining article by Jerry Fodor, in Fodor (2004). More on this in a later Essay.]

Nevertheless, in support, Meikle quotes a (by now) hackneyed series of examples:

"The commodity is the unity of use-value and exchange-value, in precisely the same way that water is H2O, that light is a stream of photons, and that Gold is the element with atomic number 79. All these statements are necessarily true. They state truths that are true of necessity, not in virtue of any logical or 'conceptual' connexions, but in virtue of the essences or real natures of the entities in question. Water is necessarily H2O. Anything that is not H2O  cannot be water..., and the 'cannot' is ontological not epistemic.... We did not always know this, of course; it was a discovery people made about the essence of water (and one which may need to be recast if future theoretical development requires it)." [Ibid., pp.22-23. Italic emphasis in the original.]

The Gold example is not too clever, since its atomic number depends on our counting system, and neither is the light example all that convincing (since there are scientists who question the existence of photons). The water example is no less fraught, since water is not even contingently H2O; hydrogen bonding means its structure is far more complex. [On this and other problematic issues that Essentialism faces see VandeWall (2006). See also van Brakel (2000), and Hacker (2007), pp.29-56.]

It could be argued that Meikle had this base covered too, for he added:

"[I]t was a discovery people made about the essence of water (and one which may need to be recast if future theoretical development requires it)." [Ibid.]

But, that just makes this an epistemic truth, and not the least bit "essential", or "ontological".

However, we will for the moment assume that these 'difficulties' can in some way be neutralised -- although, in an Essay on the nature of science, to be published at this site in 2008, we will see that this is not the case; there it will be shown that modern-day Essentialism is a fundamentally flawed dead end. Naturally, the latter theory also faces the serious objections I have raised against this way of seeing the world, explored at length in Essay Twelve Part One.

Meikle also ignores the fact that the sort of essentialism he lionises depends on Possible World Semantics [PWS] in order to work. Sure he tries to damp this down somewhat (on pp.23-25), but all he succeeds in doing is undermining the case he has built-up for accepting his brand of essentialism in the first place -- for PWS merely turns de re necessities into super-duper empirical, extensional truths, and de re simply de sappears.

This 'difficulty' will also be put to one side for the present. [However, readers should also consult this paper, which outlines several serious objections to modern-day essentialism, but with a warning that the author then proceeds to defend an Aristotelian version of the same. These issues will also be tackled later.]

In addition, I will not be asking (here) other awkward questions about the precise origin of these allegedly natural necessities, and how they can possibly cause change, but the following passage (in blue and red, taken from Part One) will give the reader some idea of how I will be tackling that topic at a later stage:

A quotation from Baker and Hacker (1988) underlines the futility of this "aristocratic" approach to knowledge (although they do not use that particular word, and are not making this particular political point) -- which, incidentally, also reveals why dialecticians (like Rees, and the others quoted here) have become fixated on a search for a metaphysical (and ultimate/rational) "why" of things:


"Empirical, contingent truths have always struck philosophers as being, in some sense, ultimately unintelligible. It is not that none can be known with certainty…; nor is it that some cannot be explained…. Rather is it that all explanation of empirical truths rests ultimately on brute contingency -- that is how the world is! Where science comes to rest in explaining empirical facts varies from epoch to epoch, but it is in the nature of empirical explanation that it will hit the bedrock of contingency somewhere, e.g., in atomic theory in the nineteenth century or in quantum mechanics today. One feature that explains philosophers' fascination with truths of Reason is that they seem, in a deep sense, to be fully intelligible. To understand a necessary proposition is to see why things must be so, it is to gain an insight into the nature of things and to apprehend not only how things are, but also why they cannot be otherwise. It is striking how pervasive visual metaphors are in philosophical discussions of these issues. We see the universal in the particular (by Aristotelian intuitive induction); by the Light of Reason we see the essential relations of Simple Natures; mathematical truths are apprehended by Intellectual Intuition, or by a priori insight. Yet instead of examining the use of these arresting pictures or metaphors to determine their aptness as pictures, we build upon them mythological structures.


"We think of necessary propositions as being true or false, as objective and independent of our minds or will. We conceive of them as being about various entities, about numbers even about extraordinary numbers that the mind seems barely able to grasp…, or about universals, such as colours, shapes, tones; or about logical entities, such as the truth-functions or (in Frege's case) the truth-values. We naturally think of necessary propositions as describing the features of these entities, their essential characteristics. So we take mathematical propositions to describe mathematical objects…. Hence investigation into the domain of necessary propositions is conceived as a process of discovery. Empirical scientists make discoveries about the empirical domain, uncovering contingent truths; metaphysicians, logicians and mathematicians appear to make discoveries of necessary truths about a supra-empirical domain (a 'third realm'). Mathematics seems to be the 'natural history of mathematical objects' [Wittgenstein (1978), p.137], 'the physics of numbers' [Wittgenstein (1976), p.138; however these authors have recorded this erroneously as p.139, RL] or the 'mineralogy of numbers' [Wittgenstein (1978), p.229]. The mathematician, e.g., Pascal, admires the beauty of a theorem as though it were a kind of crystal. Numbers seem to him to have wonderful properties; it is as if he were confronting a beautiful natural phenomenon [Wittgenstein (1998), p.47; again, these authors have recorded this erroneously as p.41, RL]. Logic seems to investigate the laws governing logical objects…. Metaphysics looks as if it is a description of the essential structure of the world. Hence we think that a reality corresponds to our (true) necessary propositions. Our logic is correct because it corresponds to the laws of logic….


"In our eagerness to ensure the objectivity of truths of reason, their sempiternality and mind-independence, we slowly but surely transform them into truths that are no less 'brutish' than empirical, contingent truths. Why must red exclude being green? To be told that this is the essential nature of red and green merely reiterates the brutish necessity. A proof in arithmetic or geometry seems to provide an explanation, but ultimately the structure of proofs rests on axioms. Their truth is held to be self-evident, something we apprehend by means of our faculty of intuition; we must simply see that they are necessarily true…. We may analyse such ultimate truths into their constituent 'indefinables'. Yet if 'the discussion of indefinables…is the endeavour to see clearly, and to make others see clearly, the entities concerned, in order that the mind may have that kind of acquaintance with them which it has with redness or the taste of a pineapple' [Russell (1937), p.xv; again these authors have recorded this erroneously as p.v, RL], then the mere intellectual vision does not penetrate the logical or metaphysical that to the why or wherefore…. For if we construe necessary propositions as truths about logical, mathematical or metaphysical entities which describe their essential properties, then, of course, the final products of our analyses will be as impenetrable to reason as the final products of physical theorising, such as Planck's constant." [Baker and Hacker (1988), pp.273-75. Referencing conventions in the original have been altered to conform to those adopted here.]

As should now be clear from all that has gone before, DM-theorists have bought into this view of 'necessary truths' (even if few of them use that particular phrase, although Lenin and Dietzgen seem to have been rather fond of it; more on this in Essay Thirteen).

For example, dialecticians in general regard change as the result of the relation between internally-linked opposite (logical?) properties of objects and processes. But, why this should cause change is simply left entirely unexamined (indeed, it is left as a brute fact, as the above passage suggests it must); in reality this account of change is a consequence merely of a certain way of describing things (and a fetishised way, at that), as we will see.

Nevertheless, as we have already seen, there is no reason why contradictory states of affairs should cause change any more than there is a reason to suppose that non-contradictory states should. Both of these options rely on descriptions of the alleged relations between objects and processes (not on evidence since (as we saw earlier) it is not possible materially to verify their existence); they supposedly capture or picture processes in nature that are held to make other objects or processes alter/'develop'....

Moreover, the infinite regress (or "bad infinity") dialecticians hoped to avoid by appealing to 'internal contradictions' now simply reappears elsewhere in their theory. When it is fleshed-out, this theory just relates objects and processes to yet more objects and processes, as well as to 'negations', 'opposites', and 'interpenetrations', and the like (i.e., just more "brute facts").

But, despite this, how does Meikle tackle the problem of change?

"The poles of an opposition are not just united. They also repel one another. They are brought together in a unity, but within that unity they are in tension. The real historical existence of the product of labour in the commodity-form provides an analogue of the centripetal force that contains the centrifugal forces of the mutual repulsion of use-value and exchange-value within it." [Ibid., p.26.]

There are so many metaphors in this passage, it is not easy to make sense of it. Nevertheless, it is reasonably clear that Meikle has reified the products of social relations (use- and exchange-values, etc.), and in this reified state they become the actual agents, with human beings (or, perhaps, commodities themselves) the patients. How else are we to understand the word "repel" here? Do they actually repel each other (like magnets, or electrical charges), or do we do this?

And do these "opposites" show any sign of turning into one another, as the DM-worthies assured us they must?

Furthermore, how can the forms that underpin use- and exchange-value (i.e., equivalent and relative form) provide an analogue of the forces Meikle mentions? If forces are to act on other forces, or other bodies, they need to fulfil a handful of crucial conditions first, the most important of which is to have the decency to exist. But, we were told these two forms can't co-exist. How then can they repel (or provide the wherewithal for other objects and processes to repel) anything?

This, of course, is the unforgiving rock upon which we have seen all such idealist speculations founder.

It could be argued that these 'repulsions' occur in our thought about the simple commodity form. But even there, they cannot exist together, for if they could, they would not 'mutually exclude' one another!

Or, are we to imagine there is a tussle taking place in our heads, such that, when we think of the one, it elbows out of the way (out of existence?) the other? Perhaps then, depending on circumstances, equivalent form can be declared the winner over relative form by two falls to a submission (UK rules)?

Figure Two: Equivalent Form Slam Dunks Relative Form In A Skull Near You

Furthermore, even if they could exist together in thought, this will not help, since it would make a mess of Meikle's appeal to de re necessities. This retreat into the ideal would leave him with a few seriously undernourished de dicto 'skeletons' to bounce around inside his head.

But, perhaps there is a way out of this bottomless pit of meticulously-constructed confusion? Meikle continues:

"But in its simple form, the commodity is an unstable equilibrium. It is pregnant with possibilities, which history may present either with the conditions for the realisation of these possibilities, or with the indefinite variety of conditions that will frustrate their realisation. Given the right conditions, the embryo will develop its potentiality; and the simple form of value will undergo the metamorphoses that will take the commodity from its embryo through infancy to early adolescence with the attainment of the universal form of value, money." [Ibid., p.26.]

It now seems that metaphor is all Meikle has to hand in his bid to make this mystical process the least bit comprehensible. And it is quite clear where all this reification has led him: the commodity itself invented money, not human beings!

Or, perhaps, the commodity mesmerised human beings into inventing money.

Once more, on this view, we are the patients, while these metaphorical beings are the real agents of social change!

[Independently of this, we have already seen that this view of change cannot work.]

Is there then any way of re-configuring this overall theory of change that is capable of extracting it from the materialist shredder before the switch is thrown? Well, Meikle turns to Aristotle for assistance, but before he does that completely, he in effect concedes the truth of the above observation, for it seems that these value forms do indeed force humans to do their bidding:

"This line of development is not accidental or fortuitous; it is not a process of aggregating contingent and extraneous additions. It is, rather, process of development of the potentialities within, and the increasing differentiation of, an original whole. If history does not block the growth of exchange activity, then that growth will find out the inadequacy of the simple form of value. Then, looked at from the point of view of efficient causation, those engaged in that activity, being rational and inventive in the face of the problems thrown up by their developing class interests, will act so as to solve their practical difficulties by measures that overcome that insufficiency to the requirements of their developing commerce. The solution to their practical problems is the money-form." [Ibid., pp.26-27.]

Now, this either means that those involved in the invention of money were the sad puppets of those ('selfish'?) value forms, or they had a clear understanding of the nature of use- and exchange-value, and equal to that of Marx, too -- but two and a half thousand years earlier --, so that they could make the correct/rational choices. Otherwise, how could those value forms exercise any sort of causal input here?

But, doesn't this make dangerous concessions to teleology, to final causation? No problem; Meikle tackles this unexpected difficulty head-on:

"Looked at from the point of view of final causation, money is the final cause of this phase of social development. This is not to say that final causation is a form of efficient causation in which the future acts on the past, such that the developed form beckons from the future to the past less developed form; rather, the embryonic entity has a structure that develops, if it develops, along a certain line. Thus, final causation and efficient causation, here, are not mutually exclusive but mutually supportive: the one explaining the emergence of the other, and the other the success and development of the one. What we have here is a development that, barring accidents, will take its course -- an evolution that is necessary; its final form immanent as a potentiality within its original one." [Ibid., p.27.]

But, this solves nothing, for it seems to mean that some sort of plan or program must have been written into these value forms that determines how they should develop, rather like a fertilised egg or seed has a genetic code that we are told does likewise -- which suspicion is amply confirmed by Meikle's frequent use of embryonic language.

[That, of course, implicates this view of things with other, well-known ancient mystical ideas connected with belief in the Cosmic or Orphic Egg (a topic briefly mentioned in Part One of this Essay, and again in Essay Eleven Parts One and Two, but more fully in Essay Fourteen Part One (summary here).]

But, perhaps this is once again too quick, for Meikle now introduces the aforementioned Aristotelian ideas in order to neutralise this problem:

"The necessity that Marx sees in the line of development of the value-form is that which Aristotle contrasts with events that are 'accidental' and it is bound up with organic systems and Aristotle's conception of ousia. Where there is constant reproduction there is a whole system, an ousia." [Ibid., p.27]

Meikle then quotes Stephen Clark:

"[E]verything that happens phusei, 'by nature', happens always or for the most part, but nothing that happens apo tuches, by 'chance', or apo tautomatou, 'just of itself', happens thus frequently. Therefore, no natural events are thus purely accidental, and therefore all natural events are non-accidental. But all non-accidental events are heneka tou, 'serve some purpose', are given sense by their ends.... The fact that rain is always being produced makes it impossible to doubt that there is an organic system here, and such systems are 'finalistically' identified. To answer the question 'what is it?' we must reply in terms of its natural line of development...genesis, the process of coming-to-be-, is what it is because ousia is what it is, and not vice versa." [Clark (1975), pp.60-61, quoted in Meikle (1979), pp.27-28. Italic emphases in the original.]

Once more, this fails to solve the problem, for the necessities pictured here work only if one is prepared to anthropomorphise nature. This is because, as soon as it is asked why events cannot do otherwise (than they in fact do), it becomes obvious that certain events must exercise some sort of control over others, directing then along the right "line" (which is why Meikle found he had to use that phrase). This is quite clearly the point too of all that talk about "ends" and "purposes" in Aristotle -- which were part of an openly religious doctrine that Meikle just ignores, and which only works if nature is controlled by some 'Mind' or other.

Hence, it is worth noting that dialecticians can only make their 'theory' seem to work if they adopt and/or copy the a priori thought-forms of ruling-class thinkers (Aristotle (alongside Plato) is in fact one of the two most important figures, here). Meikle firmly nails his colours to this particular mystical mast; for Aristotle, if nature has a purpose, then the status quo must be in harmony with it, and thus cannot legitimately be challenged. In that case, the rule of the elite is not 'accidental', but serves some 'end'. [The reader will no doubt now appreciate more fully why I asserted this back in Essay Two.]

[This topic was discussed at length in Essay Three Part Two, and the reader is referred there for more details. It will also be covered in Essay Three Part Five, as well as in an Additional Essay on 'mind and cognition', to be published in 2008. The theoretical background to all this will be outlined in Essay Twelve Parts Two and Three (summary here).]

Of course, Meikle would have done well to have noted that Marx warned his readers not to take this use of Hegelian jargon seriously:

"...[A]nd even, here and there in the chapter on the theory of value, coquetted with the mode of expression peculiar to him." [Marx (1976), p.103. Bold emphasis added.]

More on that here.

Now, there are better ways of making Das Kapital comprehensible; we do not need to appeal to mystical Hegelian and/or Aristotelian concepts to make it work. [I will, however, leave that to another time.]

In which case, it is still far from clear what Meikle thinks these "dialectical contradictions" are, or how they can make anything change --, unless, that is, we are prepared to anthropomorphise nature and society, and read human traits into inanimate objects and processes.

[On Quine, see Arrington and Glock (1996), Glock (2003), Hacker (1996), pp.189-227. See also this PDF (which is an essay on Quine, by Hacker).]

71. Naturally, and once again, these comments will have to remain tentative until we are told what (if anything) DM-theorists mean by the phrase "dialectical contradiction". Since this ground has been raked over several times already, yet another pass here will be avoided.

72. Of course, someone might foolishly try to 're-define' their financial status by declaring that a £5 ($10) bank balance was really £1,000,000 ($2,000,000). While this neat ploy might make an ideal millionaire out of a fake one, it would have no material impact on his or her finances (except perhaps, a negative one).

Since the ordinary word "contradiction" already has a sense (in everyday material life), redefining it in a way that is unconnected with material practice would similarly have no physical impact on reality, no matter how ideal a cure it proved to be for one's ailing theory.

To be sure, it could be argued that dialecticians are at liberty to use words any which way they like, and it is not up to 'thought-police' (such as the present author) to try to stop them.

DM-theorists can indeed use words as they please (not that they need my permission to do so), but they cannot then claim connotations for these words that partially or wholly apply to other words that already have established uses, which theirs then try to ape or replace. So, they are not at liberty to claim their use of "contradiction" is in any way connected with its ordinary use, or even with its employment in FL -- not without causing confusion (and, mercifully so far, mostly to themselves).

In that case, this novel use of "contradiction" need  to be explained -- since the connections this word once had with its supposed vernacular 'twin' have long ago been severed, leaving it adrift, and thus meaningless -- something that dialecticians have signally failed to do (it must be admitted, after not trying all that hard for over 150 years).

And that is why I have been repeatedly asking for such a clarification. [More on this in Essay Twelve, Part One.]

However, as a mater of fact, DM-apologists are not using this word in any which way they please. Just like those who use jargon associated with, say, the Christian Trinity (whose terms (unsurprisingly) originated in the same wing of NeoPlatonism from which Hegel heavily borrowed), dialecticians have imported this and other obscure terms-of-art from Hermetic Hegelian Philosophy -- whose application conditions defy explication to this day --, which that brands their system mystical Christianity's poor relation.

Dialecticians should feign no surprise, therefore, when they are accused of being mystics; because they cannot explain what their words mean in materialist terms, using the vernacular, or more technical language, their words are as much a mystery to them as they are to anyone else.

[Those who think that ordinary language is far too limited to do duty here, should read this and this, and then reconsider their folly.]

73. On this, see Notes 70 and 72, above.

74. A genuine example of an "internal relation" might help here: if the meridian at Greenwich were to be abolished, the whole system of latitudes would automatically go with it. This is not at all like the elimination of poverty. Poverty will be eradicated not by destroying wealth, but by extending it, and by abolishing class division (etc.).

It could be argued here that this misconstrues the nature of the link between poverty and wealth under Capitalism, making it into something abstract that exists between two unchanging concepts. Contrary to this, dialecticians hold that wealth and poverty are dialectically linked --, and not just to each other. They are related to, and are constituted by, the Mode of Production in which they occur. Hence, under Capitalism, wealth cannot exist without the creation of poverty. To eradicate the latter, Capitalism must be abolished. In a fully socialist society, the present connection between wealth and poverty would vanish.

However, the link even here is still causal (wealth creates poverty under capitalism, and it does this under the operation of well-known historical, economic and social causes); dressing these up in pseudo-logical finery cannot change that fact -- but it does succeed in mystifying something that has clear material roots.

75. It could be objected that DM-theorists do not disagree with this, even though they actually maintain that these material forces are "dialectically inter-linked". Hence, no dialectician of any sophistication thinks that concepts can, of themselves, cause change or initiate struggle, only that the material roots of struggle are mediated by the ideas people form of their circumstances and the contradictory interests these engender.

Now, worded differently, this would not be inconsistent with anything written in these Essays, since it involves concepts drawn from HM.

Nevertheless, if the above is meant to illustrate the real meaning of F50, then we would once more have an example of the effects of the effects being used to explicate the action of a force, or set of forces. That impasse was discussed at length earlier.

F50: Capitalism offers A, but delivers C instead, where C is a paradoxical outcome.

However, while dialecticians might object to the accusation that they believe that concepts enter into conflict with one another -- on the contrary, they could point out, this is how Hegel saw things. By way of contrast they emphasise the fact that it is real people and real forces in the material world that conflict.

However, when the language dialecticians use in order to express their ideas is examined, this accusation in fact forces itself upon us. On this see Note 70 above and Note 76, below.

76. The details relating to this will be set out elsewhere. However, it could be argued once more that this assertion is unfair to DM in that it was in fact dialecticians who first complained that FL uses lifeless and dead concepts, and thus could not explain change.

However, the truth is that it is DM-theorists who employ concepts that come to life only if they are anthropomorphised, and are viewed as the abstract expression of conflict (i.e., in effect, these are the fetishised analogues of social forms, as we have seen -- for example, in Note 70). This is revealed, for example, by their profligate use of words like "contradiction" and "negation", in inappropriate circumstances, in connection with natural processes, and now in relation to social change (on this see Note 59b). In contrast, the rejection of this approach (advocated here) allows concepts to live by re-humanising them (but only in relation to social development), by revealing them for what they are: the conditioned products of social relations among human beings.

So, in HM, in place of the fetishised theses found in DM, we have concepts enlivened by human practice and struggle, expressed in the material language of ordinary life. In this way, it is possible for a description of the social world to become fully human -- a small but important step in the fight to make it fully human.

Once again, if this is regarded as unfair or inaccurate, the reader is referred back to Essay Three Part One (here and here), where the linguistic moves behind this pernicious form of Idealism were exposed, Essay Three Part Two where the roots of this approach to Philosophy were traced back to traditional ruling-class and Idealist forms-of-thought, Essay Two where the dogmatic and Idealist nature of DM was established, Essay Four where the anthropomorphic nature of DL was highlighted, Essay Five where the fetishised nature of the language Engels used to depict motion in reality was exposed, Essay Seven where it was also shown that the 'Three Laws of Dialectics' were based on a fetishised view of discourse, Essay Eight Part One where further aspects of this anthropomorphic doctrine were unmasked, earlier sections of this Essay where the application to nature of concepts drawn from Hegel was shown to be animistic, and to Essays Twelve and Fourteen (summaries here and here) where these sordid threads are traced back to mystical ruling-class doctrines that no self-respecting socialist, or materialist, should want to touch with someone else's bargepole.

Indeed, it has been a unifying theme of all the Essays posted at this site that the application to nature of concepts drawn from Hermetic Philosophy has branded DM as an Idealist/mystical theory, and further, that this has compromised the scientific status of HM. Anyone who still takes exception to the claim that dialecticians use animistic notions drawn from Hermetic Philosophy (where conflict is seen in linguistic terms -- and are then projected back onto nature and society) --, should express no surprise when the constant warning has been that this is where this sorry tale was in fact heading.

The solution is, therefore, for recalcitrant comrades to stop complaining, and point their fingers in the right direction: at the DM-classicists who imported these ruling-class ideas into Marxism.

[DL = Dialectical Logic.]

77. Hence, consider these sentences:

F58: Force P1 contradicts P2 in so far as some or all of E1 and E2 are contradictory (internally, or to one another).

F58a: Force P1 contradicts P2 in so far the event set one or other produces (i.e., E3) is internally contradictory.

Given that one or more of the elements of E3 (or even E3 itself) could be internally contradictory, F58, or perhaps F58a, might allow the interpretation of "contradictions" as opposing forces to stand.

Unfortunately, even if sense could be made of contradictory contemporaneous events, the link between forces and 'internally contradictory' sets of events would once again be severed by what these two sentences say. Hence, even if F58 and F58a were correct, they would still fail to connect the 'contradiction' between forces and the 'contradictions' internal to a set of subsequent events.

Now, let us suppose P1 and P2 operate as the above propositions indicate. In F58a, only E3 would take place. If the latter was 'internally contradictory', presumably parts of it (i.e., a sub-event of E3, say, E3i) would constitute the postulated 'internal contradiction'. In that case, F58a would collapse back into F58.

On the other hand, if (all of) E3 was in this state because of its 'internally contradictory' dispositional properties, then this too would be an unviable option, for reasons that have already been considered; see the discussion of F57 in the main text.

However, as far as F58 itself is concerned, if one event prevents another from happening, no contradiction is implied since such a 'conflict' would have only one real term -- as noted several times already. [See for example, Note 55.]

Nevertheless, this might allow for the consideration of more complex examples allegedly drawn from HM. On this, see the discussion above, in Note 70.

77a. The reference to 'p and q', and 'p and not p', in relation to F63 might seem a little obscure to some:

F63: Hence, propositions that express the fact that one or more of E1-En have been prevented from taking place contradict propositions that express an expectation that they will occur.

If "p" stands for, say, "E1 has been prevented from taking place" then "not p" must stand for "It is not the case that E1 has been prevented from taking place", as opposed to "E1 is expected to take place". Since the latter is clearly not of the form "not-p", the use of "q" to represent this logically unconnected sentence in fact suggests itself.

78. The import of this claim is obscure at best, even if many Physicists hold this doctrine true. However, since this idea seems to have no real bearing on the issues aired at this site, no more will be said about it here.

79. This alternative presents us with a small clue why it is that HM works --, and just where DM self-destructs. Clearly, only human beings (as individuals or as members of classes) can form aims and intentions (even if these are sometimes only dimly perceived); plainly, therefore, this fact would allow F67 to be re-written in a way that made it conducive to HM -- the exposition of which will not be attempted here.

80. To be fair, this problem afflicts every account of causality found in traditional Philosophy (Metaphysics), and not just DM. [This topic will be discussed in more detail in a later Essay.]

In that case, DM is merely the runt of this eminently traditional ruling-class litter.



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Weiner, P. (1968) (ed.), Dictionary Of The History Of Ideas: Studies Of Selected Pivotal Ideas (Scribner).

White, R. (1996), The Structure Of Metaphor (Blackwell).

Williams, L. (1980), The Origins Of Field Theory (University Press of America).

Wilczek, F. (2006), Fantastic Realities. 49 Mind Journeys And A Trip To Stockholm (World Scientific).

Williams, C. (1981), What Is Existence? (Oxford University Press). [This book can be accessed at Google Books, but the link is too long for me to embed it in this page!]

Wilson, J. (2007), 'Newtonian Forces', British Journal for the Philosophy of Science 58, 2, pp.173-205.

Wittgenstein, L. (1976), Wittgenstein's Lectures On The Foundation Of Mathematics: Cambridge 1939, edited by Cora Diamond (Harvester Press).

--------, (1978), Remarks On The Foundations Of Mathematics, edited by Elizabeth Anscombe (Blackwell, 3rd ed.).

--------, (1998), Culture And Value, edited by G. H. von Wright (Blackwell, 2nd ed.).

Woods, A., and Grant, T. (1995), Reason In Revolt. Marxism And Modern Science (Wellred Publications).

Zilsel, E. (2000), The Social Origins Of Modern Science (Kluwer Academic Press).

Word Count: 86,280

Latest Up-date: 07/12/08

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