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:
(a) Gravity Is Annoyingly Undialectical
(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
(c) A First Attempt At Clarification
(d) AR-Forces
(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?
(b) John Rees And Concrete Forces
(c) The Impertinent Explanation
(f) Not What The System Ordered
(g) An Apparent Contradiction At Last!
(6) Last Rites
(a) Dialectics In ER
(c) Dialectics And The Revival Of Teleology
(d) Coup De Grace
(e) For Dialectics, Truth Is The Hole, And It's Six Feet Deep
(8) Well, What Are 'Dialectical Contradictions' Anyway?
(a) The Best Article I Have Read
(b) Yet Another Syntactic Mess
(c) Rosa's Pedantry?
(e) Law Of Identity Mis-Identified
(f) More Dark Sayings From Hegel's Dungeon
(g) 'Difference' Made Unrecognisable
(h) The Fog Thickens
(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.
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]...is 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.
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 parts. Ex 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'.
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.
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