Essay Seven Part One
Engels's Three 'Laws' Of Dialectics
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'.
If you are viewing this with Mozilla Firefox you might not be able to read all the symbols I have used.
[A US comrade (Brian Jones) has attempted to respond to a letter I sent to the International Socialist Review about several of the issues raised in this Essay. You can read the original letter here, comrade Jones's reply here, and my response here. A UK comrade has also tried to respond to some of my criticisms. You can read the details here and here.]
This Essay is just under 95,000 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) Not Everything Changes In 'Leaps'
(3) Reciprocal?
(5) Awkward Facts Dialecticians Prefer To Ignore
(6) Isomers Refute First 'Law'
(7) Tautomers, Resonance And Mesomers -- More Nails In The Coffin?
(8) Counterexamples Just Keep Stacking-Up
(10) Trotsky In The Soup
(11) "Quality" Defined?
(12) Mickey Mouse Science
(B) The Interpenetration Of Opposites
(1) Why Dialectics Cannot Explain Change
(2) Is Everything Really A 'Unity Of Opposites'?
(3) Suicidal Cats
(4) Not Just Bad News For Cats
(5) Plastic Laws
(6) Lenin Maxes Out
(7) Single-celled Reactionaries?
(8) Every Confirmation Is Also A Refutation
(9) The Dialecticians' Dilemma
(10) The Revenge Of The Petty-Bourgeois Cell
(iii) Change Into What?
(iv) A New Theory?
(11) Engels, Marx And Mathematics
(12) Dialectics Meets The Calculus And Comes To Nought
(13) Dialectical -- Or Just Dotty?
(14) Second 'Law' Incompatible With The First?
(C) The Negation Of The Negation
(2) Terminator Four: The Rise Of Monsanto
(3) Socialism Introduced From Without -- Perhaps By Aliens
(D) Notes
(E) References
Abbreviations Used At This Site
The Three 'Laws'
For many dialecticians, "Three Laws Of Dialectics" encapsulate the core ideas of classical DM. Others regard these 'Laws' as far too crude and formulaic. TAR, however, takes a middle line, and downplays their significance somewhat, preferring to define DM in terms of mediated Totality, and change through internal contradiction, etc. [p.5.] Nevertheless, its author noted that:
"The 'three laws' are...useful reminders of forms in which dialectical contradictions sometimes work themselves out.... The three laws are not, even in Hegel, the only way in which dialectical development can take place. They cannot be understood without the broader definition of the dialectic discussed above [pp.3-8]. They are not, as Marx and Engels were quick to insist, a substitute for the difficult, empirical task of tracing the development of real contradictions, not a suprahistorical master key whose only advantage is to turn up where no real historical knowledge is available." [Rees (1998), pp.8-9.]
[DM = Dialectical Materialism; TAR = The Algebra of Revolution; i.e., Rees (1998).]
However, as Essay Two has shown, this is precisely how these 'Laws' (and other dialectical principles) have been interpreted by dialecticians for over a century: as just such a key.
Indeed, in a recent article in Socialist Review, John Rees endorsed this 'Law' unreservedly; on the basis of just one example (the hardy perennial, water freezing and/or boiling) he was happy to assert:
"Indeed this is a feature of many different sorts of change, even in the natural world. Water that rises in temperature by one degree at a time shows no dramatic change until it reaches boiling point when it "suddenly" becomes steam. At that point its whole nature is transformed from being a liquid into a vapour.
"Lower the temperature of water by a single degree at a time and again there is no dramatic change until it reaches freezing point, when it is transformed from a liquid into a solid -- ice.
"Dialecticians call this process the transformation of quantity into quality. Slow, gradual changes that do not add up to a transformation in the nature of a thing suddenly reach a tipping point when the whole nature of the thing is transformed into something new." [Rees (2008), p.24.]
From that, Rees "suddenly leaps" to this conclusion:
"This is why Marx described the dialectic as 'an abomination to the bourgeoisie' and why Lenin said of this method that it 'alone furnishes the key to "self-movement" of everything existing; it alone furnishes the key to "leaps", to the "break in continuity"...to the destruction of the old and the emergence of the new'". [Ibid. Bold emphasis added. Quotation marks altered to conform to the conventions adopted here.]
Yet more a priori dogmatism, based on little or no evidence -- as we will see, Rees ignores the many cases where "qualitative" change is not "sudden", just as he ignores the many examples where this 'Law' does not work.
Nevertheless, this Essay is aimed at showing that these 'Laws' are at best false, at worst terminally vague, and in the case of the last two, far too confused even to be assessed for their truth or falsehood.
They are certainly of no use at all in helping revolutionaries understand and therefore change the world.
Engels summarised these 'Laws' in the following way:
"The law of the transformation of quantity into quality, and vice versa; The law of the interpenetration of opposites; The law of the negation of the negation." [Engels (1954), p.62.]
Earlier, he had characterised them thus:
"Dialectics as the science of universal inter-connection. Main laws: transformation of quantity into quality -- mutual penetration of polar opposites and transformation into each other when carried to extremes -- development through contradiction or negation of the negation -- spiral form of development." [Ibid., p.17.]
Engels outlined his first 'Law' as follows:
"...[T]he transformation of quantity into quality and vice versa. For our purpose, we could express this by saying that in nature, in a manner exactly fixed for each individual case, qualitative changes can only occur by the quantitative addition or subtraction of matter or motion (so-called energy)…. Hence it is impossible to alter the quality of a body without addition or subtraction of matter or motion, i.e. without quantitative alteration of the body concerned." [Ibid., p.63. Emphasis added.]
But, exactly how Engels knew that it was impossible to "alter the quality of a body without addition or subtraction of matter or motion" he annoyingly kept to himself. His certainty can't have been based on the limited evidence available in his day, for there is no way it could have confirmed that it was "impossible" to alter the "quality" of a body in the way he says. Even the vastly increased body of data extant today can't show that this is an "impossibility".
Perhaps he was simply careless in his choice of words in these private notebooks? Maybe so, but no dialectician since has pointed this out: that it is not possible to derive an impossibility from a set of contingent data items, no matter how large that set is.
This puzzle is made all the more acute when we recall that for Engels, matter itself is just an abstraction [cf., Engels (1954), p.255]; in that case, it seems energy must be, too. If so, how can anything be altered by the addition (or subtraction) of an abstraction?
Even so, Engels did at least try to deny that his:
"...laws [have been] foisted on nature and history as laws of thought, and not deduced from them." [Ibid., p.62.]
He also declared:
"Finally, for me there could be no question of superimposing the laws of dialectics on nature but of discovering them in it and developing them from it." [Engels (1976), p.13. Bold emphasis added.]
But, his precipitous deduction of a necessary law (i.e., one that uses the word "impossible") from only a handful of cases -- largely drawn from certain areas of nineteenth century chemistry, buttressed merely by a few quirky, anecdotal examples taken from everyday life and/or from the popular science of Engels's day -- is a neat trick dialecticians alone seem capable of performing. Even if Engels had access to evidence several orders of magnitude greater than we have today, that would still not justify his use of "impossible" here.
Less partisan observers might be forgiven for concluding that Engels either did not know what the word "foisted" meant, or he hoped no one would notice when he actually indulged in a little of it himself.
Despite this, Engels already had an answer to this objection (and one he derived from Hegel):
"'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. 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, and no one talks of the eternal character of the laws of nature than the natural scientists.... All true knowledge of nature is knowledge of the eternal, the infinite, and hence the essentially absolute.
"...[This] can only take place in an infinite asymptotic progress." [Engels (1954), pp.234-35. Italic emphases in the original.]
However, since the scientists in Engels's day (from whose work he was generalising) were Christians, as was Hegel, you'd expect them to talk this way. But, their own conclusions (about these alleged "laws") do not follow from the evidence, any more than the existence of God does. As we will see in a later Essay, in their attempt to explain the content of their work to non-specialists, scientists often indulge in amateur Metaphysics, but this should no more influence us than their political opinions do. And, since scientists are constantly changing their minds over what these 'eternal' laws are, only the unwise would base their philosophy on shifting sands such as these.
As I argue in Essay Eight Part Two:
"How is it possible to translate the word 'infinite' as 'law-governed process'? Now Engels tries to equate the two, but an 'always' and 'at all times' are not 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 see this idea re-surface here in such Hermetically-compromised company. [On this see here, and here; the first is Swartz (2006), the second Swartz (2003).]" [This is quoted from here, as part of my demolition of this aspect of Hegel's a priori Superscience.]
Nevertheless, Engels's first 'Law' is at best only partially true; as we shall see, countless processes in nature in fact 'disobey' it, so it cannot be a law (in any sense of that word). Even where it seems to work, it does so only because Engels left several key terms undefined -- in which indeterminate state they remain to this day.
Engels's first 'Law' is supposed to work discontinuously (i.e., "nodally"), allowing nature and society to develop by making "leaps" (a term all DM-fans like to use, even while they leave it studiously vague).
Here is how Hegel depicted things:
"It is said, natura non facit saltum [there are no leaps in nature]; and ordinary thinking when it has to grasp a coming-to-be or a ceasing-to-be, fancies it has done so by representing it as a gradual emergence or disappearance. But we have seen that the alterations of being in general are not only the transition of one magnitude into another, but a transition from quality into quantity and vice versa, a becoming-other which is an interruption of gradualness and the production of something qualitatively different from the reality which preceded it. Water, in cooling, does not gradually harden as if it thickened like porridge, gradually solidifying until it reached the consistency of ice; it suddenly solidifies, all at once. It can remain quite fluid even at freezing point if it is standing undisturbed, and then a slight shock will bring it into the solid state." [Hegel (1999), p.370, §776. Bold emphasis added.]
And here is Engels:
"With this assurance Herr Dühring saves himself the trouble of saying anything further about the origin of life, although it might reasonably have been expected that a thinker who had traced the evolution of the world back to its self-equal state, and is so much at home on other celestial bodies, would have known exactly what's what also on this point. For the rest, however, the assurance he gives us is only half right unless it is completed by the Hegelian nodal line of measure relations which has already been mentioned. In spite of all gradualness, the transition from one form of motion to another always remains a leap, a decisive change. This is true of the transition from the mechanics of celestial bodies to that of smaller masses on a particular celestial body; it is equally true of the transition from the mechanics of masses to the mechanics of molecules -- including the forms of motion investigated in physics proper: heat, light, electricity, magnetism. In the same way, the transition from the physics of molecules to the physics of atoms -- chemistry -- in turn involves a decided leap; and this is even more clearly the case in the transition from ordinary chemical action to the chemism of albumen which we call life. Then within the sphere of life the leaps become ever more infrequent and imperceptible. -- Once again, therefore, it is Hegel who has to correct Herr Dühring." [Engels (1976), pp.82-83.I have used the online version here, but quoted the page numbers for the Foreign Languages edition. Bold emphasis added.]
"We have already seen earlier, when discussing world schematism, that in connection with this Hegelian nodal line of measure relations -- in which quantitative change suddenly passes at certain points into qualitative transformation -- Herr Dühring had a little accident: in a weak moment he himself recognised and made use of this line. We gave there one of the best-known examples -- that of the change of the aggregate states of water, which under normal atmospheric pressure changes at 0°C from the liquid into the solid state, and at 100°C from the liquid into the gaseous state, so that at both these turning-points the merely quantitative change of temperature brings about a qualitative change in the condition of the water." [Ibid., p.160. Bold emphasis added.]
Here, too, is Plekhanov:
"[I]t will be understood without difficulty by anyone who is in the least capable of dialectical thinking...[that] quantitative changes, accumulating gradually, lead in the end to changes of quality, and that these changes of quality represent leaps, interruptions in gradualness…. That is how all Nature acts…." [Plekhanov (1956), pp.74-77, 88, 163. Bold emphases alone added.]
And this is what Lenin had to say:
"The 'nodal line of measure relations' ... -- transitions of quantity into quality... Gradualness and leaps. And again...that gradualness explains nothing without leaps." [Lenin (1961), p.123. Lenin added in the margin here: "Leaps! Leaps! Leaps!"]
"What distinguishes the dialectical transition from the undialectical transition? The leap. The contradiction. The interruption of gradualness. The unity (identity) of Being and not-Being." [Ibid., p.282.]
"The identity of opposites (it would be more correct, perhaps, to say their 'unity,' -- although the difference between the terms identity and unity is not particularly important here. In a certain sense both are correct) is the recognition (discovery) of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature (including mind and society). The condition for the knowledge of all processes of the world in their 'self-movement,' in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the 'struggle' of opposites. The two basic (or two possible? Or two historically observable?) conceptions of development (evolution) are: development as decrease and increase, as repetition, and development as a unity of opposites (the division of a unity into mutually exclusive opposites and their reciprocal relation).
"In the first conception of motion, self-movement, its driving force, its source, its motive, remains in the shade (or this source is made external -- God, subject, etc.). In the second conception the chief attention is directed precisely to knowledge of the source of 'self'-movement.
"The first conception is lifeless, pale and dry. The second is living. The second alone furnishes the key to the 'self-movement' of everything existing; it alone furnishes the key to 'leaps,' to the 'break in continuity,' to the 'transformation into the opposite,' to the destruction of the old and the emergence of the new." [Ibid., pp.357-58. Quotation marks altered to conform to the conventions adopted here.]
Unfortunately for these dogmatists, many things in nature change qualitatively without passing through such "nodal points" -- and not even so much as a tiny "leap".
These include the following: melting or solidifying plastic, metal, rock, sulphur, tar, toffee, sugar, chocolate, wax, butter, cheese, and glass.01 As these are heated or cooled, they gradually change (from liquid to solid, or vice versa). There isn't even a "nodal point" with respect to balding heads! In fact, it is difficult to think of many state of matter transformations (from solid to liquid (or vice versa)) that exhibit just such "nodal points" -- and these include the transition from ice to water (and arguably also the condensation of steam). Even the albumen of fried or boiled eggs changes slowly (but non-"nodally") from clear to opaque white while they are being cooked.1
Naturally, all this depends on how the duration of a "nodal" point is defined. Unfortunately DM-fans have to this day failed to specify their length (nor have they even so much as mentioned their duration -- indeed, in discussions on the Internet, this objection wrong foots most DM-fans, so they either ignore it, or call it "pedantic"). Because of this dialecticians can safely indulge in some sloppy, off-the-cuff, a priori Superscience (as they all seem fond of doing -- hardly one fails to come up with his or her own favourite and/or idiosyncratic example, tested, of course, only in the laboratory of the mind, and studiously un-peer reviewed -- which is why I have called this part of DM: Mickey Mouse Science!).
[Since writing the above, I have discovered that this is not strictly true. The very first book I have encountered (in over 25 years of trawling through the wastelands of DM-literature) that actually tries to deal this 'difficulty' is Kuusinen (1961) -- which I first obtained in 2007. Several comments on this work can be found here.]
Another recent favourite example is Steven Jay Gould's theory of "Punctuated Equilibria". Unfortunately, amateur dialectical palaeontologists have failed to notice that the alleged "nodal" points here last tens of thousands of years, at least! This is a pretty unimpressive "leap" -- it's more like a painfully slow crawl. Snails on downers move faster!
Moreover, since no individual organism actually changes into a new species, there is no obvious object or body here which alters in quality, either, as quantitative variations accumulate. This contradicts Engels once more:
"Hence it is impossible to alter the quality of a body without addition or subtraction of matter or motion, i.e. without quantitative alteration of the body concerned." [Engels (1954), p.63. Emphasis added.]
Again, we seem to have neither an Hegelian nor yet an Aristotelian "substance" in which such "qualities" can inhere, and hence change. Worse still, it is not easy to see what the alleged quantities are supposed to be in this case.
It could be objected that these "quantities" are quite clearly the many minor variations that accumulate in populations of organisms, which lead at some point to a qualitative species-change. But, many small variations are qualitative already, and many of those occur in different organisms, not cumulatively in just one organism. And novel qualitative changes introduced by mutation cannot arise slowly (and then make a DM-"leap" after they have been accumulated), since they already appear suddenly. In other words, there is no slow gradual change here leading to a mutational "leap"; mutations themselves are sudden and qualitative.
So at least here we appear to have changes in quality caused by no changes in quantity!
In any case, what precisely is being slowly quantitatively accumulated here? And in what is all this occurring? No one supposes that if, for example, several hundred thousand Canada Geese all change colour slightly (for instance, if they all become slightly pinker), that these will all additively combine somehow into one big qualitative change (i.e., very deep pink in one of them!) --, or if, say, several thousand Red Deer can all run a little faster, that all these extra cm/sec increases in each animal will add to make an extra km/sec (in one specific deer).
Natural selection, of course, will filter out those populations of organisms that produce less (surviving) offspring, so that certain characteristics are preserved and then proliferate in the descendants of those who produce the most (or which survive the most). But, speciation is the result of much more complex processes than mere additive increase (even if we knew what was being 'added' here, DM-style). [On this, see Coyne and Orr (2004).]
On the other hand, if a species is to be regarded as an object in its own right -- perhaps stretched out in time, as some taxonomists picture things --,1a then that 'object' will only seem to alter as 'changes' accumulate. This is because, if a species is defined in this way (as a temporally-extended 'object'), then it can't actually change in any straight-forward sense. [To be sure, that depends on how we define the object in question and how we depict change.]
It is no surprise therefore to find both these notions are left impressively vague by those comrades who quote this example in support of the first 'Law', which is probably why they think they can get away with it. [For example, here.]
Hence, if a species is characterised in this way (as a sort of four-dimensional 'sausage' -- i.e., as a manifold in 4-space), then even if the first 'Law' actually applied to it, this 'species' won't have changed as a result of its 'internal contradictions', or as a result of anything else, for that matter. This is because such manifolds do not change; four-dimensional objects do not 'exist' in time to change -- time is one of their 'in-built' dimensions, as it were. Indeed, and on the contrary, 'time' exists in them, they neither perdure nor endure in it. Since everything temporally-true of this manifold is true of the whole of it 'all at once' (so to speak -- because it is a single four-dimensional 'object'), it cannot lose or gain properties or "qualities" --, unless, of course, we embed it in a fifth-dimension and (confusingly) call this new context "Time", too. [But then, of course, this five-dimensional 'object' would not change, and for the same reasons. More on this in Essay Eleven Part One.]
Without this extra-dimension, any predicates true of this four-dimensional manifold will stay true of it for good, for there is no past, present or future as far as this 'object' is concerned. In that case, 'change' would perhaps amount to no more than our subjective mis-perception of a 'succession' of orthogonal hyper-plane 'slices' through this manifold that we happen to experience.
[This forms part of the so-called "Block view of time". On this, see the PDF article here. Incidentally, I take no stance on this view of time here; I will, however, in a later Essay.]
As should now seem obvious, dialecticians can only afford to view the universe in this way if they are prepared to abandon their belief in change -- or consign the latter merely to our 'subjective' apprehension of reality.
Alternatively, if a species is not defined as a four-dimensional collective sort of 'object', then because no single organism actually evolves, change to a species would not be the result of its 'internal contradictions', once more -- since, on this view, such a species would be a certain sort of collection, not an object. Moreover, in populations, individual animals/plants do not change by "contradicting" one another, howsoever that word is understood. There are no 'internal contradictions' in such populations here to cause change (or, if there are any, dialecticians have yet to point them out). Indeed, no single thing actually changes in an evolutionary sense, only whole populations, and they manifestly do so non-dialectically.1b
In that case, not only is Gould's theory not an example of this 'Law' at work, not even Darwin's is.1c
Recently, dialecticians have appealed to Chaos and Catastrophe Theory in their endeavour to show that this nineteenth century 'Law' is bang up-to-date. Processes in nature studied in this branch of science clearly change rapidly. However, it is important to note that rapid change is neither being denied or asserted in this Essay. What is being challenged is the thesis that all change is "nodal". Some are, many are not. Moreover, as we will see, the term "quality" is defined in DM-circles in terms that would rule-out many of these catastrophic changes as 'dialectical'. This is because no new DM-"qualities" actually emerge in many such transitions.
For example, in the famous "three body" problem, whatever the outcome, the planetary bodies involved are still planets and they are still satellites; their orbits are still orbits. What new DM-"quality" has "emerged" in this case, then?
[Here is a JavaScript simulation. Indeed, the transitions here appear to be non-"nodal" -- you can alter the parameter in the top left hand corner of the page.]
Moreover, chaotic (turbulent) flows, either side of the alleged "node", are still flows, and the liquids/gases involved are still the same substance. No new Aristotelian/Hegelian "quality" has "emerged" here, either.
To be sure, some chaotic systems certainly seem to conform to this 'Law' -- but, this is only because the phrase "nodal change" has been left conveniently vague, and only because few dialecticians are prepared to ask awkward (but obvious) questions about what a DM-"quality" is supposed to be. [On that, see here and here.]
However, alternative scientific and/or mathematical models of reality explain chaotic systems (indeed, they do so with far more clarity) --, and they do not fall foul of the other examples listed in this Essay that refute this 'Law'.
Facts Dialecticians Usually Ignore
Now, the difficulties the first 'Law' faces do not stop here. For example, when heated, objects change in quality from cold to warm and then to hot, with no "nodal" point separating these particular qualitative stages. The same happens in reverse when they cool. Moving bodies similarly speed up from slow to fast (and vice versa) without any "nodal" punctuation marks affecting the transition. In like manner, the change from one colour to the next in the normal colour spectrum is continuous, with no "nodal" points evident at all -- and this is also the case with the colour changes that bodies experience when they are heated to red or white heat. Sounds, too, change smoothly from soft to loud, and back, in a "node"-free environment. In fact, with respect to wave-governed phenomena in general, change seems to be continuous rather than discrete, which means that since the majority of particles/objects in nature move in such a manner, most things in reality seem to disobey this aspect of Engels's unimpressive 'Law' -- at least, at the macroscopic level.
To be sure, some wave-like changes are said to occur discontinuously (indeed, the word "node" is used precisely here by Physicists), but this is not the result of continuous background changes. For example, quantum phenomena are notoriously discontinuous, but such changes are not normally preceded by continual quantitative increases. They occur suddenly with no build-up. So, discontinuous quantum phenomena cannot be made to fit this 'Law', unless it is altered just so that they can. Of course, that done, this 'Law' would no longer be 'objective'.
Several more comments on the application of this 'Law' to microscopic and/or quantum phenomena will be considered in detail here at a later date.
In that case, at best, the 'nodal' aspect of this 'Law' is either only partially true (of certain phenomena), while it fails to be true (of others).
Dialecticians often apply this "nodal" aspect of the first 'Law' to Capitalism -- in a bid to illustrate by analogy the revolutionary change from one Mode of Production to another, as quantity allegedly builds into quality, at some point initiating a sudden revolutionary 'leap'. [An excellent example of this can be found here, a more recent one is Rees (2008); another is located here.] But, how do we know that social changes like this are not like solid-to-liquid phase or state of matter transformation we witness in metals, glass and plastic; i.e., how do we know that they are not gradual? Since Capitalism is clearly not a liquid, but a solid of sorts, the transition to socialism should, on this analogy, go rather smoothly (on this see Note 9).
Interpreted that way, it looks as if the first 'Law' is of little use to revolutionaries since it clearly suggests that they are not needed, and that Capitalism can be reformed away non-discontinuously -- a bit like the way metal, say, can slowly melt, or in the way that heads can slowly turn bald as they lose their hair. But, if dialectical revolutionaries are not needed, their antiquated theory won't be either.
In that case, this aspect of dialectics seems to be responsible for issuing its own auto-redundancy notice.2
But, this 'Law' is in difficulties in other respects, too. Clearly not every change in quantity "passes over" into a change in quality. And yet, one way of reading the "vice versa" codicil attached to this law suggests that they should:
"The first law of the transformation of quantity into quality and vice versa. For our purpose, we could express this by saying that in nature, in a manner exactly fixed for each individual case, qualitative changes can only occur by the quantitative addition or subtraction of matter or motion (so-called energy)…. Hence it is impossible to alter the quality of a body without addition or subtraction of matter or motion, i.e. without quantitative alteration of the body concerned." [Engels (1954), p.63. Bold emphasis added.]
"Yet the 'mechanical' conception amounts to nothing else. It explains all change from change of place, all qualitative differences from quantitative ones, and overlooks that the relation of quality and quantity is reciprocal, that quality can become transformed into quantity just as much as quantity into quality, that, in fact, reciprocal action takes place." [Ibid., p.253. Bold emphasis added. Quotation marks altered to conform to the conventions adopted here.]
If this is so, then we should expect all changes in quantity to "pass over" into changes in quality (or there would seem to be no point to the vice versa codicil).
However, I have not been able to find a single DM-theorist who interprets this 'Law' in this way (i.e., "reciprocally", as Engels calls it), so perhaps I am the only one who has ever noticed this loop-hole (but it's more like a Grand Canyon) in this 'Law'. But, even if this were not so, it would still be difficult to explain why only some changes in quantity "pass over" into changes in quality. One will look in vain for any attempt to address this problem in the highly clichéd and repetitive writings of DM-fans (where quantity definitely does not morph into quality) -- or for some sort of vague recognition that such a difficulty even exists.
But, the "reciprocal" action of this 'Law' is hard to understand. Is Engels saying that a "qualitative" change in matter passes over into "quantity", that is, that say, the change from, say, liquid water to steam, adds energy to the process? Or that, bald heads make them lose hair? If not, it is not easy to see what this "reciprocal" aspect implies. [More on this later.]
As we devote more thought to this 'Law' several problems arise: for example, the same number of molecules at the same energy level can exhibit widely differing properties/qualities depending on circumstances. Think of how the same amount of water can act as a lubricant, or have the opposite effect, say, on wet clothes; the same amount of sand can help some things slide, but prevent others from doing so; the same amount of poison given over a short space of time will kill, but given over a longer period (in small doses) it could benefit the recipient -- Strychnine comes to mind here.
To be sure, the effects of quantitative stasis of this sort (supervenient on qualitative change) are sensitive both to temporal constraints and to levels of concentration (of the substances involved); but this extremely vague first 'Law' said nothing of these. And, try as one might, it is not easy to see how these eminently material aspects of nature can be accommodated to the Ideal dialectical universe Engels (semi-)uncritically inherited from Hegel.
But, what sort of scientific 'Law' leaves details like this out? In fact, if a Mickey Mouse 'Law' like this were to appear in any of the genuine sciences, it would be treated with derision -- even if it had been aired in an undergraduate paper!
However, other recalcitrant examples rapidly spring to mind: if the same colour is stared at for several minutes it can undergo a qualitative change into another colour (several optical illusions are based on this fact). Something similar can happen with regard to many two-dimensional patterns and shapes (for example the Necker Cube and other optical illusions); these undergo considerable qualitative change when no obvious quantitative differences are involved. There thus seem to be numerous examples where quantity and quality do not appear to be connected in the way that DM-theorists would have us believe.3
In fact, there are so many exceptions to this 'Law' that it would be wise to demote it and consign it to a more appropriate category, perhaps along with the trite rules of thumb that sometimes work -- a bit like "An apple a day keeps the doctor away", or even "A watched kettle never boils".
Indeed, given the fact that this 'Law' has no discernible mathematical content it is rather surprising it was ever called a "law" to begin with.
Nevertheless, the situation is even worse than the above might suggest; there are countless examples where significant qualitative change can result from no obvious quantitative difference. These include the qualitative dissimilarities that exist between different chemicals for the same quantity of matter/energy involved.
For instance, Isomeric molecules (studied in stereochemistry) are a particularly good example of this phenomenon. This is especially true of those that have so-called "chiral" centres (i.e., centres of asymmetry). In such cases, the spatial ordering of the constituent atoms, not their quantity, affects the overall quality of the resulting molecule (something Engels said could not happen). Here, a change in molecular orientation, not quantity, effects a change in quality.
To take one example of many: (R)-Carvone (spearmint) and (S)-Carvone (caraway); these molecules have the same number of atoms (of the same elements), and the same bond energies, but they are nonetheless qualitatively distinct because of the different spatial arrangement of the atoms involved. Change in geometry -- change in quality.
This un-dialectical aspect of matter is especially true of the so-called "Enantiomers" (i.e., symmetrical molecules that are mirror images of each other). These include compounds like (R)-2-clorobutane and (S)-2-chlorobutane, and the so-called L- and D-molecules, which rotate the plane of polarised light the left (laevo) or the right (dextro)) -- such as, L- and D-Tartaric acid. What might at first sight appear to be small energy-neutral differences like these have profound biochemical implications; a protein with D-amino acids instead of L- will not work in most living cells since the overwhelming majority of organisms metabolise L-organic molecules. These compounds not only have the same number of atoms in each molecule, there are no apparent energy differences between them; even so, they have easily distinguishable physical qualities.
Change in quality -- identical quantity.4
In response, it could be argued that Engels had already anticipated the above:
"It is surely hardly necessary to point out that the various allotropic and aggregational states of bodies, because they depend on various groupings of the molecules, depend on greater or lesser quantities of motion communicated to the bodies.
"But what is the position in regard to change of form of motion, or so-called energy? If we change heat into mechanical motion or vice versa, is not the quality altered while the quantity remains the same? Quite correct. But it is with change of form of motion...; anyone can be virtuous by himself, for vices two are always necessary. Change of form of motion is always a process that takes place between at least two bodies, of which one loses a definite quantity of motion of one quality (e.g. heat), while the other gains a corresponding quantity of motion of another quality (mechanical motion, electricity, chemical decomposition). Here, therefore, quantity and quality mutually correspond to each other. So far it has not been found possible to convert motion from one form to another inside a single isolated body." [Ibid., pp.63-64. Bold emphases added.]
However, Engels slides between two different senses of "motion" here: (1) change of place, and (2) energy. In this way, he is able to argue that any change in the relation between bodies always amounts to a change in energy. But, this depends on the nature of the field in which these bodies are embedded (on this, see below, and in Note 4a); Engels's profound lack of mathematical knowledge clearly let him down here.
Independently of this, Engels also confused the expenditure of energy with energy added to a system. The difference between the two is easy to see. Imagine someone pushing a heavy packing case along a level floor. In order to overcome friction, the one doing the pushing will have to expend energy. But that energy has not been put into the packing case (as it were). Now, if the same case is pushed up a hill, Physicists tell us that recoverable energy has been put into the case in the form of Potential Energy.
Now, as far as can be ascertained (but again, they are not at all clear on this), in the examples of interest to dialecticians, it is the latter form of energy (but not necessarily always Potential Energy) that is relevant, not the former. The former sort does not really change the quality of any bodies concerned; the latter does. If that is so, then the above counter-examples (e.g., the Enantiomers) still apply, for the energy expended in order to change one isomer into another is generally the first sort, not the second.
To be sure, some of the energy in the packing case example will appear as heat (and/or perhaps sound), and will warm that case slightly. But that energy will not be stored in the case as chemically recoverable (i.e., structural, or new bond) energy.
Despite this, a few die-hard dialecticians might want to argue that any expenditure of energy is relevant here. That would be an unfortunate move since it would make this 'Law' trivial, for in that case it would amount to the belief that any change at all (no matter how remote), since it involves the expenditure of some form of energy somewhere (but not necessarily energy put 'into' the bodies concerned), is the cause of qualitative change to other bodies somewhere else. This would make a mockery of Engels's claim that only energy added to the bodies concerned is relevant to this 'Law'.
"Change of form of motion is always a process that takes place between at least two bodies, of which one loses a definite quantity of motion of one quality (e.g. heat), while the other gains a corresponding quantity of motion of another quality (mechanical motion, electricity, chemical decomposition)." [Ibid. Bold emphasis added.]
Several examples of this sort of change are given below. The problems these create are discussed at length in Note 5 and Note 6a, where attempts to delineate the boundaries of the local energy budget involved (which would have to be specified in order to prevent remote objects/energy expenditure being allowed to cause proximate change) are all shown to fail.
Moreover, and more significantly, Engels himself considered isomers as an example of the 'Law', even though there is no "development" in this case! [On that, see here.]
Finally, Engels seems to think it is always clear what a single body actually is:
"Here, therefore, quantity and quality mutually correspond to each other. So far it has not been found possible to convert motion from one form to another inside a single isolated body." [Ibid.]
However, nature is not quite so accommodating. In fact, when we look at the material world, and refuse to impose an a priori schema on it, we see that the picture is not as straightforward as Engels would have us believe. Indeed, as we will also see, it is easy "to convert motion from one form to another inside a single isolated body." The reader is again directed to Note 5 and Note 6a for more details.
Tautomers, Resonance And Mesomers
Even more embarrassing for this 'Law' are tautomers; these feature an:
"isomerism in which the isomers change into one another with great ease so that they ordinarily exist together in equilibrium." [Quoted from here.]
Wikipedia characterises them in the following way:
"Tautomers are organic compounds that are interconvertible by a chemical reaction called tautomerization. As most commonly encountered, this reaction results in the formal migration of a hydrogen atom or proton, accompanied by a switch of a single bond and adjacent double bond. In solutions where tautomerization is possible, a chemical equilibrium of the tautomers will be reached. The exact ratio of the tautomers depends on several factors, including temperature, solvent, and pH. The concept of tautomers that are interconvertible by tautomerizations is called tautomerism. Tautomerism is a special case of structural isomerism and can play an important role in non-canonical base pairing in DNA and especially RNA molecules.
"Tautomerizations are catalyzed by:
"1. base (a. deprotonation; b. formation of a delocalized anion (e.g. an enolate); c. protonation at a different position of the anion).
"2. acids (a. protonation; b. formation of a delocalized cation; c. deprotonation at a different position adjacent to the cation).
"Common tautomeric pairs are:
"3. ketone -- enol, e.g. for acetone (see: keto-enol tautomerism).
"4. amide -- imidic acid, e.g. during nitrile hydrolysis reactions.
"5. lactam -- lactim, an amide -- imidic acid tautomerism in heterocyclic rings, e.g. in the nucleobases guanine, thymine, and cytosine.
"7. enamine -- enamine, e.g. during pyridoxalphosphate catalyzed enzymatic reactions.
"Prototropic tautomerism refers to the relocation of a proton, as in the above examples, and may be considered a subset of acid-base behaviour. Prototropic tautomers are sets of isomeric protonation states with the same empirical formula and total charge.
"Annular tautomerism is a type of prototropic tautomerism where a proton can occupy two or more positions of a heterocyclic system. for example, 1H- and 3H-imidazole; 1H-, 2H- and 4H- 1,2,4-triazole; 1H- and 2H- isoindole.
"Ring-chain tautomerism occurs when the movement of the proton is accompanied by a change from an open structure to a ring, such as the aldehyde and pyran forms of glucose.
"Valence tautomerism is distinct from prototropic tautomerism, and involves processes with rapid reorganisation of bonding electrons. An example of this type of tautomerism can be found in bullvalene. Another example is open and closed forms of certain heterocycles, such as azide -- tetrazole. Valence tautomerism requires a change in molecular geometry and should not be confused with canonical resonance structures or mesomers." [Quoted from here; accessed 05/10/08. Paragraph numbering altered; spelling changed to conform to UK English.]
One standard Organic text defines tautomers as follows:
"Tautomers are isomers differing only in the position of hydrogen atoms and electrons. Otherwise the carbon skeleton is the same." [Clayden et al (2001), p.205.]
On enol tautomerism, it adds:
"In the case of dimedone, the enol must be formed by a transfer of a proton from the central CH2 group of the keto form to one of the OH groups.
"Notice that there is no change in pH -- a proton is lost from carbon and gained on oxygen. The reaction is known as enolization as it is the conversion of a carbonyl compound into an enol. It is a strange reaction in which little happens. The product is almost always the same as the starting material since the only change is the transfer of one proton and the shift of the double bond." [Ibid., pp.524-25.]
Even though many of these reactions require catalysts (which add no energy or matter to the original compounds), these are qualitatively different substances, refuting the first 'Law'. This is a particularly intractable series of counter-examples because it involves the "development" of one substance into another.
Resonance (mesomerism) is more controversial,4a0 but no less fatal to this 'Law':
"Though resonance is often introduced in such a diagrammatic form in elementary chemistry, it actually has a deeper significance in the mathematical formalism of valence bond theory (VB). When a molecule cannot be represented by the standard tools of valence bond theory (promotion, hybridisation, orbital overlap, sigma and pi bond formation) because no single structure predicted by VB can account for all the properties of the molecule, one invokes the concept of resonance.
"Valence bond theory gives us a model for benzene where each carbon atom makes two sigma bonds with its neighbouring carbon atoms and one with a hydrogen atom. But since carbon is tetravalent, it has the ability to form one more bond. In VB it can form this extra bond with either of the neighbouring carbon atoms, giving rise to the familiar Kekulé ring structure. But this cannot account for all carbon-carbon bond lengths being equal in benzene. A solution is to write the actual wavefunction of the molecule as a linear superposition of the two possible Kekulé structures (or rather the wavefunctions representing these structures), creating a wavefunction that is neither of its components but rather a superposition of them, just as in the vector analogy above (which is formally equivalent to this situation).
"In benzene both Kekulé structures have equal weight, but this need not be the case. In general, the superposition is written with undetermined constant coefficients, which are then variationally optimized to find the lowest possible energy for the given set of basis wavefunctions. This is taken to be the best approximation that can be made to the real structure, though a better one may be made with addition of more structures.
"In molecular orbital theory, the main alternative to VB, resonance often (but not always) translates to a delocalization of electrons in pi orbitals (which are a separate concept from pi bonds in VB). For example, in benzene, the MO model gives us 6 pi electrons completely delocalised over all 6 carbon atoms, thus contributing something like half-bonds. This MO interpretation has inspired the picture of the benzene ring as a hexagon with a circle inside. Often when describing benzene the VB picture and the MO picture are intermixed, talking both about localized sigma 'bonds' (strictly a concept from VB) and 'delocalized' pi electrons (strictly a concept from MO)." [Quoted from here; accessed 05/10/08.]
Figure One: Examples Of Resonance
In view of the fact that these are distinct qualitative variations on a common theme, created by no new energy or matter, it seems that this luckless first 'Law' is refuted once more.
Counter-Examples Just Keep Stacking-Up
Moving into Physics: if two or more forces are aligned differently, the qualitative results will invariably be altered (even when the overall magnitude of each force is held constant).
Consider just one example: let forces F1 and F2 be situated in parallel (but not along the same line of action), but diametrically opposed to one another. Here these two forces can exercise a turning effect on a suitably placed body. Now, arrange the same two forces in like manner so that they are still parallel, but act diametrically along the same line. In this case, as seems clear, these forces will have no turning effect on the same body. Change in quality with no change in quantity, once more. Since there are many ways to align forces (as there are with other vector quantities, like velocities and accelerations, etc.), there are countless counter-examples to this rather pathetic first 'Law' here alone.4a
Perhaps more significantly, this 'Law' takes no account of qualitative changes that result from (energetically-neutral) ordering relations in nature and society. Here, identical physical structures and processes can be ordered differently to create significant qualitative changes. One example is the different ordering principles found in music, where an alteration to a sequence of the same notes in a chord or in a melody can have a major qualitative impact on harmony, with no quantitative change anywhere apparent. So, the same seven notes (i.e., tones and semi-tones) arranged in different modes (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aolean and Locrian) sound totally different to the human ear. Of course, there are other ways of altering the quality of music in an energetically neutral environment over and above this (such as timing).
Another example along the same lines concerns the ordering principles found in language, where significant qualitative changes can result from the re-arrangement of the same parts of speech. For instance, the same number of letters jumbled up can either make sense or no sense -- as in "dialectics" and "csdileati" (which is "dialectics" scrambled up; but, which one of these two makes the more sense I will leave to the reader to decide).
Perhaps more radically, the same words can mean something qualitatively new if sequenced differently, as in, say: "The cat is on the mat" and "The mat is on the cat". Or, even worse: "It is impossible to understand Marx's Capital, and especially its first chapter, without having thoroughly studied and understood the whole of Hegel's Logic", compared with "It is impossible to understand Hegel's Logic, and especially its first chapter, without having thoroughly studied and understood the whole of Marx's Capital." Here there is considerable qualitative difference with no quantitative change at all.
[What are the odds that Engels would have tried to alter his first 'Law' to counter that awkward fact?]
There are many other examples of this phenomenon, but a few more should suffice for the purposes of this web site: a successful strike (one that is, say, planned first then actioned second) could turn into its opposite (if it is actioned first and planned second). Now even though the total energy input here would be ordered differently in each case, the overall energy budget of the system (howsoever that is characterised) need not be any different. So, the addition of no extra matter or energy here can turn successful action into disaster if the order of events is reversed. Of course, we can all imagine situations where this particular example could involve different energy budgets, but this is not necessarily the case, which is all I need.
There are literally thousands of everyday examples of such qualitative changes (where there are no obvious associated quantitative differences), so many in fact that Engels's first 'Law' begins to look even more pathetic in comparison. Who for example would put food on the table then a plate on top of it? A change in the order here would constitute a qualitatively different (and more normal) act: plate first, food second. Which of us would jump out of an aeroplane first and put their parachute on second -- or cross a road first, look second? And is there a sane person on the planet who goes to the toilet first and gets out of bed second? Moreover, only an idiot would pour 500 ml of water slowly into 1000 ml of concentrated Sulphuric Acid, whereas, someone who knew what they were doing would readily do the reverse. But all of these have profound qualitative differences if performed in the wrong order (for the same energy budget).5
How could Engels have missed examples like these? Is dialectical myopia so crippling that it prevents dialecticians using their common sense?
Pushing these ideas further: context, too, can affect quality in a quantitatively neutral environment. So, a dead body in a living room has a different qualitative significance compared to that same body in the morgue (for the same energy input). A million pounds in my bank account has a different qualitative feel to it if compared to the same money in your account (and vice versa). "Ceci nest pa une pipe" has a different qualitative aspect if appended to a picture of a pipe, compared to being attached to a picture of, say, a cigarette.
Indeed, "Ceci nest pa une pipe" itself can change from qualitatively false to true depending on how it is interpreted. Hence, as a depiction of what the painting by Magritte is about (i.e., a pipe) it is false. But, despite this, it is also literally true, since manifestly a picture of a pipe is not a pipe! Change in quality here, but no change in quantity.6
Figure Two: Gallic Refutation
Furthermore, qualitative change can be induced by other qualitative changes, contrary to Engels's claim:
"...[Q]ualitative changes can only occur by the quantitative addition or subtraction of matter or motion...." [Engels (1954), p.63. Emphasis added]
For example, in a 1:1 mixture of paint, one litre of brown can be made by mixing two half litres each of red and green, but the same qualitative effect can be achieved by using less or more of both (say, 2 litres of each), but in the same ratio. Here a change in the quantity of mixed paints has no effect on the qualitative properties of the mixture (i.e., its colour), while the qualities mixed do. In this case, two qualities (two colours) will have changed into a new quality (a new colour) when mixed. Not only do the same amounts (and proportions) of red and green paint exist before and after mixing, for any fixed amount of each, the two former qualities will have merged into a single one. Qualitative change produced by qualitative change.
Of course, it could be argued that the mixture contains more paint than before (which means that there actually has been a quantitative change), but this is not so. In general, prior to mixing there were n litres of each colour (and 2n litres of both) preserving the 1:1 ratio; after mixing the same amount of paint still exists, namely n litres of each (and 2n litres of both, for any n), still preserving the 1:1 proportion. The qualitative change in colour has nothing to do with the quantities involved, but everything to do with the mixing of the two previous qualities in the same ratio.
To be sure, if the ratio of the mixed paints were changed, a different qualitative outcome would emerge, but as noted above, even this does not happen "nodally", and so it seems to be of little relevance to the first 'Law'. But, if the ratio is kept the same, we would have here a change in quality created by qualities only, and not by an increase in quantity.6a
Something similar can be achieved with the mixing of most chemicals, as it can with light, sound and taste.7
Matter in general is thus reassuringly non-dialectical.
Other instances of qualitative change where there is no implied change in quantity include the following: the "Big Bang" (if it actually happened) led to the formation of a whole universe of qualitative changes, with no overall increase in energy or matter (in the universe). Now, here we have a massive change in quality (with Galaxies and planets, and all the rest, emerging out of the original debris) with no overall change in the quantity of energy (in the universe) --, unless, of course, we think to alter energy conservation laws just to save DM's neck.
On the other hand, if the 'Big Bang' is rejected, and an infinite universe is postulated, since there can be no increase in energy in the entire universe, any qualitative changes in nature will occur with no increase in universal energy.
More counter-examples rapidly stack up: a child living in, say, Paris can become an orphan (qualitative change) if both of its parents die in South Africa (meaning that no quantitative change will have happened to that child -- unless, of course, we are meant to re-interpret a change in a distant geographical/familial relation as a quantitative change).
The largest cut diamond on earth (in a safe, say, in New York) could change into the second biggest if another bigger diamond is cut in, say, Amsterdam. This example also applies to other remote changes. For example, the biggest star in a galaxy could become the second biggest if another star hundreds of millions of light years away (but in the same galaxy) grows in size (perhaps over millions of years) through accretion of matter. So, in both cases, there would be a qualitative change to the first object with no relevant matter or energy added or subtracted from/to that object. There are countless examples of remote change like this.
A cheque drawn, say, in New York will become instantaneously worthless (qualitative change) if the issuing bank in Tokyo goes bust (meaning that no quantitative change will have happened to that cheque).
A Silver Medallist in, say, the Olympics can become the Gold Medal winner in an event (qualitative change) if the former Gold medallist is disqualified because of drug-taking (meaning that no quantitative change will have occurred to that Silver Medallist).
Two identical "Keep off the Grass" signs can mean something different (qualitative change) if one of them is posted on a garden lawn and the other is positioned near a stand of Marijuana plants, at the same height above sea level (thus with no difference in energy).
A circle looks like an ellipse (qualitative change) when viewed from certain angles for no change in energy.
The same three mathematical (or physical) points can undergo a qualitative change if, say, from being arranged linearly they are then re-arranged as the corners of a triangle (with no energy added to these points). Here, there would be a qualitative change with no quantitative change, once again. There are, of course, a potentially infinite number of examples of that sort of change imaginable for 2-, or 3-dimensional shapes, for n points (be they mathematical or physical -- so this is not necessarily an abstract set of counter-instances).8
In The Soup, And Vice Versa
Worse still, as we saw earlier, the aforementioned "reciprocal" "vice versa" codicil attached by Engels to this 'Law' renders it totally useless -- if not completely crazy --, for it suggests, for instance, that qualitative change can effect quantitative material change. Consider this example of Trotsky's:
"A housewife knows that a certain amount of salt flavours soup agreeably, but that added salt makes the soup unpalatable. Consequently, an illiterate peasant woman guides herself in cooking soup by the Hegelian law of the transformation of quantity into quality…." [Trotsky (1971), p.106.]
Now, this is not an unsympathetic interpretation on my part, for, as we have already seen, Engels himself signed up to it:
"Yet the 'mechanical' conception amounts to nothing else. It explains all change from change of place, all qualitative differences from quantitative ones, and overlooks that the relation of quality and quantity is reciprocal, that quality can become transformed into quantity just as much as quantity into quality, that, in fact, reciprocal action takes place." [Engels (1954) p.253. Bold emphasis added; quotation marks altered to conform to the conventions adopted here.]
And so did Novack:
"The dialectical process of development does not end with the transformation of quantity into quality…. The process continues in the opposite direction and converts new quality into new quantity." [Novack (1971), p.92.]
This suggest that changes in quality should induce quantitative changes, that is, that new matter or energy should be created merely by qualitative change!
Hence, if this vice versa codicil is to work here, a qualitative change from, say, unpalatable soup to tasty-soup would in effect produce a quantitative pay-off: it must cause soup to have more salt in it! Clearly this magic trick will be of interest to those who still (foolishly) think that matter and energy cannot be created ex nihilo. And yet there seems to be no other way of reading the vice versa codicil except as just such a 'metaphysical blank cheque'.
Nevertheless, it is worth examining Trotsky's anecdote more closely, since it will help expose the many serious errors and confusions that afflict even the few examples dialecticians have scraped-together to illustrate their 'Law.'
"Every individual is a dialectician to some extent or other, in most cases, unconsciously. A housewife knows that a certain amount of salt flavours soup agreeably, but that added salt makes the soup unpalatable. Consequently, an illiterate peasant woman guides herself in cooking soup by the Hegelian law of the transformation of quantity into quality…. Even animals arrive at their practical conclusions…on the basis of the Hegelian dialectic. Thus a fox is aware that quadrupeds and birds are nutritious and tasty…. When the same fox, however, encounters the first animal which exceeds it in size, for example, a wolf, it quickly concludes that quantity passes into quality, and turns to flee. Clearly, the legs of a fox are equipped with Hegelian tendencies, even if not fully conscious ones. All this demonstrates, in passing, that our methods of thought, both formal logic and the dialectic, are not arbitrary constructions of our reason but rather expressions of the actual inter-relationships in nature itself. In this sense the universe is permeated with ‘unconscious’ dialectics." [Trotsky (1971), pp.106-07.]
But, what exactly did Trotsky imagine the change of quantity into quality to be, here?
Does an increase in the quantity of salt alter its own quality? Presumably not. Does the quantity of soup change? Perhaps only marginally; but even so, the quantity of soup is not what allegedly changed its own quality -- that is supposed to have resulted from the quantity of salt added.
In fact, the quantity of the original soup has not actually changed -- merely the quantity of the salt/soup mixture --; and neither has the quality of the salt altered (just its alleged quantity).
What appears to have happened (in this less than half-formed 'thought experiment') is that the addition of too much salt to the soup is supposed to change the taste of the resulting salt/soup mixture as it is experienced by the taster (perhaps the woman in this case). Hence, at a certain ("nodal") point, an increase in the quantity of salt alters the quality (i.e., the taste) of the soup, so that its acceptability changes either side of that point.
But once more, even here the increased quantity of the salt has not passed over into any change in its own quality. What has occurred is that one quality (a palatable taste) has morphed into another quality (an unpalatable taste) as a result of a quantitative change made to one ingredient (salt) added to the salt/soup mixture. So, a certain quality of the soup has changed from being acceptable to being unacceptable as a result of the increased quantity of salt the mixture contains.
However, the relevant quality of the added salt remains the same no matter how much is added. Salt is Sodium Chloride (largely), and it tastes salty whether it is delivered by the spoon, the bucket or the train-load. In that case, neither the quantity nor the quality of the salt has "passed over" into anything; there does not therefore seem to be anything in the initial part of this story for that particular aspect of the salt to "pass over" into.
Consequently, the first half of this 'Law' is either mis-stated or it does not apply in this case.
As far as the second half is concerned (i.e., the alleged alteration in quality), the postulated change relates to the taste of the soup. But manifestly, the soup remains salty no matter how much salt is poured in, as we saw. What we have here is a batch of soup that becomes increasingly salty as more salt is added.
What qualitative change then is meant to have taken place? Again, it seems that this change relates to the acceptability of the taste of the soup as perceived by the taster. Hence, at -- or slightly beyond -- the alleged "nodal" point, the taste of the soup will become objectionable to this taster. But if so, this particular change is surely confined to the one doing the tasting. Manifestly, it is not the soup that alters in this respect. On one side of the "nodal" point the soup is objectively salty (i.e., it contains dissolved salt); on the other side it is still objectively salty, but with more salt in it. The difference is that on one side, the taster tolerated the taste and continued to like it, but on the other side the taste became intolerable and she ceased to enjoy what she was eating. So, this means that the soup itself has not actually changed in this respect, merely the taster's appreciation of it that has.
So, it now seems that a change in the quantity (of salt) does not actually affect the soup –- except, perhaps, its volume (very slightly), and its composition as a salt/soup mixture. No matter how much salt is dumped into the soup it remains just that, a salt/soup mixture, only with higher proportions of the former ingredient -– and this is so even at the limit where it perhaps turns into sludge or a semi-solid lump, or whatever. A trillion tons of salt can't change that.8a
Consequently, even with respect to the relevant quality (interpreting the latter as this salt/soup mixture, if it can be so described), the concoction does not change (or, at least, not in a way that is relevant to Trotsky's purposes). Hence, a change in the quantity of salt has not "passed over" into a change in the quality of the soup (as soup), which means that the second part of this 'Law' seems to be defective, too.
If there is a qualitative change anywhere here at all (that is relevant to the point Trotsky is making) it seems to occur in the third party -– that is, in the taster. We are forced to interpret things this way unless, of course, we are to suppose that tastes actually reside 'objectively' in soups, as one of their alleged 'primary' qualities. If that were so, qualities like this (that reside in soups, and not solely in tasters) would have to be able to alter 'objectively', even when they are not being tasted! But, it can't mean that; no sane dialectician (one imagines!) believes that tastes reside in the objects we eat. Hence, if this 'Law' is to work in this case, the qualitative change must be said to reside in the soup-taster, not the soup.8b
If so, that aspect of the change here must have been induced by a quantitative change in the taster, if the 'Law' is to apply to her. But, what quantitative change could have taken place in this taster that might have prompted a corresponding change in (her) quality, or in her changed perception of a quality? Apparently none at all -- or, none that Trotsky mentioned, and none that is obvious.
Plainly here, it was a quantitative change in the salt/soup mixture that altered its quality as it was apparent to that taster, but it had no effect on a quality actually in the soup (as previous comments sought to show -- tastes do not reside in soups!). But, once again, there would now seem to be no quantitative change in the taster that initiated a corresponding qualitative change in her.
In that case, the best that can be made of this half-baked example is that while quantitative change leads to no qualitative change in some things (i.e., soups), it can prompt certain 'qualitative' changes in other things (i.e., tasters), the latter of which were not caused by any quantitative changes in those things themselves, but by something altogether mysterious.
So, the second part of the 'Law' is now doubly defective.
Of course, it could be objected that there is indeed a quantitative change in the said taster, namely the quantitative increase in salt atoms hitting her tongue. But, this just pushes the problem one stage further back, for unless we are to suppose that tastes reside in salt molecules (or in Sodium and Chlorine ions), the qualitative change we seek will still have occurred in the taster and not in the chemicals in her mouth -- and we are back where we were earlier. There seems to be no quantitative change to the taster apparent here; she does not grow another tongue or gain some more taste buds. It is undeniable that there will have been an increase in salt molecules hitting her tongue, and that these will have a causal effect on the change of taste as she perceives it, but even given all that, no change in quantity to the taster herself will have occurred.
Again, it could be objected that there is a material/energetic change here; matter or energy will have been transferred to the taster (and/or her central nervous system) which causes her to experience a qualitative change in her appreciation of the soup.
In fact, what has happened is that the original salt has merged/interacted with the taster's tongue/nervous system upon being ingested. But, it is at precisely that point that the earlier problems associated with the salt/soup mixture now transfer to the salt/nervous system 'mixture'. Since tastes do not exist in nerves any more than they exist in soups, we are no further forward. And as far as changes to the quantity of the taster is concerned, this will depend on how we draw the boundaries between inorganic salt molecules and living cells. Since this is considered in more detail below, no more will be said about it here.
In any case, it seems rather odd to describe a change in taste (or in the appreciation of taste) as a qualitative change to a taster, whatever caused it. As the term "quality" is understood by dialecticians, this cannot actually be a qualitative change of the sort they require. Qualities, as characterised by dialecticians (or, rather, by those that bother to say what they mean by this word), are those properties of bodies/processes that make them what they are, alteration to which will change that body/process into something else:
"Each of the three spheres of the logical idea proves to be a systematic whole of thought-terms, and a phase of the Absolute. This is the case with Being, containing the three grades of quality, quantity and measure.
"Quality is, in the first place, the character identical with being: so identical that a thing ceases to be what it is, if it loses its quality. Quantity, on the contrary, is the character external to being, and does not affect the being at all. Thus, e.g. a house remains what it is, whether it be greater or smaller; and red remains red, whether it be brighter or darker." [Hegel (1975), p.124, §85.]
As the Glossary at the Marx Internet Archive notes:
"Quality is an aspect of something by which it is what it is and not something else and reflects that which is stable amidst variation. Quantity is an aspect of something which may change (become more or less) without the thing thereby becoming something else.
"Thus, if something changes to an extent that it is no longer the same kind of thing, this is a 'qualitative change', whereas a change in something by which it still the same thing, though more or less, bigger or smaller, is a 'quantitative change'.
"In Hegel's Logic, Quality is the first division of Being, when the world is just one thing after another, so to speak, while Quantity is the second division, where perception has progressed to the point of recognising what is stable within the ups and downs of things. The third and final stage, Measure, the unity of quality and quantity, denotes the knowledge of just when quantitative change becomes qualitative change." [Quoted from here.]
This is an Aristotelian notion (more on this in another Essay). As Kuusinen points out:
"The totality of essential features that make a particular thing or phenomenon what it is and distinguishes it from others, is called its quality.... It is...[a] concept that denotes the inseparable distinguishing features, the inner structure, constituting the definiteness of a phenomenon and without which it cease to be what it is." [Kuusinen (1961), pp.83-84. Italic emphasis in the original.]
But, it is not at all clear that someone's liking/not liking soup defines them as a person -- or as a being of a particular sort. While scientists might decide to classify certain aspects of nature (placing them in whatever categories they see fit), none, as far as I am aware, has so far identified two different sorts of human beings: "soup-likers for n milligrams of salt per m litres of soup versus soup-dislikers for the same or different n or m". And even if they were to do this, that would save this part of DM by mere re-definition, since it is reasonably clear that these two different sorts of human beings do not actually exist -- , or, at least, they didn't until I just invented them. Once again, that would make this part of DM eminently subjective, since it indicates that changes in quality are now relative to an observer's choice of descriptive framework. Plainly, this introduces a fundamental element of arbitrariness into what dialecticians claim to be a scientific law.
If so, this particular change cannot apply to any of the qualities governed by DM/Hegelian principles (even if we knew what these were, and even if there were any). So, it now seems that this putative example of Q«Q [i.e., the change of Quantity into Quality] either undermines the meaning of a key DM-concept on which it was apparently based (i.e., "quality"), vitiating its applicability in this instance -- or it isn't even an example of the operation of this 'Law'!
Given this new twist, it now seems that quantitative changes to material bodies (such as salt/soup mixtures) actually cause changes to sensory systems (of a vague and perhaps non-quantitative -- or even non-qualitative -- kind); these in turn bring about some sort of qualitative change in the sensory modalities of some/any of the tasters involved. If this is so, the original 'Law' was woefully wide of the mark; it should have read something like the following:
E1: Change in quantity merely causes change in quantity to material bodies [no misprint!], but at a certain point this causes qualitative alterations (but these might not be Hegelian, or even neo-Aristotelian, qualities) to the way some human beings perceive the world, even though the latter have not undergone a quantitative change themselves.
Put like this, it is not at all certain that anyone would conclude this (or anything at all like it) from cooking soup (as Trotsky maintained)! And we can be pretty sure about this since not even Engels got close to this more accurate version of his own 'Law'. And neither did Trotsky! It is scarcely credible therefore that non-dialectical cooks, workers, or anyone else for that matter, would advance much further -- or even so far -– based only on their own experience.
Of course, this can only mean that peasant cooks are not "unconscious dialecticians", and neither is anyone else outside the DM-fraternity --, and this is probably because they are not quite so easily conned by Idealists.
Nevertheless, the above 'definitions' of "quantity" and "quality" are not without their own problems.
"Each of the three spheres of the logical idea proves to be a systematic whole of thought-terms, and a phase of the Absolute. This is the case with Being, containing the three grades of quality, quantity and measure.
"Quality is, in the first place, the character identical with being: so identical that a thing ceases to be what it is, if it loses its quality. Quantity, on the contrary, is the character external to being, and does not affect the being at all. Thus, e.g. a house remains what it is, whether it be greater or smaller; and red remains red, whether it be brighter or darker." [Hegel (1975), p.124, §85.]
"Quality is an aspect of something by which it is what it is and not something else and reflects that which is stable amidst variation. Quantity is an aspect of something which may change (become more or less) without the thing thereby becoming something else.
"Thus, if something changes to an extent that it is no longer the same kind of thing, this is a 'qualitative change', whereas a change in something by which it still the same thing, though more or less, bigger or smaller, is a 'quantitative change'.
"In Hegel's Logic, Quality is the first division of Being, when the world is just one thing after another, so to speak, while Quantity is the second division, where perception has progressed to the point of recognising what is stable within the ups and downs of things. The third and final stage, Measure, the unity of quality and quantity, denotes the knowledge of just when quantitative change becomes qualitative change." [Quoted from here.]
First of all, it is not too clear if there is a real distinction between "quantity" and "quality" here" if we rely on what Hegel says:
"[A] house remains what it is, whether it be greater or smaller; and red remains red, whether it be brighter or darker." [Hegel (1975), p.124, §85.]
For Hegel, house size seems to be the "quantity", here, but beyond a certain size, houses are no longer houses. Hence, a 'house' the size of a grain of sand is not a house. Isn't this a "qualitative" change? And, extremely dark red is no longer red (since it is indistinguishable from black). Another "qualitative" change? In that case, there seems to be no clear distinction between what is "quantitative" and "what is "qualitative" change here. And it is no use appealing to the 'get-out-of-a-hole-free-dialectics-card', saying that quantity has "passed over" into quality in these instances, since this slide affects the definition of these two terms. If we have no clear idea what we are talking about, then it is not possible to say what has "passed over" into what.
Secondly, as we have seen the phrases "something new" and "ceasing to be what it is" are also somewhat vague. We are not told what constitutes novelty or "ceasing to be" here. As we have seen, dialecticians including Hegel regard ice, water and steam as "something new" when we now know they are not. But this allows dialecticians to apply this 'Law' when and where they like, just as it allows them to refuse to accept certain counter-examples to it when and where they like. Several of the ones listed above will be rejected out-of-hand by dialecticians as bogus counter-examples on just such lines. For example, the heating of water from cold to very hot is a "qualitative" non-"nodal" change by ordinary standards, but it produces nothing "new" -- if by "new" we mean "new substance". But, if we mean that, then ice and steam are not "new" either.
What is finally decided upon here will, of course, depend on how we view the status of Aristotelian "essences" (or "essential properties"). However, further discussion will take us too far away form the main topic of this Essay, so no more will be said about it here.8c
'Hard' Science Vs Amateurish Anecdote
The other hackneyed examples DM-theorists regularly dredge up to illustrate this 'Law' (i.e., boiling water, balding heads, Mendeleyev's table, the alleged fighting qualities of Mamelukes, and, of late, Catastrophe and Chaos Theory), in fact only seem to work because of the way that the word "quality" has been 'defined' (or, rather, not clearly defined) by dialecticians.9
For example, in the case of boiling water, the increase in quantity of one item (i.e., heat) is alleged to alter the quality of the second (i.e., water). As noted above, "quality" is characterised in Hegel's work in Aristotelian terms (i.e., as that property which is essential to a substance/process, without which it must change into some other --, or as "determinate being", to use the Hegelian jargon; on this, see Inwood (1992), pp.238-41). And yet, by no stretch of the imagination is liquidity an essential property of water. Either side of the alleged 'qualitative' change, this substance remains H2O. Boling or freezing does not change it into another substance; water in a solid, liquid or gaseous form is still H2O. Quantitative addition or subtraction of energy does not result in a qualitative change of the required sort; no new Hegelian or Aristotelian "quality" emerges here. [On this, also see Note 9.]
Unfortunately, this means that the most widely- and over-used example in the DM-book-of-tricks that supposedly illustrates this 'Law' does not in fact do so!
In that case, this 'Law' should perhaps be re-written in the following way:
E1: An increase in the quantity of one item leads to a change in what is perhaps not one of the qualities of another.
With that, much of the 'metaphysical bite' of this 'Law' disappears; in fact it becomes rather toothless.
In addition, it seems a little odd to describe an increase in heat as an increase in quantity when what happens is that the relevant water molecules just move about faster if energy is fed into the system. Of course, it could be objected that this is precisely Engels's point; since energy can be measured (here, as an increase in heat, say), then that increase in heat is indeed an increase in quantity -- in this case "quantity of motion". But, the original idea appeared in Hegel at a time when heat was regarded as a substance, Caloric. [For Hegel's view, see here.] We now know that what really happens is that molecules just move faster -- after having interacted with still other faster moving molecules. [This is something Engels admits anyway; see Engels (1954), pp.63-64.]
So, when Engels speaks here of an increase in energy and a quantitative increase, he was either using a façon de parler, or he had not quite abandoned the old idea that heat is a substance. Of course, we might still want to call this phenomenon an increase in "energy" if we so wish, but if we do, that would merely plunge this part of the first 'Law' into complete darkness, since the word "energy" (if it is not a façon de parler) is not the name of an identifiable substance that can be qualified in this way.10
Furthermore, using "quantity" to depict the change in motion of molecules is somewhat dubious, too. Certainly, we can speak of an increase in velocity here, but there is no such thing as a quantity of velocity that could sensibly said to increase. Velocity is not a substance either, and although we certainly use numbers to depict it, we do not refer to anything called the "quantity of velocity" (except again, perhaps as a façon de parler). Since velocity is a vector, its magnitude is given by a scalar, but velocity itself is just that scalar operating in a that direction. To call the magnitude of a vector a "quantity" would be to confuse a vector (or indeed a direction) with a substance.
And this is not mere pedantry. As we saw above, this is in line with Hegel's own definition of the word:
"Quality is, in the first place, the character identical with being: so identical that a thing ceases to be what it is, if it loses its quality. Quantity, on the contrary, is the character external to being, and does not affect the being at all. Thus, e.g. a house remains what it is, whether it be greater or smaller; and red remains red, whether it be brighter or darker." [Hegel (1975), p.124, §85.]
This too is underlined by the Glossary at the Marx Internet Archive:
"Quantity is an aspect of something which may change (become more or less) without the thing thereby becoming something else.
"Thus, if something changes to an extent that it is no longer the same kind of thing, this is a 'qualitative change', whereas a change in something by which it still the same thing, though more or less, bigger or smaller, is a 'quantitative change'.
"In Hegel's Logic, Quality is the first division of Being, when the world is just one thing after another, so to speak, while Quantity is the second division, where perception has progressed to the point of recognising what is stable within the ups and downs of things. The third and final stage, Measure, the unity of quality and quantity, denotes the knowledge of just when quantitative change becomes qualitative change." [Quoted from here.]
Hence, if we adhere to this definition strictly, there can be no "quantity" of energy, because it is not a "thing", or an "aspect" of a thing in any meaningful sense of these words.
Nevertheless, even if it were appropriate to depict things in this way, neither the heat nor the faster molecules change in quality themselves. Any amount of heat still stays as heat; motion is still motion. Hence, this aspect of the 'Law' does not seem to apply to these 'phenomena'. In that case, the first 'Law' should now perhaps be re-written along the following lines:
E2: An increase in the quantity of one item (e.g., heat) leads to no qualitative change in that item, while it can cause an alteration in the quality of another item (e.g., water), which will in turn have changed in quality while undergoing no quantitative change itself -- but which qualitative change is inadmissible anyway since it is not a quality definitive of the latter (e.g., water as H2O).
This is not an impressive 'Law'; still less is this hackneyed example a convincing instance of it.
As far as balding heads are concerned, it is not easy to see how this over-worked example illustrates the first 'Law' either. This is because it is difficult to believe that someone with, say, n hairs on his or her head is hirsute, when the same person with n-1 hairs is objectively bald -- even if at some point or other (and not necessarily the same point) we all might subjectively change the words we use to depict either.
Now, if it could be shown that those with precisely n-1 hairs on their heads (for some specific n) are always objectively bald, and that this is an essential defining quality of baldness, or of bald people (in the Aristotelian/Hegelian sense just mentioned), so that a change from n to n-1 hairs always results in baldness, and which rule is true for all hirsute human beings, then the first 'Law' might have some life left in it in just this one instance. It could then be a dialectical 'Law' that applies only to balding parts of nature, but nothing else. [Which is longhand for saying it cannot therefore be a law.]
Nevertheless, even this is not so. With respect to baldness, human anatomists (or even hairdressers) have yet to define hair loss in such Aristotelian terms. Hence, and unfortunately for DM-fans, they have so far failed to categorise all follically-challenged individuals this precisely, declaring that anyone with n-1 hairs is essentially bald, whereas anyone with n hairs is still essentially non-coot. Until they do, there are no "nodal" points here, just as there seem to be no particular (Aristotelian/Hegelian) qualities definitive of bald human beings for dialecticians to latch onto. So, in this case, it is impossible to see how an 'objective' example of this dialectical 'Law' could apply --, merely a 'subjective' impression, and one that has to rely on a quirky application of an already vague Aristotelian/Hegelian 'definition' of "quality".
So it seems that the change in quality, if it occurs, takes place not in the person going bald, but in the one describing him/her/it as bald. In that case, with respect to human balding, change in the quantity of hair on one person's head will merely change the quality of someone else's opinion of him/her, and even that occurs subjectively and (possibly even) non-"nodally".
There isn't much here on which to base a dialectical 'Law', at least nothing that would fail to brand this part of DM as a fringe science, at best.
As far as the other examples dialecticians use to illustrate this 'Law' are concerned: there are far too few in number that actually work (even if the above difficulties are ignored) to justify the epithet "Law" being attached to one and all. If in comparison, say, Newton's Second Law of motion worked as fitfully as this 'Law' does (or was as vaguely-defined and was as non-mathematical), physicists would be right to refuse to describe it as a law. Hence, if the rate of change of momentum were in fact proportional to the applied force in only a few instances (and even then this was the case only if key terms were either ignored, remained ill-defined or were twisted out of shape), no one would have taken Newton seriously.
But, this is Mickey Mouse Science, after all.
In general, however, the examples usually given by DM-fans to illustrate this 'Law' are almost without exception either anecdotal or impressionistic. If someone were to submit a paper to a science journal purporting to establish the veracity of a new law with the same level of vagueness, imprecision, triteness, lack of detail/mathematics, and overall theoretical naivety, it would be rejected out-of-hand at the first stage. Indeed, dialecticians would themselves treat with derision any attempt to establish, say, either the truth of classical economic theory or the falsity of Marx's own work with an evidential display that was as crassly amateurish as this --, to say nothing of the contempt they would show for theoretical wooliness of this sort. In such circumstances, those who might be quick to cry "pedantry" at the issues raised in this and other Essays published at this site would become devoted pedants, and nit-pick with the best at such inferior anti-Marxist work.
[Indeed, they do this to my work, too; in one breath they complain about "pedantry", in the next they home in on what they assume are minor errors. Here is just the latest example; concentrate on the comments of one "Gilhyle".]
Now, anyone who has studied or practiced real science will know this to be true. It is only in books on DM (and internet discussion boards) that Mickey Mouse material of this sort seems acceptable. [Once more, the above link is an excellent recent example of this trait.]10a
At this point we might wonder where Engels's predilection for Mickey Mouse Science came from. After all, he was familiar with the careful and detailed work of contemporary scientists (like Darwin). Why then was he prepared top assert his 'Laws' were indeed laws on the basis of very little primary data (or none at all), secondary or tertiary (but nonetheless selective) evidence and sloppy analysis? We need look no further than Hegel for a clue here, for Hegel was the original Mickey Mouse Scientist (making Engels merely the Sorcerer's Apprentice).
Figure Three: Researching For A PhD In Dialectics?
Here is Hegel's 'detailed proof':
"The system of natural numbers already shows a nodal line of qualitative moments which emerge in a merely external succession. It is on the one hand a merely quantitative progress and regress, a perpetual adding or subtracting, so that each number has the same arithmetical relation to the one before it and after it, as these have to their predecessors and successors, and so on. But the numbers so formed also have a specific relation to other numbers preceding and following them, being either an integral multiple of one of them or else a power or a root. In the musical scale which is built up on quantitative differences, a quantum gives rise to an harmonious relation without its own relation to those on either side of it in the scale differing from the relation between these again and their predecessors and successors. While successive notes seem to be at an ever-increasing distance from the keynote, or numbers in succeeding each other arithmetically seem only to become other numbers, the fact is that there suddenly emerges a return, a surprising accord, of which no hint was given by the quality of what immediately preceded it, but which appears as an actio in distans [action at distance -- RL], as a connection with something far removed. There is a sudden interruption of the succession of merely indifferent relations which do not alter the preceding specific reality or do not even form any such, and although the succession is continued quantitatively in the same manner, a specific relation breaks in per saltum [leaps -- RL].
"Such qualitative nodes and leaps occur in chemical combinations when the mixture proportions are progressively altered; at certain points in the scale of mixtures, two substances form products exhibiting particular qualities. These products are distinguished from one another not merely by a more or less, and they are not already present, or only perhaps in a weaker degree, in the proportions close to the nodal proportions, but are bound up with these nodes themselves. For example, different oxides of nitrogen and nitric acids having essentially different qualities are formed only when oxygen and nitrogen are combined in certain specific proportions, and no such specific compounds are formed by the intermediate proportions. Metal oxides, e.g. the lead oxides, are formed at certain quantitative points of oxidation and are distinguished by colours and other qualities. They do not pass gradually into one another; the proportions lying in between these nodes do not produce a neutral or a specific substance. Without having passed through the intervening stages, a specific compound appears which is based on a measure relation and possesses characteristic qualities. Again, water when its temperature is altered does not merely get more or less hot but passes through from the liquid into either the solid or gaseous states; these states do not appear gradually; on the contrary, each new state appears as a leap, suddenly interrupting and checking the gradual succession of temperature changes at these points. Every birth and death, far from being a progressive gradualness, is an interruption of it and is the leap from a quantitative into a qualitative alteration.
"It is said, natura non facit saltum [there are no leaps in nature]; and ordinary thinking when it has to grasp a coming-to-be or a ceasing-to-be, fancies it has done so by representing it as a gradual emergence or disappearance. But we have seen that the alterations of being in general are not only the transition of one magnitude into another, but a transition from quality into quantity and vice versa, a becoming-other which is an interruption of gradualness and the production of something qualitatively different from the reality which preceded it. Water, in cooling, does not gradually harden as if it thickened like porridge, gradually solidifying until it reached the consistency of ice; it suddenly solidifies, all at once. It can remain quite fluid even at freezing point if it is standing undisturbed, and then a slight shock will bring it into the solid state.
"In thinking about the gradualness of the coming-to-be of something, it is ordinarily assumed that what comes to be is already sensibly or actually in existence; it is not yet perceptible only because of its smallness. Similarly with the gradual disappearance of something, the non-being or other which takes its place is likewise assumed to be really there, only not observable, and there, too, not in the sense of being implicitly or ideally contained in the first something, but really there, only not observable. In this way, the form of the in-itself, the inner being of something before it actually exists, is transformed into a smallness of an outer existence, and the essential difference, that of the Notion, is converted into an external difference of mere magnitude. The attempt to explain coming-to-be or ceasing-to-be on the basis of gradualness of the alteration is tedious like any tautology; what comes to be or ceases to be is assumed as already complete and in existence beforehand and the alteration is turned into a mere change of an external difference, with the result that the explanation is in fact a mere tautology. The intellectual difficulty attendant on such an attempted explanation comes from the qualitative transition from something into its other in general, and then into its opposite; but the identity and the alteration are misrepresented as the indifferent, external determinations of the quantitative sphere.
"In the moral sphere, in so far as it is considered under the categories of being, there occurs the same transition from quantity into quality and different qualities appear to be based in a difference of magnitude.
"It is through a more or less that the measure of frivolity or thoughtlessness is exceeded and something quite different comes about, namely crime, and thus right becomes wrong and virtue vice. Thus states, too, acquire through their quantitative difference, other things being assumed equal, a distinct qualitative character. With the expansion of the state and an increased number of citizens, the laws and the constitution acquire a different significance. The state has its own measure of magnitude and when this is exceeded this mere change of size renders it liable to instability and disruption under that same constitution which was its good fortune and its strength before its expansion." [Hegel (1999), pp.368-71, §§774-778. Emphases in the original.]
"The identity between quantity and quality, which is found in Measure, is at first only implicit, and not yet explicitly realised. In other words, these two categories, which unite in Measure, each claim an independent authority. On the one hand, the quantitative features of existence may be altered, without affecting its quality. On the other hand, this increase and diminution, immaterial though it be, has its limit, by exceeding which the quality suffers change. Thus the temperature of water is, in the first place, a point of no consequence in respect of its liquidity: still with the increase of diminution of the temperature of the liquid water, there comes a point where this state of cohesion suffers a qualitative change, and the water is converted into steam or ice. A quantitative change takes place, apparently without any further significance: but there is something lurking behind, and a seemingly innocent change of quantity acts as a kind of snare, to catch hold of the quality. The antinomy of Measure which this implies was exemplified under more than one garb among the Greeks. It was asked, for example, whether a single grain makes a heap of wheat, or whether it makes a bald-tail to tear out a single hair from the horse’s tail. At first, no doubt, looking at the nature of quantity as an indifferent and external character of being, we are disposed to answer these questions in the negative. And yet, as we must admit, this indifferent increase and diminution has its limit: a point is finally reached, where a single additional grain makes a heap of wheat; and the bald-tail is produced, if we continue plucking out single hairs. These examples find a parallel in the story of the peasant who, as his ass trudged cheerfully along, went on adding ounce after ounce to its load, till at length it sunk under the unendurable burden. It would be a mistake to treat these examples as pedantic futility; they really turn on thoughts, an acquaintance with which is of great importance in practical life, especially in ethics. Thus in the matter of expenditure, there is a certain latitude within which a more or less does not matter; but when the Measure, imposed by the individual circumstances of the special case, is exceeded on the one side or the other, the qualitative nature of Measure (as in the above examples of the different temperature of water) makes itself felt, and a course, which a moment before was held good economy, turns into avarice or prodigality. The same principles may be applied in politics, when the constitution of a state has to be looked at as independent of, no less than as dependent on, the extent of its territory, the number of its inhabitants, and other quantitative points of the same kind. If we look, e.g. at a state with a territory of ten thousand square miles and a population of four millions we should, without hesitation, admit that a few square miles of land or a few thousand inhabitants more or less could exercise no essential influence on the character of its constitution. But on the other hand, we must not forget that by the continual increase or diminishing of a state, we finally get to a point where, apart from all other circumstances, this quantitative alteration alone necessarily draws with it an alteration in the quality of the constitution. The constitution of a little Swiss canton does not suit a great kingdom; and, similarly, the constitution of the Roman republic was unsuitable when transferred to the small imperial towns of Germany." [Hegel (1975), pp.158-59.]
Readers will no doubt note that rank amateurism is not confined to Engels (or even Woods and Grant); Hegel could 'amateur' with the best of them.10a1
So, this 'Law' can be made to work in a few selected instances if we bend things enough (and if we fail to define either "quality", "node", "leap", "same body" and "addition of energy" -- or, if we ignore Hegel's own vague 'definition' of "quality" into the bargain). In contrast there are countless examples where this 'Law' does not apply, no matter how we try to twist and bend it.10b
Why Engels's first 'Law' was ever called a law is therefore something of a Dialectical Mystery.
[Other examples to which dialecticians appeal are discussed in more detail in Note 9.]
The Interpenetration Of Opposites
The second 'Law' of dialectics -- unsurprisingly -- fares no better.
We saw above how Engels depicted it:
"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.]
Here, in a published work, he says more or less the same:
"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.]
Lenin added a few extra details:
"[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?]….
"The identity of opposites…is the recognition…of the contradictory, mutually exclusive, opposite tendencies in all phenomena and processes of nature…. The condition for the knowledge of all processes of the world in their 'self-movement', in their spontaneous development, in their real life, is the knowledge of them as a unity of opposites. Development is the 'struggle' of opposites…. [This] alone furnishes the key to the self-movement of everything existing….
"The unity…of opposites is conditional, temporary, transitory, relative. The struggle of mutually exclusive opposites is absolute, just as development and motion are absolute…." [Lenin (1961), pp.221-22, 357-58. Emphases in the original.]
It is worth noting at the outset that the doctrine that nature and all it contains is a UO, and that change is powered by their 'contradictory' interaction, is also found in all known mystical religions/philosophies. [More on that in Essay Fourteen Part One (summary here). Until that Essay is published, the reader is directed here.]
Dialectics Cannot Explain Change!
Surprisingly, DM-theorists (like Lenin and Engels, quoted above) are decidedly unclear as to whether objects/processes change because of (1) a contradictory relationship between their internal opposites, or because (2) they change into these opposites, or even whether (3) change itself creates such opposites.
[FL = Formal Logic; NON = Negation of the Negation: UO = Unity of Opposites; DM = Dialectical Materialism.]
Lenin's words merely illustrate this confusion in an acute form: he speaks, for instance, of the "transitions of every determination, quality, feature, side, property into every other…."
Engels is equally unclear: "[M]utual penetration of polar opposites and transformation into each other...." The same can be said of Plekhanov:
"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. Bold emphasis added.]
And here is Mao:
"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 (1961b), pp.340-42. Quotation marks altered to conform to the conventions adopted here. Bold emphasis added.]
Once more, this seems to suggest that objects and processes not only change (1) because of their internal opposites, but also that (2) they change into these opposites (and, according to Lenin, they change into all of them!) as a result of their "struggle" with them, as well as (3) that they also produce these opposites while they change --, or they do so as a result of that change.10b1
As we are about to see, this idea -- that there are such things as "dialectical contradictions" and "unities of opposites" (etc.), which cause change -- presents DM-theorists with some rather nasty dialectical headaches, if interpreted along the lines expressed in the DM-classics (quoted above and at greater length in Note 10b1).
To see this, let us suppose that object/process A is comprised of two "internal contradictory opposites" O* and O**, and it thus changes as a result.
[The same problems arise if these are viewed as 'external' contradictions. However, as we will see in Essay Eight Part One, the latter option attracts serious difficulties of its own, anyway.]
But, O* cannot itself change into O** since O** already exists! If O** didn't already exist then, according to this theory, O* could not change at all, for there would be no opposite to bring that about. As Gollobin notes:
"Opposites in a thing are not only mutually exclusive, polar, repelling, each other; they also attract and interpenetrate each other. They begin and cease to exist together.... These dual aspects of opposites -- conflict and unity -- are like scissor blades in cutting, jaws in mastication, and two legs in walking. Where there is only one, the process as such is impossible: 'all polar opposites are in general determined by the mutual action of two opposite poles on one another, the separation and opposition of these poles exists only within their unity and interconnection, and, conversely, their interconnection exists only in their separation and their unity only in their opposition.' in fact, 'where one no sooner tries to hold on to one side alone then it is transformed unnoticed into the other...'" [Gollobin (1986), p.113; quoting Engels (1891), p.414.]
Hence,
it is no good propelling O** into the future so that it is now
said to be what
O* will change into, since O* will do no such thing unless
O** is already there, in the present, to make that happen!
So, if object/process A is already composed of a 'dialectical union' of
O* and
not-O*
(interpreting
O** now as not-O*),
how can
O* possibly change into not-O* when
not-O*
already exists?
Several alternatives now suggest themselves which might allow dialecticians to dig themselves out of this hermetic hole. Either:
(1) O* 'changes' into not-O*, meaning there would now be two not-O*s where once there was one (unless, of course, one of these not-O*s just vanishes into thin air -- see below); or:
(2) O* does not change, or it disappears. Plainly, O* cannot change into what already exists -- that is, O* cannot change into its opposite, not-O* without there being two of them (see above). But even then, one of these will not be not-O* just a copy of it. In that case, O* either disappears, does not change at all, or changes into something else; or:
(3) Not-O* itself disappears to allow a new (but copy) not-O* to emerge that O* can and does change into. If so, questions would naturally arise as to how the original not-O* could possibly cause O* to change if is has just vanished. Of course, this option merely postpones the evil day, for the same difficulties will afflict the new not-O* that afflicted the old. If it exists in order to allow O* to change, then we are back where we were to begin with.
Anyway, as should seem obvious, among other things already mentioned, alternative (2) plainly means that O* does not in fact change into not-O*, it is just replaced by it. Option (1), on the other hand, has the original not-O* remaining the same (when it was supposed to turn into its own opposite -- O* -- according to the DM-classics), and options (2) and (3) will only work if matter and/or energy can either be destroyed or created from nowhere!
Naturally, these problems will simply re-appear at the next stage as not-O* readies itself to change into whatever it changes into. But, in this case there is an added twist, for there is as yet no not-not-O* in existence to make this happen. This means that the dialectical process will grind to a halt, unless a not-not-O* pops into existence to start things up again.
But what could possibly engineer that?
Indeed, at the very least, this 'theory' of change leaves it entirely mysterious how
not-O* itself came about
in the first place. It seems to have popped into existence from nowhere, too.
[Gollobin (above) sort of half recognises this without realising either his error
or the serious problems this creates.]
But, not-O* cannot have come from
O* itself, since
O* can only change because of the operation of
not-O*,
which does not yet exist! And pushing the process into the past (via a
'reversed' version of the NON)
will merely reduplicate the above problems.
[However, on the NON, see below.]
Now, it could be objected that all this seems to place objects and/or processes in fixed categories, which is one of the main criticisms dialecticians make of FL. Hence, on that basis, it could be maintained that the above argument is entirely misguided.
Fortunately, repairs are easy to make: let us now suppose that object/process A is comprised of two changing "internal/external opposites" O* and O**, (the latter once again interpreted as not-O*) and it thus develops as a result.
The rest still follows as before: if object/process A is already composed of a changing dialectical union of O* and not-O*, and O* 'develops' into not-O* as a result, how is it possible for O* to change into not-O* when not-O* already exists?
Of course, it could be argued that not-O* 'develops' into O* while not-O* 'develops' into O*.
[This objection might even incorporate that eminently obscure Hegelian term-of-art: "sublation". More on that presently.]
But, if this were so, while it was happening these two would no longer be 'opposites' of one another --, not unless we widen the term "opposite" to mean "anything that an object/process turns into, and/or any intermediate object/process while that is happening". Naturally, that would make this 'Law' work by definitional fiat, rendering it eminently 'subjective', once more.
But, if we ignore that 'difficulty' for now, and even supposing it were the case that not-O* 'developed' into O* while not-O* 'developed' into O*, and such process were governed by the obscure term "sublation", this alternative will still not work (as we are about to see).
Indeed, developing this option further before it is demolished, it could be argued that Engels had himself anticipated the above objections when he said:
"[RL: Negation of the negation is] a very simple process which is taking place everywhere and every day, which any child can understand as soon as it is stripped of the veil of mystery in which it was enveloped by the old idealist philosophy and in which it is to the advantage of helpless metaphysicians of Herr Dühring's calibre to keep it enveloped. Let us take a grain of barley. Billions of such grains of barley are milled, boiled and brewed and then consumed. But if such a grain of barley meets with conditions which are normal for it, if it falls on suitable soil, then under the influence of heat and moisture it undergoes a specific change, it germinates; the grain as such ceases to exist, it is negated, and in its place appears the plant which has arisen from it, the negation of the grain. But what is the normal life-process of this plant? It grows, flowers, is fertilised and finally once more produces grains of barley, and as soon as these have ripened the stalk dies, is in its turn negated. As a result of this negation of the negation we have once again the original grain of barley, but not as a single unit, but ten-, twenty- or thirtyfold. Species of grain change extremely slowly, and so the barley of today is almost the same as it-was a century ago. But if we take a plastic ornamental plant, for example a dahlia or an orchid, and treat the seed and the plant which grows from it according to the gardener's art, we get as a result of this negation of the negation not only more seeds, but also qualitatively improved seeds, which produce more beautiful flowers, and each repetition of this process, each fresh negation of the negation, enhances this process of perfection. [Engels (1976), pp.172-73. Bold emphases added.]
"But someone may object: the negation that has taken place in this case is not a real negation: I negate a grain of barley also when I grind it, an insect when I crush it underfoot, or the positive quantity a when I cancel it, and so on. Or I negate the sentence: the rose is a rose, when I say: the rose is not a rose; and what do I get if I then negate this negation and say: but after all the rose is a rose? -- These objections are in fact the chief arguments put forward by the metaphysicians against dialectics, and they are wholly worthy of the narrow-mindedness of this mode of thought. Negation in dialectics does not mean simply saying no, or declaring that something does not exist, or destroying it in any way one likes. Long ago Spinoza said: Omnis determinatio est negatio -- every limitation or determination is at the same time a negation. And further: the kind of negation is here determined, firstly, by the general and, secondly, by the particular nature of the process. I must not only negate, but also sublate the negation. I must therefore so arrange the first negation that the second remains or becomes possible. How? This depends on the particular nature of each individual case. If I grind a grain of barley, or crush an insect, I have carried out the first part of the action, but have made the second part impossible. Every kind of thing therefore has a peculiar way of being negated in such manner that it gives rise to a development, and it is just the same with every kind of conception or idea....
"But it is clear that from a negation of the negation which consists in the childish pastime of alternately writing and cancelling a, or in alternately declaring that a rose is a rose and that it is not a rose, nothing eventuates but the silliness of the person who adopts such a tedious procedure. And yet the metaphysicians try to make us believe that this is the right way to carry out a negation of the negation, if we ever should want to do such a thing. [Ibid., pp.180-81. Bold emphases added.]
Engels's argument seems to be that "dialectical negation" is not the same as ordinary negation in that it is not simple destruction. Dialectical negation "sublates"; that is, it both destroys and preserves, so that something new or 'higher' emerges as a result. Nevertheless, we have already seen here, that Hegel's use of this word (i.e., "sublate") is highly suspect, and we will also see below that this 'Law' (i.e., the NON) is even more dubious still (partly because Hegel confused ordinary negation with 'cancelling out', or with destruction, as did Engels).
Well, despite all this, is it the case that the above comments neutralise the argument presented in this part of the Essay? Is the argument here guilty of the following:
"These objections are in fact the chief arguments put forward by the metaphysicians against dialectics, and they are wholly worthy of the narrow-mindedness of this mode of thought." [Ibid.]
To answer this, let us once again suppose that object/process A is comprised of two changing "internal opposites" O* and not-O*, and thus develops as a result. On this scenario, O* would change/develop into a "sublated" intermediary, but not into not-O* -- incidentally, contradicting the DM-worthies quoted earlier. O* should, of course, change into not-O*, not into some intermediary.
Putting this minor quibble to one side, too, on this 'revised' view, let us suppose that O* does indeed change into that intermediary. To that end, let us call the latter, "O*1" (which can be interpreted as a combination of the old and the new; a 'negation' which also 'preserves'/'sublates').
If so, then O*1 must remain forever in that state, unchanged, for there is as yet no not-O*1 in existence to make it develop any further.
[Recall that on this 'theory', everything (and that must include O*1) changes because of a 'struggle' with its opposite.]
So, there must be a not-O*1 to make O*1 change further. To be sure, we could try to exempt O*1 from this essential requirement on an ad hoc basis (arguing, perhaps, that O*1 changes spontaneously with nothing actually causing it), and yet if we do that, there would seem to be no reason to accept the version of events contained in the DM-classics, which tells us that every thing/process changes because of the operation of opposites (and O*1 is certainly a thing/process). Furthermore, if we make an exemption here, then the whole point of the exercise would be lost, for if some things do and some things do not change according this dialectical 'Law', we would be left with no way of telling which changes were and which were not subject to it.
[This would also mean that the second 'Law' was not a 'law' either, just like the first.]
This is, of course, quite apart from the fact that such a subjectively applied exemption certificate (issued to O*1) would mean that nothing at all could change, for everything in the universe is in the process of change, and is thus already a 'sublated' version of whatever it used to be.
Ignoring this, too, even if O*1 were to change into not-O*1 (as we suppose it must, given the doctrine laid down by the DM-prophets), then all the earlier problems simply reappear, for this could only take place if not-O*1 already existed to make it happen! But not-O*1 cannot already exist, for O*1 has not changed into it yet!
Once more, it could be objected that the dialectical negation of O* to produce not-O* is not ordinary negation, as the above seems to assume.
In that case, let us say that O* turns into its 'sublated' opposite not-O*s, but if that is to happen, according to the Dialectical Gospels, not-O*s must already exist! If so, and yet again, O* cannot turn into not-O*s, for it already exists! On the other hand, if not-O*s does not already exist, then O* cannot change, for O* can only change if it struggles with what it changes into, i.e., not-O*s.
Once again, we hit the same non-dialectical brick wall.
It could be objected that the above abstract argument misses the point; in the real world things manifestly change. For example, it might be the case that John is a boy, but in a few years time it will be the case that John is a man. Now, the fact that other individuals are already men, does not stop John changing into a man (his opposite), as the above argues. So, John can change into his opposite even though that opposite already exists.
Or so it could be claimed.
But, this theory tells us that things/processes change because of a struggle with their opposites, and with what they become. Are we now to assume that John has to struggle with all the individuals that are already men if he is to become a man himself (if we now treat all these other men as John's opposites)? And are we to suppose that John struggles with what he is to become, even before it exists? If not, then the above response is beside the point. And, in view of the fact that John must turn into his opposite, does that mean he has to turn into these other men, or even into one of them? But he must do so if the Dialectical Holy Books are to be believed.
Anyway, according to the DM-worthies quoted above, John can only change because of a struggle between opposites taking place in the here-and-now. Are we now really supposed to believe that "John is a man" is struggling with "John is a boy" -- or that manhood is struggling with boyhood?
Some might be tempted to reply that this is precisely what adolescence is, and yet, in that case, John-as-boy and John-as-a-man would have to be locked in struggle in the present. [Of course, adolescence cannot struggle with anything, since it is an abstraction.] But, John-as-a-man does not yet exist, and so 'he' cannot struggle with John-as-boy. On the other hand, if John-as-a-man does exist, so that 'he' can struggle with his youthful self, then John-as-boy cannot change into 'him', for John-as-a-man already exists!
To be sure, John's 'opposite' is whatever he will become (if he is allowed to develop naturally), but, as noted above, that opposite cannot now exist otherwise John would not need to become him!
Looking at this more concretely, in ten or fifteen years time, John will not become just any man, he will become a particular man. In that case, let us call the man that John becomes "ManJ". But, once again, ManJ must exist now or John cannot change into him (if the DM-worthies quoted earlier are to be believed), for John can only become a man if he is locked in struggle with his own opposite, ManJ. But, if that is so, John cannot become ManJ since ManJ already exists!
Consider another concrete example: wood being fashioned into a
table. Once more, according to the dialectical classicists, all objects and
processes change because of a 'struggle' of opposites, and they all also change
into those opposites.
So, the wood that is used to make a table, according to this 'theory', has to
'struggle' with what it turns into, that is, this wood has to 'struggle' with
the table it turns into!
In that case, the table must already exist, or it could not 'struggle' with the
wood from which it is to be made.
But, if the table already exists, then the wood cannot be changed into it.
On the other hand, if the table does not already exist, then the wood cannot
'struggle' with its own opposite, that is, it cannot 'struggle' with the table
it has yet to become.
Either way, change could not happen, according to this 'theory'.
And it is little use introducing human agency here, for if a carpenter is required to make a table, then he/she has to 'struggle' with the wood to make it into that table (since we are told that every object and process in nature is governed by this 'Law'). But, according to the Dialectical Holy Books, objects and processes 'struggle' with their dialectical 'opposites', and they turn into those opposites. If so, wood must turn into the carpenter, not the table!
With a crazy theory like this at its core, is it any wonder
Dialectical Marxism is a by-word for failure?10b2
[These, of course, are simply more concrete versions of the argument outlined above.]
Consider another hackneyed example: water turning into steam at 100oC (under normal conditions). Are we really supposed to believe that the opposite that water becomes (i.e., steam) makes water turn into steam? This must be so if the Dialectical Saints are to be believed.
Hence, while you might think it is the heat/energy you are putting into the water that turns it into steam, what really happens, according to these wise old dialecticians, is that steam makes water turn into steam!
In that case, save energy and turn the gas off!
In fact, let us track a water molecule to see what happens to it. To identify it, we shall call it "W1", and the steam molecule it turns into "S1". But, if the DM-Worthies above are correct, S1 must already exist, otherwise W1 could not change into it! Again, if that is so, where does S1 disappear to if W1 changes into it?
In fact, according to the Dialectical Magi, since opposites turn into one another, S1 must change into W1 at the same time as W1 is turning into S1! So while you are boiling a kettle, according to this Superscientific 'theory', steam must be turning back into the water you are boiling, and it must do so at the same rate!
One wonders, therefore, how dialectical kettles manage to boil dry.
This must be so, otherwise when W1 turns into S1 -- which already exists, or W1 could not change into it -- there would have to be two S1s where there used to be one! Matter created from nowhere!
Of course, the same argument applies to water freezing (and to any and all other alleged examples of DM-change).
It could be objected that the opposite that liquid water turns into is a gas; so the dialectical classicists are correct. However, if we take them at their word, then that gas must 'struggle' with liquid water in the here-and-now if water is to change. But that gas does not yet exist; in which case, water would never boil if this 'theory' were true. But even if it did, it is heat that causes the change not the gas! However we try and slice it, this 'theory' is totally useless -- that is, what little sense can be made of it.
This, of course, does not deny that change occurs, only that DM cannot account for it.
Alternatively, if DM were true, change would be impossible.
Whichever way we try to re-package this 'Law' we end up with insuperable problems, ones that cannot simply be Nixoned away.
[As far as social change is concerned, see here, here and here.]
However, all this is, of course, just an elaboration of the following example of a priori Superscience invented by the Mystery-Meister himself:
"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." [Hegel (1975), p.174. Bold emphases added.]
As this quotation indicates, and as Essay Eight Part Three will show, Hegel made a quasi-logical attempt to delineate such opposites, but his reasoning was defective from beginning to end, and demonstrably so. The bottom line was that, far from specifying that each object was paired with its unique dialectical 'other', Hegel inadvertently conceded that objects and processes were confronted on all sides by countless 'others'.
Leaving that aside, and ignoring for the moment the question of how Hegel, Engels, Lenin and Plekhanov knew this 'Law' was true of everything in the entire universe, for all of time (this topic was examined in more detail in Essay Two), it is worth pointing out that some things seem to have no internally-interconnected opposites. For example, electrons, which, while they appear to have several external opposites (but not only is it not clear what the opposite of an electron is -- is it a positron or is it a proton? --, it is clear electrons do not seem to turn into either of them), they seem to have no internal opposites as far as can be ascertained. In that case, they must be changeless beings -- or, if they do change, that cannot be as a result of their "internal contradictions". Moreover, they do not even change into their alleged external opposites (positrons or protons).10c Admittedly, electrons had only just been discovered in Lenin's day, but that just makes his dogmatism even more puzzling -- especially when it is recalled that it was he who insisted that all knowledge is provisional and relative.
Is Everything A 'Unity Of Opposites'?
[It is worth noting here that these comments depend on what dialecticians mean by an "internal opposite"; sometimes they seem to mean "topologically-internal", sometimes "logically-internal". This ambiguity is examined in more detail in Essay Eight Part One. However, much of this and subsequent sections depend on interpreting "internal opposites" in one way -- topologically. The other alternative (i.e., interpreting "internal opposites" logically) will also be considered presently.]
Despite this, once more, it is difficult to believe Lenin and the others were serious in claiming that everything is a UO -- just as it is impossible to give credence to the idea that "every determination, quality, feature, side, property [changes] into every other…."
Are we really supposed to believe that, say, a domestic cat is a UO? But, what is the opposite of a cat? A dog? A tulip? A tin of beans?
Is it a 'non-cat'? And yet, if a 'non-cat' were the opposite of a cat, it would mean that if everything does indeed change into its opposite, cats must change into everything that they are not -- that is, they must change into any one or more of the following 'non-cats': oak trees, sandy beaches, cuff links, dog baskets, rift valleys, petrol stations and galaxies, to name but a few. [The 'obvious' dialectical response to this objection will be considered shortly.]
Not only that, but according to Lenin cats must contain all these things if they are indeed unities of their opposites (or, they must be "internally related" to them in some way) -- i.e., they must presumably be a unity of cat and 'non-cat' --, especially if the latter (i.e., this 'non-cat') is what causes a cat to change. Is, therefore, each unassuming domestic moggie a repository of all its myriad opposites, and do these opposites contain their own sets of opposites, ad infinitem, like glorified Russian dolls?
Well, it seems they must if, according to Lenin: "every determination, quality, feature, side, property [changes] into every other…." If change is the result of an internal struggle between opposites (declared above to be an "absolute" by Lenin), and everything changes into everything else, then cats must both contain and change into (at some point) a host of things, which must in turn contain and change into even more (or, perhaps, back into cats).10d
It is little use complaining that these are ridiculous conclusions; if everything changes into its opposite, then they must follow. Those who still object should rather pick a fight with dialecticians -- not me -- for championing such a crazy view of reality.
[The obvious objection that this discussion ignores 'mediated essences' is fielded in Note 10e.]10e
Figure Four: Another Dialectical Catastrophe?
So, if cats do change, as they do, then they must change into their opposites. But where are these 'opposite cats'? And how do they feature in and cause the changes they allegedly produce in the original animal? On the other hand, if they do not do this, does this mean that feline parts of nature are not subject to dialectical law? Is this why cats have nine lives?
Now, Engels did try to answer these fatal objections by arguing that we must learn from nature what the actual properties of objects and processes are in each case, and hence, presumably, what each can legitimately change into. [To be sure, he made this point in relation to the first and third of his 'Laws', but there is no reason to believe he would have denied this of the second 'Law'.] Once more, he also pointed out that dialectical negation is not annihilation. [Engels (1954, p.63 and (1976), p.181.]
However, nature is annoyingly ambiguous on this score. For example, lumps of iron ore can turn, or be turned into many different things (with or without the addition of labour, etc.). These include: car parts, aeroplane components, ships, magnets, cutlery, pots and pans, anchors, scaffolding, chains, bollards, cranes, tubes, engines, ornaments, jewellery, girders, weapons, tools, instruments, wire, furniture, doors, gates, railings, railway tracks, wheels, zips, bars, handcuffs, bullets, iron filings, rivets, nails, screws, steel wool, and helmets, cytochrome nitrogenase, haemoglobin, hematite, magnetite, taconite, countless ferrous and ferric compounds (including rust, Ferrous and Ferric Sulphides, Fools Gold, etc., etc.), to name but a few.
Are we to believe that all of these reside inside each lump of iron? How can they all be 'logically-related' to iron ore? If not, what exactly is the point of this 'Law'? Again, if these items don't exist inside each lump of iron -- or even if they do not confront them as antagonistic external or 'logical' opposites --, how is it possible for human labour and/or natural forces to turn iron into such things while remaining in conformity with 'dialectical Law'? Does human labour counteract, or work with the 'Laws' of dialectics? If a lump of iron does not ('logically', or physically) 'contain', say, a carving knife, how is it possible for human beings to change iron into carving knives, and for them to do so dialectically? Are there changes in reality that are not governed by dialectics?
Are these iron 'Laws' not in fact applicable to iron itself?
In that case, exactly which opposites are ('logically'/physically) united in, or with iron ore?
Of course, it could be argued that the above considerations completely misconstrue the nature of this 'Law'. No one supposes that cats and nuggets of iron ore contain their opposites.
Indeed, this is how Woods and Grant explained things:
"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 are two kinds of matter, which can be called positive and negative. Like kinds repel and unlike attract." [Woods and Grant (1995), p.65.]11
However, if nature works in pairs (at least), what is the paired opposite of a cat that causes that animal to change? If cats have no opposites, then it must be the case that feline parts of nature (at least) do not work in pairs. But, what applies to cats must surely apply to countless other things. What then are the external and/or internal opposites of things like Giraffes, Snowy Owls, Mountain Gorillas, Daffodils, Oak trees, Chinese Puzzles, broom handles, craters on the Moon, copies of Anti-Dühring, and the question mark at the end of this sentence? All of these are subject to change, but not, it seems, as a result of any obvious oppositional pairing or tension. [Is a question mark, for example, really locked in a life-and-death struggle with other items of punctuation? Or with its Hegelian 'other'? But, what is the 'other' of a "?"? An "!"?]
It could be objected to this that in the case of cats (and many of the other objects listed above), the opposites concerned are plainly "male" and "female". But even if that were so, these are manifestly not "internal opposites" (and neither are they "internally related" to each other -- they are causally, historically and biologically related; sexual diversity is not a logical feature of reality -- if it were there would be no hermaphrodites or asexual organisms), so change here cannot be the result of 'internal contradictions'. But even if this were not so, is it really the case that males and females must always conflict? [Anyone who has, for example, seen Leopard Slugs mating might be forgiven for thinking that these fortunate creatures have had a dialectical exemption certificate encoded into their DNA at some point. They do not 'conflict'!]
To be sure, modern medicine is quite remarkable; a few snips of the surgeon's scissors and Bob's your aunty. Despite that -- and this should hardly need pointing out -- males do not change into females (nor vice versa) of their own accord!
Moreover, while it is true that cats are able to reproduce because of well known goings-on between males and females, cats themselves do not change because of the relationship between male and female cats. If they did, then a lone cat on a desert island would be capable of living forever (or, at least, of not changing). In that case, as long as this eternal (and miserably celibate) moggie stayed clear of members of the opposite sex, it would be able to look forward to becoming a sort of feline Super-Methuselah.
But, what are we to say of those organisms that do not reproduce sexually --, and worse, what are we to make of, say, hermaphrodites? Are the latter an expression of some sort of cosmic/natural bourgeois plot against DM?
And what should we conclude about things like broom handles and copies of Trotsky's IDM? Do they change because of the tension created by their own inner/outer or 'logical' opposites? But what could these possibly be? Is the opposite of IDM, Mein Kampf or Stalin's Problems of Leninism? Could it even be these Essays?!
Does this mean, therefore, that IDM will change into one of my Essays? Well, perhaps TAR will, since my work was originally aimed specifically in opposition to that book. In which case, had this work not been undertaken, would TAR and IDM have been eternally changeless books?
[IDM = In Defense of Marxism; TAR = The Algebra of Revolution; RIRE = Reason In Revolt.]
In that case, the above passage from RIRE does little to help resolve this problem.
On the other hand, if cats change not as a result of the machinations of their external or 'logical' opposites, but because of their 'internal contradictions', then factors internal to cats must surely be responsible for their development (if we interpret "internal" topologically, since we seem to have got nowhere interpreting it 'logically'). Should we now look inside cats for these illusive opposites? If so, do these appear at the level of its internal organs? But what is the opposite of, say, a cat's liver? Does it have one? If not, is it an everlasting liver? On the other hand, if it does, will a cat's liver one day turn into a cat's 'non-liver' (a bus stop, say)?
In order to discover what the 'internal contradictions' are in this case, perhaps we should delve even deeper into the inner workings of these awkward, feline aspects of 'Being'?
If cats' livers have no opposites, then perhaps their liver cells do? But once more, what is the opposite of a cat liver cell? A kidney cell? A blood cell? (An onion cell?)
As we ferret further into the nether regions of feline inner space, perhaps these elusive opposites will appear at the molecular or atomic level? Some dialecticians seem to think so -- but they have only been able to pull this dodge by ignoring their own claims that all of nature works in pairs. [In that case, we have yet to be told what, say, the River Amazon is twinned with, let alone what the Oort Cloud's dialectical alter ego, its 'other', could possibly be.]
Nevertheless, it could be argued that 'internal opposites' actually involve the relations that exist between sub-atomic and inter-atomic forces and processes at work inside lumps of iron, cats, and much else besides.12
But, if each thing (and not just each part of a thing), and each system/process in the Totality, is a UO (as we were assured they were by the above DM-luminaries), then cats and iron bars (and not just electrons, π-mesons (Pions) and positrons, etc.) must have their own internal and/or external opposites -- that is, if they are to change.
So, for a cat to become a 'non-cat' -- which is, presumably, the 'internal' or 'external' opposite it is supposed to turn into --, it must be in dialectical tension with that opposite in the here-and-now if the latter is to help cause it to change. [We saw this in an abstract form earlier.] If not, then we can only wonder what dialecticians imagine the forces are (and from whence they originate) that cause cats and lumps of iron to change into whatever their opposites are imagined to be.
And even if molecular, inter-atomic or sub-atomic forces actually power the development of cats, cats in general will still have to change because of their paired macro-level opposites (whose identities still remain a mystery). It is not as if each cat is struggling against all the protons, electrons and quarks that exist beneath its skin. Nor are we to suppose that cats are constantly conflicting with their internal organs, fur and whiskers. If they were, then according to DM-lore recorded earlier, cats would have to turn into their internal organs, fur and whiskers, and the latter would have to turn into cats!
And even if these sub-atomic particles were locked in a sort of quantum wrestling match, one with another, the changes they induced in the average dialectical moggie must find expression in macro-phenomena at some point, or cats would not alter at all. But what on earth could those macro-phenomena be?
Furthermore, if change is to be located ultimately at the quantum level, then what are all those sub-atomic particles changing into? Many are highly stable. But, even supposing they weren't, if the DM-classics are to be believed, then whatever they change into must exist right now if it is to cause them to change into it. And yet, if these opposites already exist, the original particles cannot change into them. The best that could happen here, assuming the truth of DM, is that these 'opposite particles' must replace the originals (which then magically disappear). But, that is where we came in.
In which case, given this view of nature, things do not actually change, they just vanish, and other things take their place -- and they do so undialectically, too, since their opposites will have just vanished. But, plainly, with no more opposites, they cannot change any further.
Moreover, if the forces that cause change to cats are solely internal to cats, then as far as the mutability of such mammals is concerned, they must be hermetically sealed-off from the rest of nature (as must everything else -– this dire dialectical difficulty is examined in more detail in Essay Eight Part One, and Essay Eleven Part One and Part Two), otherwise change would not be internal to cats.
If, on the other hand, the causes of feline change are external to cats, then 'internal contradictions' can't be responsible for changing them into 'non-cats', and we are back where we started.
Furthermore, if we now ignore this 'either-or', and claim that cats change because of 'internal' and 'external' contradictions, then we would be faced with the prospect of cats changing into their internal and external opposites, if the Dialectical Prophets are to be believed. But, and once more, if these opposites already exist (which they must do if they are to help bring about such changes), then cats could not change into them!
The same difficulties apply to sub-atomic particles: if the forces that cause change are solely internal to such particles, then as far as their mutability is concerned, they must be hermetically sealed-off from the outside world, otherwise change would not be internal to these particles. If, on the other hand, the causes of particulate change are external, then 'internal contradictions' can't be responsible for changing them into a 'non-whatever'.
Alternatively once more, if the opposites of such particles cause them to change into such opposites, then they need not bother, for those opposites already exist. On the other hand, if those opposites do not already exist, what could possibly cause these changes?
In the macro-world, the idea that change is the result of 'internal contradictions' would seem to mean that when, say, a cat gets run over, that cat actually self-destructs, and the car that hit it had nothing to do with flattening it. One might well wonder then why nature produced such suicidal beasts. [Is this perhaps an example of natural de-selection?]
Of course, it could be argued along Leibnizian lines that had the cat been internally strong enough it would have survived this unequal tussle with the car. So, the real cause of this cat's changed shape is in fact to be found inside that cat. [This argument is outlined here.] As we will see in Essay Eight Part One, some DM-theorists do indeed argue along similar lines.
There is something to be said for this argument, but fortunately not much. Whatever it is that causes a cat to alter when run over is clearly not whatever it is that maintains that cat's anatomical integrity from day to day. Something must have upset this regime in order to transform that cat's shape; cats do not spontaneously flatten themselves. Few of us would be happy to be told by a Leibnizian drunk driver that it is not his fault that the family pet is spread half-way across the road because the cat itself is the cause of its radically altered anatomy. In such cases, we clearly have an example of interacting causes for the demise of that cat, none of which can be put down solely to events internal to that unfortunate animal. Of course, dialecticians do not deny this, but as Essay Eight Part One will show, their 'theory' cannot account for it after all.
Someone could object that dialectics can account for such catastrophic reconfigurations of cats. A combination of internal and external forces is the cause of their new geometry. But even that will not work, for if a cat is to change into a flat cat, then according to the DM-worthies quoted here (where we are told that all objects and processes "inevitably" turn into their opposites), such a flat cat must already exist to flatten the non-flat cat into a flat cat. So the driver (unless we are desperate enough to describe her/him as a "non-flat cat", on the basis that he/she is the obvious cause of the flattened cat in question), given this new turn of events, did not flatten the cat, the non-existent non-flat cat did that.
[Or, of course, if we are even more desperate to find a cause to rescue this theory, we could suppose there to be ethereal flat cats (in a nether world somewhere) working some sort of evil on their less pancake-like counterparts this side of the veil -- and just in time, too, for lorries to run them over. Too stupid an explanation to contemplate? Well DM-theorists already postulate the existence of all manner of weird and wonderful 'abstractions', which are nowhere to be found in material reality, to account for events and processes in nature. So, perhaps this is an 'abstract' non-flat cat? (In fact, those who already "understand dialectics" should be able to get their heads around this conundrum with ease.)]
Furthermore, if we opt for that earlier get-out clause and describe the driver as a "non-flat cat", so that at least we would have here a dialectical sort of cause of flat cats, then that driver (this non-flat cat) must likewise turn into her/his opposite, too, if the Dialectical Gospels are to be believed. Alarmingly, that opposite must either be a non-driver (this option dialectically disqualifying her/himself in the act), or a flat cat! So, in this Hermetic pile-up, both driver and cat become flat cats!
A nice coincidence of opposites, this!
Despite this, and whatever their commitment to this 'Law' amounts to, one supposes(!) that no dialectician still in command of her/his senses would excuse, say, a policeman for inflicting on her/him actual bodily harm on the grounds that Leibnizian nature unwisely failed to incorporate into the heads of militants the ability to withstand Billy Clubs. Once again, dialectics would be disproved in practice; gashed heads on picket lines are not produced by "self-development".
Alternatively, if the causes of feline (or cranial!) mutability are both internal and external, then change cannot be the sole result of 'internal contradictions', and things would not be self-developing, as Lenin alleged.
Alas, there does not seem to be any way we can lever into this picture an 'opposite' that non-flat cats turn into so that that 'opposite' can help produce the required flattening.
So, even while unfortunate moggies turn into such pancake-like non-cats in traffic accidents, the opposite that they 'develop' into cannot have been part of the UO that ironed them into that novel shape.
In which case, it remains a mystery what the 'opposite' of a cat is (which a cat must turn into) which is part of the UO that brings about such topological re-configurations --, if the DM-worthies are to be believed. Is there a third causal item here (as we supposed above), yet to be discovered either by Zoology, forensic science, time travellers, or cat psychics -- over and above the non-flat cat and the flat cat -- that is part of this feline tragedy?
If not, can DM in fact help explain dead moggies?
This flat catastrophe is not just isolated to furry mammals; it applies to Materialist Dialectics, too --, for if all things change into their dialectically-paired opposites, and change is caused by the dialectical tension between such things and such opposites, and if Capitalism is to change into Socialism, then Socialism must now exist somewhere for this to happen!
The same must be said for the connection between, say, capitalism and communism
(or better, Capitalist Relations of Production [CRAP]), and Socialist
Relations of Production [SORP]) --, and indeed for the connection between the forces and
relations of production (where it is patently obvious that neither of these change into the other
(their opposites)).
For the purposes of argument, let us assume that SORP does not actually exist in the here-and-now. But, given
the above DM-theses, if CRAP is to change into SORP, SORP must already exist
in the here-and-now for CRAP to change into it, and for that change to
be produced by it.
But, if that opposite (SORP) already exists it cannot have come from CRAP
(its 'opposite') since CRAP can only change because of the action of its own
opposite (namely -- SORP!) -- unless SORP exists before it exists!
[The same comments would apply to "potential SORP" (or even to some sort of "tendency to produce SORP", be this a 'sublated' tendency or
indeed actuality, it
matters not), but the reader is left to
work the details out for herself.]
So, this opposite (SORP) must have popped into existence from nowhere --, or it must
always have been in existence, if DM is correct.
Once more, this is not to deny change, nor is it to suggest that the present author does not want to see the back of CRAP, and the establishment of SORP; but if DM were correct, this will never happen.
To be sure, in the real world very material workers struggle against equally material Capitalists, but neither of these turn into one another, and they cannot help change CRAP into SORP, since neither of these is the opposite of CRAP or SORP, nor vice versa, either.
[On the 'contradictions' Marx that speaks about in Das Kapital, see here. On 'real material contradictions', see here.]
If it is further complained that in many of the above examples it is human intervention that has changed things that already occur naturally, and because of that, different principles apply (since our activity will have interfered with the normal operation of the natural opposites of things like iron ore).
But, aren't we part of nature?
Putting this awkward reminder to one side for now, what about substances that did not exist (so far as we know) before human beings made them?
Is plastic, for instance, governed by dialectical 'Law'? What then is the natural opposite of polyethylene? Is it the same as that of Polypropylene, polybutylene terephthalate (PBT), polystyrene, polyvinyl chloride (PVC), and polymethylpentene (TPX)?
If not, has humanity made things that are above and outside the dialectical 'Law'? Again, if not, and if each of these plastics has an opposite (which they must have, or they would not change), how is it that human labour was able to make each of them at the same time as making their opposites? Was this done by default, as it were? But, if human labour turns these substances into all manner of things, do they not therefore have countless artificial (or is it natural?) opposites? [I.e., do they have as many opposites as the things we can change them into?] And were all these artificial opposites created the moment the original substances were manufactured? All of them?
On the other hand, and once again, if these opposites only pop into existence when these plastics are changed into them (meaning that human labour cannot have created these opposites in the act of inventing the original plastics), how is it possible for those non-existent opposites to 'contradict' the existent unchanged plastic so that the plastic could be changed into them?
But worse, if the opposite of, say, PVC causes it to change, how then does human labour feature anywhere in the transformation? What is the point of building factories and studying polymer chemistry if the opposite of PVC changes lumps of PVC into plastic buckets all by itself? When human beings work on PVC to change it into all the many things that they do (using complex techniques and expensive machinery), are they merely onlookers -- not part of the action, as it were --, but, just viewing things that would have happened anyway, naturally?
Or, have the capitalists discovered a way of by-passing dialectical 'Law' (perhaps as part of their hatred of Marxism)? Is all plastic therefore reactionary?
But, if human labour [HL] can change such things into their opposites, then that must mean that HL is the opposite of, say, PVC, otherwise it could not actually change it (according to the above DM-worthies). In that case, HL must change into PVC!
Of course, dialecticians can be found who will tell you that exchange value [EV] is "condensed labour power" [LP], and hence LP and EV are 'opposites'. But, if that is the case, according to the Dialectical Gospel, LP must struggle against EV. Has anyone ever witnessed this abstract wrestling match?
This is, of course, a serious problem, since use value [UV] is supposed to contradict EV, too -- but, UV and EV do not seem to struggle much either.
Again, even this cannot work, for if LP turns into EV, then they must both exist at the same time, as we have seen dozens of times already. Otherwise one of these opposites (EV) could not bring about a dialectical change in the other (LP). And whatever intermediaries we throw in here to rescue thus self-destructing 'theory' (be they very real workers, machines, banks, or CRAP itself), if such things are to cause a DM-style change, they must be opposites of one another or of EV and/or LP, and hence they must turn into one another (if the Dialectical Holy Books are to be believed). In that case we might well wonder where all those workers are who are changing into EVs? And where on this planet is CRAP morphing into, say, a hydro-electric dam (if the relations of production really do 'contradict' the forces of production)?
[CRAP = Capitalist Relations of Production.]
Once more, this is not to deny such changes, merely to underline the fact that DM cannot account for it.
Of course, in Marxist economics we have LP and Capital [C] cycles, and the like, but does LP actually struggle against C? Not obviously so, it would seem. As we have already noted, very material workers struggle against their equally material bosses, but how is it possible for LP to struggle against C?
Someone might object that this misrepresents DM; it is the inherent dialectical contradiction between capital and labour (or that between their relevant classes) that foments struggle.
Perhaps so, but until we are told what a 'dialectical contradiction' is, that response itself is devoid of sense (since it contains a meaningless phrase: "dialectical contradiction". [More on that in Essay Eight Parts One, Two and Three.]
Furthermore, is it really the case that everything turns into its 'opposite', made to do so by 'struggling' with its 'opposite', as Hegel, Engels, Lenin, Mao and Plekhanov said? To be sure, certain states of matter do change into what might conventionally be called their "opposites" (e.g., a hot object might change and become cold; something above might later be below, and so on -- but even here, these opposites do not cause these changes!), but this is certainly not true of everything. Do men, for instance, turn into women, fathers into sons, brothers into sisters, left- into a right-hands, the working class into the capitalist class, forces of production into relations of production, use values into exchange values, negative numbers/electrical charges into positive numbers/electrical charges, electrons into protons, and matter into 'anti-matter'? If not, what is the point of saying that everything does do this? And why claim that objects and processes have internal or external opposites if in most cases they feature nowhere in the action, or, again, if many things do not turn into them?12a
Furthermore, if Lenin were correct when he said that "every determination, quality, feature, side, property [changes] into every other…", it would mean that everything (and every property) must change into every other property!
But, if that were so, heat, for example, must change into, say, colour, hardness and generosity (and much else besides); liquidity must transform itself into brittleness, circularity and inquisitiveness (and much else besides); gentleness must mutate into velocity, opacity and bitterness (and much else besides); squareness must turn into arrogance, honesty and duplicity (and much else besides), and so on.
Is there a single person on the planet not suffering from dialectics who believes any of this?
Once again, if these bizarre changes are not the case (as they plainly are not!), and if such things are not implied both by these terminally vague 'Laws' and by what Lenin said, what is the point of him asserting that this is precisely what everything does?
Indeed, that was the point of the observation made earlier about dialecticians vacillating between the idea that UOs cause change and the belief that things change into their opposites -- sometimes veering toward the doctrine that change produces these opposites (and perhaps all of them). The first of these alternatives is examined in Essay Eight Part One, but if the second alternative were the case, we would surely witness some bizarre transformations in nature and society as men changed into women, cats into dogs, banks into charities and the Capitalist Class into the Working Class -- and then back again!
However, as has been argued in detail above, if change merely creates these opposites then, plainly, that development could not have been the result of a tension between two opposites that actually co-existed -- clearly so, since at least one of them would not yet exist! Hence, with respect to objects in the latter category, change would create them, not them it.
This completely scuppers the DM-account of change for it is now clear that there is nothing in the DM-scheme-of-things that could cause the many different sorts of change we see in nature and society.
In which case, if change occurs then dialectics -- the much vaunted science of change -- cannot explain it. Indeed, if DM were true, change could not happen.
However, turning to specifics, Engels claimed that:
"…life consists precisely and primarily in this -- that a living thing is at each moment itself and yet something else. Life is therefore also a contradiction which is present in things and processes themselves, and which constantly asserts and resolves itself; and as soon as the contradiction ceases, life, too, comes to and end, and death steps in." [Engels (1976), p.153.]
But what is the 'contradiction' supposed to be here? Is it that: (1) living cells contain dead matter; (2) life is a constant struggle to avoid death; (3) life can only sustain itself by a constant struggle with dead matter; or is it that (4) the contrast and/or conflict between these two (processes), life and death, creates the dynamism we see in living things? And, what on earth is this (5) "something else" that each living thing is supposed to be, or to become, according to Engels?
As far as (1) is concerned, the contrast between living and dead matter seems to depend on the obsolete idea that there is an intrinsic difference between living and dead molecules -- that there is a 'life force' at work in nature. While it is unclear whether Engels believed this or not (in fact, in several places he seems to have rejected this notion, e.g., Engels (1954), p.282), it is reasonably clear that subsequent dialecticians do not. So, it seems reasonable to conclude that this cannot be what underlies the 'contradiction' in this case.
With respect to (2): while it is undeniable that most living things constantly strive to stay alive, it is still unclear what the alleged UO is supposed to be here. If a living cell is a UO, and the scene of a bitter struggle between life and death -- in the sense that each cell contains within itself both life and death, slugging it out, as it were --, what physical form do these mysterious processes/beings take? It is not as if we could easily identify either or both -- as we can with, say, with magnetic or electrical phenomena. There, the presence of apparently opposite poles and/or charges is verifiable and measurable. Here (with respect to life), there do not seem to be any easily identifiable opposing forces.
But, if dialecticians are correct, and everything is indeed a UO, each living cell should (it seems) contain death within itself, and not just have it confronting it externally. But what material form does 'death' take? Are we to imagine that a black, shrouded figure, sickle in hand, inhabits every living cell? If not, how is 'death' to be conceived in this case? Indeed, what form does 'life' itself take? Is it perhaps an incarnation of the Archangel Gabriel? Or, maybe Louis Pasteur?
On the other hand, if this particular UO is a set of opposing processes (or, indeed, if this is to be regarded as a special type of interaction between certain sorts of forces), as options (3) and (4) seem to suggest (these picturing living systems constantly battling against disintegration, the latter perhaps manifested in catabolic reactions), then we are surely on firmer ground.
But, why would anyone want to call such a set-up a UO? What exactly are the opposites that are struggling here? It is not as if inside each vibrant cell there is another older (or even a decaying) cell waiting to emerge, nor yet one that is fighting the embattled host cell all the time, stabbing it 'inside the back', as it were. Nor is it credible to believe that the products of catabolism and anabolism are themselves locked in constant struggle. Indeed, it is not easy to see catabolism as directly 'contradictory' even to anabolism (howsoever the word "contradiction" is understood). These processes do not oppose one another by preventing the other working, or by immediately picking apart what the other has produced; they just work in different ways, often in separate parts of the cell.
They certainly do not turn into one another (as we have been led to believe they should by the dialectical worthies). Nor do the inputs of one always turn into the outputs of the other. For example, the Krebs metabolic cycle produces water and carbon dioxide from carbohydrates, fats and proteins. But no cycle in animal cells does the reverse. Sure, these products are broken down, but not in a reverse Krebs cycle.
So, anabolic and catabolic processes do not typically confront one another in normal cells, opposing whatever the other does. To imagine such processes as 'contradictory' would be about as intelligent as, say, believing that a group of men digging a road up somewhere were 'contradicting' ("opposing" or "struggling against") another group mending or extending that same road a few hundred yards down the way. Or, that, say, the manufacture of aeroplanes 'contradicts' the scrapping of aluminium chairs.
And, even if it were accurate to describe catabolism as undoing the results of anabolism, that would still not amount to either of them 'contradicting' one another. Undoing is not 'contradicting' -- if it were, then doing would be tautologious!
Of course, if someone were to insist that despite the above such processes are contradictory, they would owe the rest of us an explanation of the literal nature of the contradiction allegedly involved here. In that case, it would be pertinent to ask how either process could possibly be "gainsaying" the other.12b
But even if this were to be rejected, too, DM would still not be out of the non-dialectical woods. While it could be argued that in this case we do have 'opposites' that are internal to cells, we do not as yet have opposites internal to anabolic or catabolic processes themselves. So, if either of these two cause the other to change, that would clearly be another example of an externally-motivated transformation. Moreover, anabolism would have to turn into catabolism, and vice versa, if the Dialectical Gospels are to be believed.
However, according to Lenin all change is internal, and everything develops of itself:
"Dialectical logic demands that we go further…. [It] requires that an object should be taken in development, in 'self-movement' (as Hegel sometimes puts it)…." [Lenin (1921), p.90.]
Even though anabolic processes certainly involve objects (i.e., molecules), if they undergo development, that cannot be the result of an interaction with catabolic process (because that would be an external influence once more). On the other hand, if they do alter each other (but how?), then Lenin's "demand" will have to be withdrawn.
Nevertheless, here, as elsewhere, DM-descriptors look decidedly figurative -- except, in this case it is not easy to see what the trope could possibly be. But, if they are merely figurative, that might be all to the good; it would at least allow the interpretation of the 'contradictions' uncovered in this 'Law' to be interpreted, say, poetically. No one minds if poets contradict themselves (e.g., Walt Whitman), or one another.
Even if the word "struggle" were substituted for "contradict", the situation would not change noticeably. Since literal struggles can only take place between agents, that would mean that this part of DM could work only if biochemical reactions in vivo were personified, or if they were under the control of an agent of some sort. In that case, this use of the word "struggle" would clearly be figurative, too. [More on this here, here, and here.]
Every Confirmation Is Also A Refutation
However, it could be objected that the above considerations are highly abstract, and are thus irrelevant (although it is not easy to see how the average cat is abstract when flat or otherwise). Hence, it could be argued that DM is in fact concerned with real material contradictions confirmed in practice.13
But, how could such things be checked to make sure they were genuine "material contradictions"? Fortunately, John Rees explained how (but in relation to concepts drawn from HM (i.e., Historical Materialism)):
"[O]nce we are sure that our concept of 'capital' is a true reflection of the actual existing capital –- then we can also be sure that any further categories that emerge as a result of contradictions which we find in our concepts will necessarily be matched by contradictions in the real capitalist world." [Rees (1998), p.110.]
However, Rees added the following proviso:
"This…is only a safe assumption on the basis of constant empirical verification…." [Ibid., p.110.]
The idea appears to be that any contradictions that remain (in a theory that has itself been thoroughly checked against reality at every stage) must "of necessity" be a genuine reflection of actual objects and processes in nature and society. This safeguard is necessary to rid 'materialist dialectics' of the Idealist 'excesses' of Hegel, as well as prevent any of its theories from being. or becoming. defective (in that defective theories are self-contradictory; more on this in Essay Eleven Part One). [Rees (1998), pp.52-53, 108-18.]
Nevertheless, as far as DM-contradictions are concerned, it is not at all clear how this process is supposed to work -- even when it is executed exactly as intended. Presumably, on this basis, 'incorrect' contradictions will be eliminated because: (1) they were self-contradictions, or (2) they are falsified by experience, or (3) they could not be verified (by appropriate methods).
But, with respect to any of the contradictions that might be retained (and thus seen to be correct 'reflections' of reality), how could investigators be sure that future contingencies will never arise (in the shape of further evidence) that require their elimination? [On this, see below.]
Even so, (1) cannot be right, otherwise we should have to reject Engels's analysis of motion, which pictures it as self-contradictory. [On this, see Essay Five.]
Moreover, in connection with option (2), what evidence could possibly refute a contradiction? How is it possible for a contradiction to be falsified by experience? Presumably, that would occur if propositions appertaining to experience contradicted something that was already contradictory to begin with. But, what sort of monstrosity would that be?
Consider again Engels's depiction of the contradictory nature of living cells:
"We saw above that life consists precisely and primarily in this –- that a living thing is at each moment itself and yet something else. Life is therefore also a contradiction which is present in things and processes themselves, and which constantly asserts and resolves itself; and as soon as the contradiction ceases, life, too, comes to and end, and death steps in." [Engels (1976), p.153.]
"Abstract identity (a = a; and negatively, a cannot be simultaneously equal and unequal to a) is likewise inapplicable in organic nature. The plant, the animal, every cell is at every moment of its life identical with itself and yet becoming distinct from itself, by absorption and excretion of substances…, in short, by a sum of incessant molecular changes which make up life….
"Life and death. Already no physiology is held to be scientific if it does not consider death as an essential element of life (note, Hegel, Enzyklopädie, I, pp.152-53), the negation of life itself, so that life is always thought of in relation to its necessary result, death, which is always contained in it in germ. The dialectical conception of life is nothing more than this…. Living means dying." [Engels (1954), pp.214, 295.]
[The problems connected with Hegel and Engels's egregious understanding of Identity will be tackled in Essays Six, Eight Part Two and Twelve.]
The new batch of difficulties Engels's view face can be brought out by the following argument:
L1: Cell C1 is both alive and not alive.
L2: Experimental evidence shows that C1 is alive.
L3: Experimental evidence also shows that C1 is also not alive.
L4: L2 falsifies L1.
L5: L3 falsifies L1.
L6: However, the conjunction of L2 and L3 verifies L1.
L7: Therefore, L1 has been falsified and verified.
[It is worth noting that this 'argument' is not valid, and is only reproduced here to try to make sense of what Rees and Engels could possibly have meant.]
As seems plain, a confirmation of a DM-contradiction is of a piece with its refutation.
Of course, it could be argued that observation could confirm that a cell is alive and not-alive all at once -- i.e., that contradictions can in fact be observed. This response will be considered below.
But, as noted above, if reality itself were contradictory, the 'falsification' of a contradiction would also amount to its automatic 'verification', and vice versa. So, it seems that option (2) above is closed-off as far as the investigation of DM-contradictions is concerned. This must mean that Rees's requirement that contradictions be tested against experience is an empty gesture, since, with respect to DM-contradictions, if reality were contradictory, it would both confirm and refute their presence. In which case, DM-theorists would have no reason whatsoever to reject any contradictions that appeared in their theory; but, at the same time, they would have eminently good reasons for rejecting all of them (at least to prevent their theory from becoming defective). [More on this in Essay Eleven Part One.]
The quandary now facing dialecticians we might call the "Dialecticians' Dilemma" [DD]. The DD arises from the uncontroversial observation that if reality is fundamentally contradictory then a true theory should reflect this supposed state of affairs. [Why this is so is explained here.] However, and this is the problem, in order to do this any such theory must contain contradictions itself, or it would not be an accurate reflection of nature. But, if the development of science is predicated either on the removal of contradictions from theories, or on the replacement of older theories with newer, less contradictory variants, as DM-theorists contend, then science could not advance toward a 'truer' account of reality. This is because scientific theories would then reflect the world less accurately, having had all (or most) of their contradictions removed.
[Of course, if the advancement of science is not dependent on the removal of all or most contradictions, then scientists would face intractable difficulties of their own -- for example: how to tell a defective theory (one that is shot through with contradiction) from a theory that is not so afflicted. Fortunately to date, scientists have not adopted these ill-advised dialectical tactics, and have remained annoyingly loyal to the protocols of FL.]
[FL = Formal Logic.]
Conversely, if a true theory aims to reflect more accurately the contradictions in nature (which it must do if reality is contradictory) then, in order to be consistent with such dialectical demands, scientists should not attempt to remove contradictions from -- or try to resolve them in or between -- theories. Clearly, on that score, science could not advance, since there would be no reason to replace a contradictory theory with a less contradictory one. Indeed, if DM were correct, scientific theories would become more contradictory -- not less -- as they approach more closely the truth about avowedly 'contradictory' reality. This, of course, would mean that scientific theory as a whole would become more defective with time!
On the other hand, if science advanced because of the elimination of contradictions then a fully true theory should have had all (or most) of these removed. Science ought then to reflect (in the limit) the fact that reality contains no contradictions!
[It is worth noting here that critics of DM have already arrived at that unhelpful conclusion, and they managed that without an ounce of dialectics to slow them down.]
However, according to DM, scientific theories should be replaced by ones that depict reality as fundamentally contradictory, this despite the fact that scientists will have removed every (or nearly every) contradiction in order reach that point. On the other hand, if scientists failed to remove contradictions (or, if they refused to replace an older theory with a newer, less contradictory one), so that their theories reflected the contradictory nature of reality more accurately, they would then have no good reason to reject any particular theory no matter how inconsistent it proved to be.
Whichever way this rusty old DM-banger is driven, the 'dialectical' view of scientific progress (and of 'contradictions') hits a very material brick wall in the shape of the DD each time.
Once more, it could be objected that dialecticians do not believe that scientific theories should have all or most of their contradictions removed if science is to advance, merely the ones that hold up progress.
However, dialecticians have so far failed to distinguish those contradictions which are the mere artefacts of a defective theory from those that supposedly reflect the 'objective' state of the world. But, how might these be distinguished in DM-terms? How is it be possible to decide whether a contradiction is an accurate reflection of reality or whether it's a result of a faulty theory, if all of reality (including scientific theory) is contradictory?
An appeal to practice here would be no help since that takes place in the phenomenal world, which is riddled with DM-contradictions and so must be contradictory itself! In that case, it is to be wondered how practice can help confirm (or refute) a theory if its deliverances are themselves part of the same contradictory reality on test. We saw above that confirmation and refutation are all of a piece, anyway, given DM. Moreover, as we will see in Essay Ten Part One, practice is no friend of dialectics, anyway.
For example, DM-theorists generally argue that the wave-particle duality of light confirms the thesis that nature is fundamentally dialectical; in this case, light is supposed to be a UO of wave and particle. Precisely how they are a unity (i.e., how it could be true that matter at this level is fundamentally particulate and fundamentally non-particulate all at once) is of course left eminently obscure. Exactly how this phenomenon helps account for the material world is even less clear.
Even though all dialecticians refer to this 'contradiction', not one has explained how and why it is a contradiction, nor less how and why it is a 'dialectical contradiction' (even if we knew what these were).
Consider these two propositions:
Q1: Light is a wave.
Q2: Light is particulate.
Now, Q1 would contradict Q2 if the following were the case:
Q3: No wave can be particulate.
Q4: Light must be one or the other, wave or particle.
[Q4 is required or Q1 and Q2 would merely be inconsistent.]
But is Q3 true? Surely not, for if physicists are correct, light is both! However, independently of that, there are plenty of examples of waves in nature which are particulate; e.g., sound waves, water waves and Mexican waves. So, Q3 is in fact false!
Moreover, Q4 could be false, too. Light could turn out to be something else about which we do not yet have a concept. That, of course, would make Q1 and Q2 merely inconsistent. Do 'dialectical logicians' know what to do with 'dialectical inconsistencies'?
But, even if in some way this were a contradiction it does nothing to explain change -- unless we are supposed to accept the idea that the fact that light is a particle changes it into a wave, and vice versa. Are we to conclude that these two states/processes are 'struggling' with each other? But what is the point of that? What role does this particular 'contradiction' play either in DM or in Physics? At best it seems to be merely ornamental.
[One benighted DM-fan, when confronted with this objection in a private correspondence, said that these were 'illustrative' contradictions (even though they do no dialectical work). This can only mean that dialecticians resemble fundamentalist Christians -- who think that, say, the three-dimensionality of space 'illustrates' the Trinity, God having left this and other clues littered across reality for us to find. [Don't believe me? Then check this out.] In a similar way, and with regard to dialectics, perhaps 'Being' Itself has sent this conundrum our way to inform DM-fans they are on the right path to Dialectical Nirvana: the 'illustrative', but useless, duality of wave and particle!]
At worst, of course, all the problems we met earlier in connection with the DM-'theory' of change would apply here too.
Now, if we put to one side the 'solution' to this puzzle offered by, say, Superstring Theory, there are in fact more than a handful of Physicists -- with, it seems, a more robust commitment to scientific realism than the average dialectician can muster -- who believe that this 'paradox' can be resolved within a realist picture of nature. [Evidence appears here, and here.] Whether or not they are correct need not detain us since DM-theorists (if consistent) ought to advise these rather rash realists not to bother trying to solve this riddle. This is because dialectics has already provided us with an a priori solution: since nature is fundamentally contradictory there is in fact no solution --, which paradoxical state of affairs should, of course, simply be "grasped", or "Nixoned".
However, in this case it is possible to see how practice cannot help; if experiments are conducted that allegedly show that light is both a particle and a wave, then DM-theorists would have no reason to question this supposedly contradictory data, nor to try to resolve this difficulty.
[However, so far experiments have merely shown that under certain conditions light is particulate, under others it is wave-like, but not both.]
Nevertheless, anyone not committed to such an obtuse view of reality would have good reason to question it, and this might, for all anyone knows, assist in the advancement of science.
Not so with DM-fans, whose advice could permanently hold things up.13a
In that case, practice alone cannot distinguish between these two views (the realist and the dialectical), even though one of these will seriously hold up progress. Moreover, since we know that practically any theory can be made to conform to observation if enough adjustments are made elsewhere, this criterion is doubly defective.
[This allegation will be substantiated in more detail in Essay Ten, and in a later Essay on the nature of science.]
[QM = Quantum Mechanics.]
Once more, in advance of any test, DM-theorists should (again, if they are consistent) advise scientists not to bother trying to refute the orthodox interpretation of QM, or resolve the paradox upon which it is based, since there is no point in view of their a priori theory, which sees nature as fundamentally contradictory.
Unfortunately, if physicists took this advice, science could not advance to a superior view of nature (if one exists) by eliminating this alleged contradiction. At best, this a priori DM-approach to knowledge would close available options down, forcing scientists to adopt a view of reality that might not be correct -- and, given what we already know about the history of Physics, probably isn't correct.13b
Fortunately, there is little evidence so far that Physicists have taken any note of this aspect of dialectics, even if any of them have ever heard of it.
Now, only those who disagree with Lenin about the incomplete nature of science (or, alternatively, who have a rather poor grasp of the history of Physics) would risk concluding that contemporary science has a final and complete picture of reality, at least in this particular area. If so, Physics could only advance by eliminating this paradox -- hence eliminating one of the best examples in the DM-Grimoire which allegedly show that nature is fundamentally contradictory.
Of course, only those who wish to foist their ideas on nature would object at this point.
On the other hand, if DM-theorists' advice to scientists is that they should in general try to replace contradictory theories (such as this part of QM as it is alleged to be) with less logically-challenged ones, then they will have to abandon the idea that nature is fundamentally contradictory -- at least here. This conclusion is all the more pressing in view of the fact that some scientists think they have already solved this problem -- David Bohm, for example, being one.14
But, this is just the DD once again: the DM-inspired belief in the 'contradictory' nature of reality, coupled with the claim that science can only advance by removing contradictions cannot, it seems, distinguish between contradictions that hold up the progress of science (and which are therefore artefacts of a defective or incomplete theory) from those that reveal the essentially 'contradictory' nature of reality.
Although some (like Plekhanov) have acknowledged the problem, it remains unresolved to this day.
The various ways there might be for DM-theorists to escape from the hole they have dug themselves into will be examined in a later Essay, and there shown to fail.
Dialecticians are therefore advised to stop digging.
In addition, it is unclear how option (3) above itself is supposed to work. How would it be possible for anyone even to try to verify a DM-contradiction? For example, does humanity possess technology sensitive enough to observe time intervals of the order of, say, 10-100 seconds, so that Engels's claims about motion can be checked? What then about intervals of 10-1000 seconds? And yet, observations of motion would have to be made using time intervals of this order of magnitude (and far better) in order to confirm whether they remain contradictory at this level of accuracy, at least. But, where do we stop?
Naturally, some might want to appeal to Planck time intervals (of the order of 5 x 10-44 seconds) to provide a natural place to halt, but this is no help at all. A single one of these Planck 'instants' is, so we are told, 1026 times shorter than the shortest time interval so far measured -- an alto-second (or 10-18 seconds). In that case, there is little prospect that these far shorter intervals will ever be measured. And since Planck intervals are theoretical entities, the chances are that they too will be revised away one day (in line no doubt with Lenin's claim that knowledge is never final).
Anyway, the answer to this particular 'difficulty' is irrelevant. That is because, no matter how slender the time frame, no measurement could conceivably test whether a moving object was in two places at once, only whether it is in two places in the same finite interval. [More on this in Essay Five.]
The Revenge Of The Petty-Bourgeois Cell
To resume the argument -- more specifically: with respect to the alleged contradiction outlined in L1, above (i.e., "Cell C1 is both alive and not alive"), how would it be possible to confirm the alleged fact that a cell was alive and dead at the same time? Certainly, just looking at cells won't help. Nor is it much use referring to the vagueness of the boundary between life and death. This is because Engels himself regarded living cells as a unity of living and dead processes while such cells were still alive, and this is the alleged contradiction that requires verification.
Now, it is worth reminding ourselves at this point that confirmation is required to prevent this theory being branded dogmatic, a priori and thus Idealist. This is in fact a demand that DM-theorists also insist upon:
""All three are developed by Hegel in his idealist fashion as mere laws of thought: the first, in the first part of his Logic, in the Doctrine of Being; the second fills the whole of the second and by far the most important part of his Logic, the Doctrine of Essence; finally the third figures as the fundamental law for the construction of the whole system. The mistake lies in the fact that these laws are foisted on nature and history as laws of thought, and not deduced from them. This is the source of the whole forced and often outrageous treatment; the universe, willy-nilly, is made out to be arranged in accordance with a system of thought which itself is only the product of a definite stage of evolution of human thought." [Engels (1954), p.62. Bold emphasis alone added.]
"Finally, for me there could be no question of superimposing the laws of dialectics on nature but of discovering them in it and developing them from it." [Engels (1976), p.13. Bold emphasis added.]
"The dialectic does not liberate the investigator from painstaking study of the facts, quite the contrary: it requires it." [Trotsky (1986), p.92. Bold emphasis added]
"Dialectics and materialism are the basic elements in the Marxist cognition of the world. But this does not mean at all that they can be applied to any sphere of knowledge, like an ever ready master key. Dialectics cannot be imposed on facts; it has to be deduced from facts, from their nature and development…." [Trotsky (1973), p.233. Bold emphasis added]
"A consistent materialism cannot proceed from principles which are validated by appeal to abstract reason, intuition, self-evidence or some other subjective or purely theoretical source. Idealisms may do this. But the materialist philosophy has to be based upon evidence taken from objective material sources and verified by demonstration in practice...." [Novack (1965), p.17. Bold emphasis added]
"This…is only a safe assumption on the basis of constant empirical verification…." [Rees (1998), p.110.]
"Our party philosophy, then, has a right to lay claim to truth. For it is the only philosophy which is based on a standpoint which demands that we should always seek to understand things just as they are…without disguises and without fantasy….
"Marxism, therefore, seeks to base our ideas of things on nothing but the actual investigation of them, arising from and tested by experience and practice. It does not invent a 'system' as previous philosophers have done, and then try to make everything fit into it…." [Cornforth (1976), pp.14-15. Bold emphasis added.]
"Engels emphasises that it would be entirely wrong to crudely read the dialectic into nature. The dialectic has to be discovered in nature and evolving out of nature....
"Of course, that does not mean we should impose some a priori dialectical construct upon nature. The dialectic, as Engels explains time and again, has to be painstakingly discovered in nature....
"Engels did not make the laws of nature dialectical. He tried, on the contrary, to draw out the most general dialectical laws from nature. Not force artificial, preconceived, inappropriate notions onto nature." [Jack Conrad, Weekly Worker, 30/08/07. Bold emphasis added.]
Once more, then: how is it possible to confirm that cells are indeed as dialecticians say they are?
Perhaps a digression into the nature and application of vague predicates (such as "...is alive", or "...is dead") would be useful here --, at least as far as this DM-contradiction is concerned?
However, such a detour is unlikely to help. This can be seen from a consideration of another less fraught but equally vague distinction: the equally vague boundary between night and day.
In relation to this, few DM-theorists would want to argue (it is to be hoped!) that daylight is itself a contradictory combination of night and day at any specific point on earth not near the boundary of the Sun's moving shadow. Hence, at mid-day in high summer on the Tropic of Cancer in blazing sunlight, say, only a complete fool would want to argue that because the boundary between night and day is vague, and because day eventually turns into night, bright daylight is a contradictory combination of night and day (or of darkness and light). And even if it were possible to find a few maverick, hard-core DM-fans who were prepared to argue along these lines, even fewer would agree with them -- except they might both agree and disagree, just to wind them up.
Less supercilious critics would ask such confused comrades for the empirical evidence that backs up the odd idea that light itself (in the form of bright mid-day tropical sunshine) is a UO of light and darkness (or, perhaps of night and day 'dialectically' slugging it out). Indeed, they might also want to know what work this idea could possibly do in DM, even if it were correct. Are we to suppose that light 'struggles' with its opposite darkness at mid-day? Presumably not. Must we then argue that darkness makes light change into darkness, and vice versa (as the DM-classicists tell us that such 'opposites' must)? If so, this innovative piece of Physics will no doubt force scientists to re-write their theory of light, for up until now they had recklessly assumed that light was created by the way sub-atomic particles behaved, and that this was the result of a transformation of one form of matter/energy into another. They had certainly given no thought to the possibility that it was the result of the operation of a privation -- the lack of light -- on light itself, which made nightfall occur! The latter, of course, has more to do with the rotation of the Earth, and nothing at all to do with a battle between photons and/or a lack of one.
In that case, it seems that this 'dialectical union' of light and dark does no work at all, even if we were tempted to believe in it.
So, in places, and at times, even potentially vague predicates have clear applications -- or they can be paraphrased so that they mimic ones that do. In that case, in order to test Engels's claims about living things, we would need a way of deciding whether a certain cell was a UO while it was still unambiguously alive. That is why it was claimed above that a digression into the applicability of vague predicates would be of no assistance to dialecticians. No matter how vague the predicate, it would still not be possible to verify Engels's claim that a cell is alive and dead at the same time (or that it is a dialectical mix of the two) while it was still clearly alive.
Even at the boundary between the life and death, we do not possess equipment sensitive enough to verify Engels's a priori thesis, even if we knew how to go about doing it.
Of course, it would always be open to a DM-supporter to point out that a living cell is constantly exchanging dead matter with its environment, or that certain parts of the cell are not actually alive while the rest of that cell is, as noted earlier. Nevertheless, exactly how this confirms the claim that a cell is alive and dead all at once is still unclear. At best, it would simply demonstrate that living things contain dead matter. It would no more show that when a cell is alive it is also dead than would an analogous claim demonstrate that people are clothed and naked at the same time because we all have nothing on underneath our underwear, and were contradictory UOs for all that.
On the other hand, if anyone were foolish enough to so suppose, then they would have to suppose further that one of these opposites (being naked, say) was locked in 'dialectical' tension with the other (being clothed), which would perhaps 'explain' why we put clothes on and take them off at various times in the day!
Again it could be objected that the issue is actually this: living things are changing all the time; hence, they are a dialectical unity of living and dead matter/processes. Cells constantly absorb dead matter from their environment and turn it into living matter. Dialecticians certainly do not maintain that an organism (or a cell) is wholly alive and completely dead all at once, as the above foolishly suggests. Cells are a dialectical union of two contradictory processes, which process is slowly changing the host organism, or perhaps even killing it. Or so it could be argued.
Nevertheless, such a response will not do. This discussion is centred on the controversial idea that DM-'contradictions' can be verified or falsified in some way, nit that they can be re-jigged theoretically every time this theory encounters an objection. [That will be considered in other Essays.] This was required in order to silence claims that DM is just another form of Idealism. The introduction of more jargon here does not constitute confirmation. It does however increase suspicion that this is all that dialecticians can offer in order to 'substantiate' their theory: more words. And if that were so, the requirement that dialectics be confirmed (somehow) by checking it against material reality would be just an empty gesture.
It could, however, be objected that the above quotations clearly show that dialectics is also concerned with generalisation. Dialecticians try to deduce general laws from nature, and this is all that Engels has done here. Since that is what scientists also do, where is the problem?
The nature of science and what scientist actually do will be examined in another Essay, but in advance of that it is worth directing the reader to this section of Essay Eleven Part One, where this topic is dealt with in more detail.
However, to return to more pressing matters: how is even this generalisation to be confirmed? In view of the fact that scientists do not just make generalisations and then not test them, how might we test this DM-claim about life and death?
Manifestly, it is not possible to verify this particular DM-claim (i.e., that cells are a dialectical union of two contradictory processes). As it stands, this thesis is as a priori as anything else found in DM. Certainly, no one doubts that living things absorb dead matter from their environment, but how this verifies the claim that they are a dialectical unity of this or that still remains obscure. Still less does it support the claim that life is 'contradictory'.
Clearly we need to examine this more closely. Perhaps the intended contradiction is meant to be something like the following?
C1a: Cell C1 is a combination of living and dead matter/processes.
But, once again, in what way is a combination of living and dead matter a contradiction? If it were, then presumably any collection of alleged opposites would be contradictory. Thus, presumably, the human body would be contradictory simply because it comes equipped with a left and a right hand -– perhaps, meaning that those who have lost a limb in an accident are not quite as contradictory as their less orthopaedically-challenged friends. Indeed, in like manner one could argue that we contradict ourselves every time we look in a mirror, turn around, walk backwards, or shake hands. Apart from sounding enigmatic, what would such claims prove? Other than representing an appeal to yet another linguistic trick (i.e., that of combining a word with its alleged opposite, as in the schematic "C1 is A and non-A", or "C1 is A and B", where "A" and "B" are opposites), there is nothing to support this view.
[Indeed, quite the opposite, as we will see in Essay Eight Parts One, Two and Three.]
Naturally, dialecticians might want to cling onto this way of describing things, but if empirical evidence is to decide on such issues (as Engels, Novack, Cornforth, TAR and RIRE (among others) maintain), a verbal artifice like this will hardly do. Otherwise why bother saying that DM requires verification (to avoid being labelled "Idealist") if it can only be 'confirmed' by yet more word-juggling? If such an approach were generalised, then scientists themselves would only ever need to concoct a few verbal tricks of their own, and count that as an adequate verification of any given pet theory. That would certainly mean that they could save time and money which is unwisely 'wasted' at present on 'pointless' experiments!
Once more it could be objected that this completely misses the point: left and right hands may be opposites, but they are not dialectically united in change, and neither are mirror images. The parts of a cell are united in this way as contradictory processes.
Even if this were so, it would still not show that this 'unity' amounted to a contradiction -– nor would it demonstrate that this aspect of DM had been verified, or even that it was verifiable (or capable of being confirmed by any sort of confrontation with reality, as opposed to being compared with a few more words wrenched from the dialectical phrasebook).
Presumably, the contradiction between living and dead matter only arises inside the cell; this alleged contradiction is not thought to exist between just any old aggregates of living and dead matter. For a dialectical unity to hold, the two types of matter must enter into some sort of close proximity with one another -- an organic union, perhaps? --, and some form of "mediation" must exist between them, or they must be connected by an "internal relation" of some sort. In that case, it would seem that dead matter must enter the cell and link up/interact with living matter, in a process of some kind -- but in an as yet unspecified manner.
However, what stops us from saying that when 'dead' matter does do this, when it enters the call, it becomes living matter? Clearly, in that case, there would no longer be anything for a DM-'contradiction' to latch onto, since there would only be one type of matter/process in the cell: the living sort.
Naturally, DM-theorists will want to challenge this latest move -– but they may only do so by advancing an opposite stipulation that dead matter remains dead when it enters the cell, to rebut my contrary stipulation above. This counter-proclamation would then allow them to continue to claim that the dead matter in question becomes part of a dialectical union/process with living matter when inside the cell.
Now, it is worth emphasising this: such a DM-move could only ever be based on a stipulation. This is because the mere inspection of cellular processes -- no matter how detailed or fine-grained this proves to be -- could not tell us which of these two alternatives is correct. It is not possible to see that dead matter remains dead/alive inside a cell, any more than it is possible to see when night becomes day (or confirm it in any other way that is not itself based on yet more stipulation). To be sure, the examination of living cells reveals all sorts of activity going on -– but observation alone cannot decide which aspects of this activity are living and which are not. This is, of course, part of the problem that scientists face trying to define life. [Are prions, for instance, alive? They are certainly active inside cells.]
It might be objected here that it is possible to confirm that when non-living matter enters a cell it remains in the same state for a while until it is metabolised by that cell. Hence the above contentions are wrong.
However, what we actually see and what we might want to say are two different things. To illustrate this, let us track, say, a single sugar molecule, S1, as it passes across a membrane into a cell. Naturally, in order to do this we will have to assume god-like powers of vision, but, ignoring this formidable obstacle for the present, we might want to say that while on the outside S1 is non-living, and -- in view of the objection just noted -- we might continue to maintain that it is still non-living soon after it enters the cell. Once inside, S1 will naturally mingle with other molecules that form part of the metabolic processes of that cell.
For the sake of clarity, let us call the latter set of molecules M, all the while allowing for that set to change its content. But, are any of molecules belonging to M actually alive themselves? If we are to derive a contradiction here we need to be in a position to say that some are alive in order to further maintain that both live and non-live molecules co-exist, side by side (as part of a 'contradictory' process). Otherwise, there would be no way to identify both halves of the 'contradiction' here.
But, would we be able to see (or would we be able to verify in any other way) that any of the elements of M are alive, whatever we finally decide to say? In order for us to verify (as opposed to having either to assume or to stipulate again) that a 'contradiction' exists here, we would have to register an instrumental/sensory impression of some sort that confirmed that certain cellular molecules belonging to M are indeed alive at the same time that S1, its latest recruit, isn't. But, to what could we appeal here? Unless we are to suppose that there is something special about living molecules, which makes them look alive, or that they exhibited, or were controlled by, a "vital force" of some description (that could also be observed in some way), any subsequent declaration that these molecules are alive could only ever be based on yet another stipulation.
Of course, the above analysis looks rather reductionist. Presumably, no dialectician would want to argue that molecules taken singly actually contradict one another in this way -- in the sense that while one or more of them is alive another nearby is not --, even if collections of them are still regarded as UOs in their own right. Although DM-theorists certainly talk about sub-atomic particles doing just this! Indeed, Hegel himself spoke of acids and bases as contradictory (i.e., that one was the "other" of the other), and they could hardly do that if their individual molecular structures failed to do likewise.
Even so, dialecticians might want say, as indeed they do, that life "emerges" at certain levels of molecular organisation, as quantity turns into quality (etc.).15 Hence, it is only at such higher levels of complexity that the contradiction arises, or becomes apparent. Naturally, that would mean the above criticisms are badly off target. Or so it could be argued.
However, to reiterate, this dispute came about because it was assumed that it is possible to see, verify, or confirm (in some way or other, by an appeal to something empirical) the existence of DM-'contradictions', which could then be used to describe them as "material contradictions". This is needed, it was claimed, in order to avoid DM sliding back into the Idealist quagmire from which it had emerged. Short of that, DM would be no different from Hegelian Idealism, in this respect at least.
In the present case the 'contradiction' was supposed to be the following: that inside a living cell certain types of living matter exist alongside others that aren't alive, in some sort of 'dialectical process/union/tension' with one another. Difficulties then arose over ascertaining what sense could be made of the claim that there was a dialectical 'contradiction' here, and over the question whether this 'dialectical' link could be confirmed by observation, or by some other empirical means, as DM-theorists themselves demand of their own theory.
It now turns out that this particular thesis can only be verified by an appeal to yet another rather shaky DM-'Law', but not by an appeal to anything empirical. If this is correct, it seems that the existence of DM-'contradictions' can only be confirmed by reference to Q«Q –- but not when compared with reality --, as we had been led to believe all along.
[RIRE = Reason in Revolt, i.e., Woods and Grant (1995); Q«Q = The Law of the Transformation of Quantity into Quality, and vice versa.]
As we saw earlier, Q«Q is either a conventionalised but badly-stated 'Law' (more accurately, it is at best a trite rule of thumb that often fails to work), or it is another example of metaphysical confusion. It certainly can't bear the weight that this latest challenge places upon it. But even if it could, we still await empirical confirmation of Engels's claims about living cells; an appeal to more theory is no help at all.
Once more, it could be objected that the above fails to comprehend the dialectical process underlying knowledge, the interplay between the abstract and the concrete. But, even if this process were relevant, reliable or comprehensible, in what way could it help us understand how it is possible to verify this allegedly dialectical process by observation, or by any other empirical means? Clearly, the above difficulties (concerning empirical confirmation) afflict dialectical processes just as much as they do alive/dead 'dialectical' molecules.15a
[DM-epistemology (including the alleged relation between the 'abstract' and the 'concrete') is examined in more detail in Essay Two, Essay Three Parts One, Two and Three, and Essay Ten Part One.]
Or, are we to suppose that DM-theorists can 'intuit' processes of this sort in nature and society non-empirically? Must we concede that they have a special way of confirming their Supertruths by methods non-dialectical-infidels do not possess -- one they cannot actually explain to anyone else? If so, how are they different from old-fashioned mystics?
Inside or outside the cell, then, we seem to be unable to confirm the presence of 'contradictions' -- except stipulatively --; certainly not by observation, or by experiments that are themselves observation-based (or that are free of yet more ad hoc stipulations), and which are not merely "thought experiments".
Incidentally, to return to an earlier difficulty, not even a god-like observer could see (or confirm in any other empirical way) whether certain molecules were alive or dead -- at any level of complexity or detail -- without recourse to a prior stipulation to guide 'Him/Her/It' in this regard. In that case, short of such a convention, not even an 'Ideal Observer' could verify the presence of 'contradictions'.
And, if that is so, the claim 'contradictions' exist in nature and society can't have been derived from experience (or even by a process of abstraction) -- it can only have been projected onto reality as an a priori metaphysical dogma.
Now, even though John Rees repeatedly refers his readers to the necessary empirical checks that must be made in order to verify the presence of DM-'contradictions', what we actually find in their place in TAR (and in other DM-texts, such as DN, AD, DMH, FPM, PN, IDM and RIRE) are a few superficial, conceptual, quasi-investigations into things like motion, identity, living and dead matter, matter in general, and the nature of the reality -- with little or no empirical evidence to back them up (that has not itself been slanted by yet more stipulations). [These allegations were thoroughly substantiated in Essay Two.]
[DN = Dialectics of Nature; AD = Anti-Dühring; DMH = The Development Of The Monist View Of History; FPM = Fundamental Problems Of Marxism; PN = Philosophical Notebooks; IDM = In Defence of Marxism.]
All this is not the least bit surprising; no empirical verification of a contradiction is possible -- even in theory -–, as was demonstrated earlier.
Now, DM-theorists might sincerely believe that there is a 'contradiction' between living and dead matter, life and death (or, indeed, that there are other 'contradictions' in society and nature) -- and, moreover, that there are 'dialectical' processes at work all over the place --, but until they inform us which particular set of observations or experiments (not themselves dependent on further stipulations) confirm these acts of faith, they cannot consistently maintain that their ideas have been continually checked against reality, and verified by experience. In fact, they have yet to provide so much as a vague description of how the existence of a single 'contradiction' can be confirmed in nature or in society.
[Graham Priest's allegations to the contrary will be examined in a later Essay.]
In fact, we have yet to be told what a "dialectical contradiction" actually is!
Of course, the above objections leave unchallenged the naive idea that DM-'contradictions' had originally been discovered, or were prompted by observation, or, indeed, that they had ever been based on empirical evidence of any sort. In fact, as is well-known, most of them were simply lifted from Hegel (and from earlier Idealists). Even those that were not borrowed in this way were based on principles found in Hegel's work. Subsequent observations to 'verify' these 'contradictions' were be otiose, anyway -– that is, if DM-theorists ever bothered to carry any such tests out. John Rees certainly mentions none of the experiments he performed in this regard, neither do Woods and Grant -- the same can be said of Engels, Dietzgen, Plekhanov, Lenin and Trotsky. Dialecticians have not gone down in history as great experimental scientists.
Self-appointed Superscientists, certainly.
Experiments would be otiose because it is not possible to see (or to experience) 'contradictions' in nature without a decision having already been made to call them such (the latter choice itself being based on an explicit or implicit Idealist convention borrowed from thinkers who were part of an ancient, mystical, philosophical tradition). This helps explain why so little evidence appears in DM-texts, and why there is none at all that substantiates the claim that 'contradictions' exist in nature and society, all the time.
Those who doubt this should compare the average DM text (even those that sincerely try to prove there is a dialectic of nature, such as RIRE, or Gollobin (1986)) with a bona fide scientific/technical paper that has been published in any random issue of, say, Nature. The difference between this version of Mickey Mouse Science and genuine science will immediately be apparent.
In the place of hard evidence, what we invariably find in DM-texts are the same hackneyed examples wheeled out year after year. These include the following hardy perennials: boiling or freezing water, cells that are alive and dead, grains of barley that 'negate' themselves, magnets that are UOs, Mamelukes ambiguous fighting ability when matched with French soldiers, Mendeleyev's Table, the sentence "John is a man", homilies about parts and wholes (e.g., "The whole is greater than the sum of the parts", etc., etc.), characters from Molière who discover they have been speaking prose all their lives, laughably poor attempts to depict the principles of FL (i.e., "Yay, Yay", and "Nay, Nay" -- anything more than this "comes of evil"), particle and wave 'duality', 'emergent' properties popping into existence all over the place, etc., etc. Even then, we are never given a scientific report on these phenomena; all we find in DM-texts are a few brief, impressionistic sentences/paragraphs on each. At its best (in, say, Woods and Grant (1995), or Gollobin (1986)), all we get is secondary evidence, specially-selected, and heavily slanted in the favoured direction.
In contrast, and in relation to, say, economics, Marxists are keen to provide masses of data and analysis; and they update this data regularly. But, when it comes to dialectics all we encounter is watery-thin 'evidence', and even thinner reasoning. Small wonder then that to its Marxist opponents, like myself, this area of our theory is regarded as laughably weak -- and treated with the contempt it deserves.
Nevertheless, even though the examples of 'contradictions' referred to by dialecticians are seen by them as instances of genuine DM-principles at work in nature and society, they are invariably mistakenly identified as such. Without exception these alleged 'contradictions' turn out to be anything but contradictions; they are invariably little other than badly described, paradoxical, quirky, and oppositional situations -–, or they are just plain contraries. Even then, little or no evidence is presented to substantiate the hyper-bold extrapolations DM-theorists regularly advance from even this impoverished evidential base to all of nature for all of time. In place of adequate evidence we are offered sketchy, half-baked analyses, derived from a few superficial "thought experiments" (and even these are badly worded) -- with a little homespun Stone Age Logic thrown in for good measure. Our intelligence is then insulted with the claim that this Dialectical Mishmash is the very epitome of the scientific method!
[Again, these serious allegations are thoroughly substantiated in the Essays posted at this site.]
There thus seems to be no way of interpreting living cells as UOs other than in a poetic or figurative sense -- as a sort of throwback to the romantic era in Biology, but otherwise of little relevance to modern science. And yet, once again, this is no real surprise given that the ideas found in DM originated in mystical Hermetic Theology (which occult belief system we know for a fact had a profound influence on the aforementioned Romantics and Natürphilosophers of Hegel's day, and thus on Hegel himself [On this see Essay Fourteen Part One (summary here).]
This part of dialectics, therefore, clearly depends on obsolete mysticism, not on modern science. It is no surprise then to find it cannot be confirmed in any way.
So, no literal sets of internal opposites are apparent here; DM-UOs are thus at best figurative. But, are these dialectical figures of speech of much use to DM-theorists keen to parade their scientific credentials? Indeed, are they of any assistance to revolutionaries in their endeavour to understand both the development of Capitalism and how it can be overthrown?
Well, once again, given the fact that dialectics has dominated revolutionary thought for over a hundred and forty years, and during that time Dialectical Marxism has enjoyed legendary lack of success, the only viable response to the above questions must be a resounding "No!". If practice is a test of truth, dialectics stands condemned out of its own contradictory mouth. In that case, this 'theory' is clearly of no use to revolutionaries either in their endeavour to understand Capitalism or their desire to end it.
In fact, these are not even good metaphors. For example, as we have already seen, workers do not contain capitalists (their alleged internal 'opposites') literally or metaphorically; the same is probably true vice versa. And, even though Capitalism contains both workers and capitalists, as entire classes they do not seem to change into one another. More or less the same can be said of the forces and relations of production and of the alleged 'contradiction' between use and exchange value. Do factories, power lines and transport systems literally 'struggle' against mill owners, bankers, unions and/or bourgeois politicians? Do they even seem do this figuratively? Does the hypothetical use value of, say, a sugar spoon 'struggle' against its monetary (or exchange) value? Does the actual use of an escalator in a shopping mall 'struggle' against…, well, what? Do any of these objects collectively or severally have the wits, brains or brawn to 'struggle' against anything at all? Does a single one turn into the other, as we were told they must?
[Certainly, these and other things cause capitalism to change all the time, but not by 'contradicting' anything, for the reasons given above, in Essays Five and Eight Parts One, Two, and Three, as well as for those summarised below.]
This is not to deny either the irrationalities found in Capitalism or the horrors we see every day, but since agent-orientated verbs like "contradict", "struggle", "oppose" (etc.) are clearly out of place in the study of inanimate matter (save we use them figuratively, or perhaps animistically -- but we have just seen that these metaphors are particularly ill-suited to the task) and social reality, these comments will strike those with a reasonably secure grasp of the vernacular (and who have an equal dislike of anthropomorphic language) as entirely uncontroversial.
Nor is this to claim that HM cannot account for such things either; indeed it can, but it needs no help from Hermetic mysticism in order to do so. In fact the reverse is the case: dialectics mystifies this otherwise scientific theory.
However, the fact that these assertions will sound controversial only to DM-fans suggests that linguistic naivety is their only conceivable defence.
Living Things Change Into...What?
As far as option (5) above is concerned -- the "something else" that each living thing is supposed to be, or to become, according to Engels, i.e., whatever it was he imagined living things were supposed to change into --, no obvious candidates come to mind. Engels was perhaps appealing to the alleged fact that the LOI does not apply to living matter, and that living things are constantly changing into "what they are not" -- that is, that at any moment a living thing is "A and not A", "itself and something other" (etc.). But, as we saw earlier, this can only mean that whatever it is that livings things "are not", it must already be present in or near (whatever it is) if this combination is to count as a UO, and all living things are to change into what they "are not".
[LOI = Law of Identity.]
In this instance, one suspects that Engels simply confused a logical principle with an empirical fact: since anything that changes must change into "what it is not" (as a mater of discursive logic, although there are exceptions even to this rule)15b -- either in whole or in part -- Engels clearly thought that this general (I would say grammatical) point applies to living things (indeed, to anything) as it changes.
Now, this brings us back to the problems we noted earlier about the confused way that DM-theorists picture change -- outlined above in general, but in particular in the case of domestic cats. These hapless animals, it seems, must undergo some sort of dialectical change into what they "are not" (or they would remain the same, clearly). And this is just the logico-verbal trick DM-theorists put to no good, having inherited more than their fair share of dubious ideas from Hegel's very own shaky 'logic'.
However, as with other examples of metaphysical word-juggling (found throughout traditional Philosophy), this one has a tendency to strike back, especially at those who use it unthinkingly. In that case, since living things are clearly not cars, not calculators, not mountains, not Quasars, not sewage systems, not volcanoes, not books on DM -- meaning, of course, that all of these (and more) are "what living things are not" --, Engels's formulation that living things are constantly changing into "what they are not" must imply that all living cells are constantly changing into cars, calculators, mountains, Quasars, sewage systems, volcanoes and books on DM. The fact that living things do not do this (to anyone's knowledge) suggests that they do not actually change into "what they are not", or anything remotely like it. Here, material reality once again refutes another dotty piece of dialectical chicanery.
And, it is no good complaining that this makes a mockery of Engels's claim, since his confusion of a logical principle with an empirically determinable fact invites such ridicule. Moreover, dialecticians have no way of neutralising the above objection, or, rather none that leaves this piece of quirky Hegelian word-magic intact. If it is logically true that everything changes into "what it is not", and what an object "is not" is everything that it logically is not, then it must change into everything in the universe that it logically is not.
[Hegel tried to deflect this untoward implication of his 'logic' by appealing to a unique dialectically-united "other" with which objects and processes are pared, so that when they change they do so in a determinate manner. But, Hegel inadvertently holed this idea of his well below the waterline, for it was obvious to him (and the rest of humanity!) that objects and processes can change in many ways -- more on that here. In that case, dialecticians cannot appeal to this defective "other" to neutralise the above objection.]
In which case, things do not change because of logical principles magicked into existence as a result of Hegel's tenuous grasp (even) of AFL.
[AFL = Aristotelian Formal Logic.]
On the other hand, if Engels's formulation does not mean this (i.e., that things do not change into what they "are not"), what then does it mean? While this saying might look profound, no sane content can be attached to it.
Once again, it could be objected that this makes a nonsense of Engels's claims, not because they are confused, but because of the repeated refusal of the present author to interpret him in a sympathetic way. Well, quite apart from the fact that dialecticians are not known for their sympathetic reading of their opponents' writings (a quick leaf through Lenin's Materialism and Empirio-Criticism will amply confirm that accusation -- as should a five minute 'debate' with a dialectical clone on an internet discussion board), the above account actually takes Engels words seriously, and literally. When that is done, it is easy to see that no material sense can be made of them. Anyone who still disagrees is welcome to make of them what they can.
[They would then of course be the dialectical equivalent of those who still think sense can be made of the Christian Trinity.]
However, whatever sense can be made of Engels's enigmatic prose, it is quite clear that dialecticians have totally misconstrued the LOI. As will be argued in detail in Essays Six, and Eight Parts Two and Three, in relation to the LOI, if a living thing changes, then anything identical to it will change equally quickly. That, of course, makes identity no enemy of change.
With that observation alone much of DM falls apart.
But, if we absolutely must view nature metaphorically/poetically/mystically -- as DM-theorists seem impelled to do, given their acceptance of many of the Hermetic ideas they found in Hegel -- it could now be argued against them that nature is not in fact driven by "contradictions"; it is actually powered by 'dialectical tautologies'.
As a result of the present author's own incautious (but temporary, and wholly insincere) dalliance with metaphysical Superscience/Poetry, and no little word-juggling to boot, this observation can easily be confirmed by the way that each living thing changes: Every single one that we know of changes identically quickly as it itself does, and each and every one of them alters into something which has changed just as much as each itself has, and which "something" is identical to the thing it has just changed into. Now, since this 'thesis' is apparently tautologious -- or it is at least poetically so -- we might be tempted into calling this new sort of word-juggled 'theory': Dialectricks.
Anyway, the words I have used can easily be 're-defined' on sound and 'consistent' dialectical lines so that the above 'thesis' becomes "tautologious" -- of course, with "tautologious" understood in a special and permanently unexplained sort of way, rather like the way that "contradiction" has its own special and permanently unexplained DM-sort of sense. Indeed, we could insist that just as "contradict" means "conflict", "tautologious" means "harmonious", and dig our heels in DM-style, 'Nixoning' away any and all quibbles on the grounds that erstwhile critics do not "understand" Dialectricks.
Once again, this (temporary) a priori 'theory' of mine has the advantage of being consistent with every conceivable observation -- unlike dialectics with its dubious DM-'contradictions'. Whether things stay the same, or change (fast or slow, it matters not), they do so no faster than they themselves manage to do it, and they all change into things that are identical with whatever they have just changed into. That, naturally, makes this tautologically-poetic 'theory' of mine far more 'scientific' than DM.
I have absolutely no doubt that Marxism will be no less unsuccessful if we adopt Dialectricks, too.
[As noted above, those still unconvinced by this sort of 'innovative logic' clearly do not "understand" Dialectricks, but that is probably because they suffer from too much lack of tenderness for the world.
Moreover, those impatient with crazy 'logic' like this perhaps need to turn an equally critical eye on the same sort of lunacy found in DM all the time.]
Diabolic Logic Confronts Mathematics
Engels rehearsed several rather odd ideas in AD and DN, which are so questionable that even some of his fans find them "unhelpful".
For example, Helena Sheehan claims that Engels's adherence to "inappropriate Hegelian terminology" lies behind some of his less defensible musings [Cf., Sheehan (1993), p.41.], even though she is highly sympathetic to his ideas in general. [Ibid., pp.25-48.] The authors of The Dialectical Biologist also reject some of Engels's ideas as "quaint". [Levins and Lewontin (1985), p.279.] Two other comrades (Paul McGarr and Phil Gasper) similarly distanced themselves from certain unspecified failings in Engels's work. [Cf., McGarr (1994), p.155, which accuses some of Engels's examples of being "trite", and Gasper (1998), p.144, which says several of them are "not very convincing".] This is even though both comrades are quite willing to accept many of Engels's other whacky ideas at face value, subjecting them to very little critical scrutiny.
But, who is to decide which of Engels's examples (illustrating the operation of the "laws of dialectics") are "inappropriate" and "unhelpful" (to use TAR's own words; cf., p.75), and which are not?
To assist the reader to decide for herself, here are a few of Engels's more 'interesting' ideas:
"[I]t is a contradiction that the root of A should be the power of A…[as it is] that a negative magnitude should be the square of anything…. The square root of minus one is therefore not only a contradiction, but even an absurd contradiction…. [Again, there is the] contradiction that in certain circumstances straight lines and curves may be identical…that lines that intersect…can nevertheless be shown to be parallel…." [Engels (1976), pp.153-54.]
Again, which of these is "unhelpful", "inappropriate", or just plain confused? Indeed, many of the above ideas are difficult to square with a materialist theory of any kind, let alone Engels's "dialectical" inversion of it.
If mathematical entities like the above are contradictory (as Engels says they are), then they should change. But which of them are changing? And what are they changing into? On the other hand, if they are changeless, what is the point of calling them contradictory? And yet, if they are contradictory, why do they remain in the same state forever? Indices will not one day turn into Matrices, neither will Affine Transformations change into Hermite Polynomials. Not even negative numbers turn into positives. Sure, we can multiply negative integers so that they yield positives, but no one supposes that the original numbers have changed, otherwise no one would be able to use them again. Indeed, multiply -2 by -1 to obtain 2 and both the -2 and -1 are still on the page/screen, unchanged. They certainly do not change through 'internal contradictions'. What, for example, is the 'internal contradiction' in -2? Is it -4/2, or 8/-4, or -8/-1 x -1/4...? [More on that, here.]
Or are we to suppose that when -2 'changes' into 2 when multiplied by -1, that -2 and 2 must have been locked in struggle? Well, it seems they must if they are 'opposites' (and their struggle turns the one into the other, as the Dialectical-classicists claim). But, what then of the -1? How does it feature in this quasi-Platonic drama? It is certainly not the 'opposite' of 2 or -2, and yet it seems capable of 'changing' both, and of mapping any number onto its 'opposite'. Indeed, if we multiply -2 serially by the entire set of negative integers we will obtain the set of positive even integers. Does this mean that -2 has an infinite number of 'opposites'?
More to the point, where are the real 'material forces' these 'contradictions' supposedly represent? And, where is the "careful empirical work" that substantiates odd claims such as these, evidence that DM-theorists, TAR's author and Engels in particular, insist must always be produced? [TAR, pp.108-12. On this, see Essay Two.]
Moreover, Engels's claims make little sense even in their own terms. For example, the iterative rule uk = (-a)k [where "k" and "a" are integers] alternately produces negative and positive values of a, depending on whether k is odd or even. But, where is the "development" in this process? Where is the "new content" arising from old conditions? In fact, and to spoil the party, when a = 0, the result of the iteration is always the same -– i.e., zero. Is this an example of a change that produces no change? Is this yet another 'contradiction'? Or, is this part of mathematics reactionary?
Engels also uses the rather strange term "absurd contradiction" ("The square root of minus one is therefore not only a contradiction, but even an absurd contradiction") without explaining the difference between this sort of contradiction and an ordinary one. This is especially puzzling since many of the 'contradictions' Engels regards as scientifically important look just as absurd.
Moreover, with respect to his comments about "the square root of minus one", what is so contradictory about Complex Numbers? What are they developing into? What are they locked in "struggle" against?
Is, for example, the expression "a + bi" the contradictory of "-a + bi", "a – bi", "-a – bi", "1/(a + bi)", "1/(a - bi)", "1/(-a - bi)", or "1/(-a + bi)"? If the answer is any particular one of these, then why is "a + bi" not changing into it, as we were assured that all contradictory opposites in the end do?
Perhaps then, each complex number is the contradictory only of its complex conjugate (in this case "a + bi" would supposedly 'contradict' "a – bi"), since the product of the two yields a Real Number, namely "a2-b2". But why does this make them contradictory? Once more: these two conjugates do not turn into one another.
And yet, 1/(a + bi) x a + bi = 1, so why aren't these two 'contradictory'? And, what development is there here?
Moreover, after any randomly chosen conjugate pair has been multiplied out on paper, there are countless trillion copies of the very same symbols awaiting multiplication queuing up in 'abstract space', all of which will yield identically the same results with no detectable development over the many thousands of years the human race will be dong this (if we survive that long!). Or, to put the same point materially: anyone can write out and then multiply -- in impeccably physical ink, on boringly material paper -- "1 + i" and "1 - i" but the result will not change: (1 + i)(1 - i) = 2. Once more, if the planet and/or humanity lasts that long, it will yield this result in one hundred million years time, and still on paper, still written in ink. [Hence, this is just as much a material example as it is an 'abstract' one.]
Of course, if you believe everything is contradictory from the start, mathematical objects and processes will naturally be classified accordingly, even where the indications are that they aren't the least bit dialectical -- having failed to notice perhaps that numbers do not 'struggle' amongst themselves (and neither do variables, lines, planes or manifolds), nor do they mirror any identifiably material developments in the real world.16
Even so, how is any of this different from imposing DM on the subject matter, something dialecticians continually protest they do not do?
Of course, Engels focussed part of his comments on "the square root of minus one", but this must have been a mistake, since minus one has two square roots: "i" and "-i" [since i2 = -1, and (-(i))2 = -1], which fact alone rather ruins Engels's point (unless, of course, we now introduce into mathematics the idea that certain of its structures dialectically dither, as it were). But, what he'd have said of the potentially infinite roots of unity there are in complex number theory, we will never know. For:
zn = 1, there are n roots (where z is a complex number, n = 1, 2, 3, ... )
Furthermore, Engels's comment about lines and curves is no less ill-considered. The fact that some things have a dual aspect (if this is indeed the case with lines and curves) in no way makes them contradictory. If it did, then we would have to say that the number seven, for instance, was potentially infinitely contradictory, because among other things it is the sum of countless odd and even numbers, it is also one of the square roots of forty-nine and is identical to the rational number 147/21 -– in addition to being the result of the application of innumerable other functions to arbitrary sets of numbers and expressions (such as "49x6/7x6", for x ¹ 0).
And yet, despite its infinitely 'contradictory' nature, 7 never actually changes. Are all the "material forces" in nature that 7 'reflects' in eternal equilibrium, therefore? Has this number been knobbled by the CIA?
And if lines and planes are contradictory, what are they 'struggling' with, and what are they 'developing' into?
Even in dialectical terms, none of this makes any sense.
Moreover, it is not at all clear why Engels regarded this as contradictory: the "the root of A" is also "the power of A". It might well be the case if roots and powers were themselves contradictory to one another, and this meant that one will turn into the other as a consequence. But, who apart from Engels and a few of his die-hard disciples would want to admit to that?
On a similar basis, one might just as well argue that because 10 is a square root of 100, and 102 = 100, and 10 = 100½, and log10102 = 2, and log10010 = ½ that the log function is deeply contradictory in that it 'contradicts' the relevant powers and roots of 10 and 100, which 'contradict' one another into the bargain. But, even given the recklessly profligate nature of DL, is it possible for four items to contradict one another all at once? If it is, should we not now abandon the idea that all concepts/objects/processes are paired UOs (their unique Hegelian "others") in favour of the more generous notion that they consist of countless UOs -- in the event dialectically adjusting the word "opposite" to accommodate this new development of the concepts involved -- now that we can see that each concept/object/process has a potentially infinite number of 'opposites'? But, tinkering with the meaning of the word "opposite" just to cater for this rapidly burgeoning theory would be no less of a conventionalist cop-out here than it would be anywhere else.
Once more: how would that be different from imposing DM on the facts?
It is worth recalling that Engels's comments on this topic did not appear in an obscure or minor DM-work, nor were they scribbled hastily on the back of an envelope. They were published in a widely recognized and accepted DM-classic, one that has inspired generations of DM-fans, and one that Engels rather oddly claims to have "read" to Marx. [That must have taken days. Can you imagine it! One wonders how often the ageing Marx must have nodded off, not fully realising the nature of what it was that some would later claim he accepted!]
Certainly, Lenin and Trotsky did not find these rather peculiar ideas at all "unhelpful", or "quaint" -- or, if they did, they remained diplomatically quiet about it.17
On the other hand, if we are now supposed to ignore these foibles -– in the way that scientists today disregard, say, Newton's alchemical and theological ramblings -–, then why not disregard the other equally strange claims Engels made? Why should we now accept Engels's assertion that ice "contradicts" water, that life is "contradictory", that grains of barley are "negated" to form mature plants?
But, how exactly does ice 'contradict' water? Does it oppose it? Do they exist together at the same time locked in struggle? Does one force the other to emerge from the shadows as the temperature changes? And, does something higher emerge as "new content arises from old conditions" if ice is melted and refrozen hundreds of times? [Engels (1976), pp.154-82.] Water has been freezing and thawing for billions of years. Has it morphed into something higher? Is it ever going to become H3O as a result?
[NON = Negation of the Negation.]
It could be argued that this is a spurious counter-example to the NON; as Cornforth points out:
"In many processes the working out of their contradictions results in a directed or forward movement, in which the process moves forward from stage to stage, each stage being an advance to something new, not a falling back to some stage already past.
"Other processes, however, are not characterised by such a forward movement.
"For instance, water when cooled or heated undergoes a qualitative change, passes into a new state (ice or steam), but the movement is without direction and cannot be called either progressive or retrogressive.
"...If some processes have direction and others have not, this depends solely on the particular character of the processes themselves and of the conditions under which they happen." [Cornforth (1976), pp.108-09.]
We will have occasion to look at Cornforth's account of change in Essay Eight Part One, where it will soon become apparent that he, along with other DM-theorists, is not too clear about what constitutes a process, an object or a system. So, the non-development of water is not a counter-example after all. But, what about a genuine development: the negation of feudalism to form Capitalism, and the negation of that in turn to form a socialist society? Certainly, Cornforth does not count this as non-progressive, but as a clear example of development via the NON:
"[C]apitalist private property arises only on the ruin and expropriation of the pre-capitalist individual producers.... But when capitalist private property is itself negated -- when 'the expropriators are expropriated' -- then the individual property of the producers is restored once more, but in a new form, on a higher level....
"When capitalism arose, the only way forward was through this negation of the negation....
"The principle of the negation of the negation is thus an expression of the simple truth that one cannot put the clock back and reconstitute the past. One can only move forward into the future through the working out of all the contradictions contained within the given stage of development and though the negations consequent on them." [Ibid., pp118-19. Italic emphasis in the original.]
Cornforth was not alive to see it, but one wonders what he'd have made of the events in the former USSR and Eastern Europe between 1989 and 1991 (and now, perhaps, in China). If history cannot go back, only forward, then the sort of free market capitalism that has swept through these countries (without a single worker lifting a finger to defend his/her state) must represent a higher stage of property relations: the negation of the negation of the negation. Either that, or the NON no longer works (and perhaps never did).
Of course, if this is denied, then the only response possible is that, contrary to what Cornforth said, DM-theorists do not in fact learn from history, they impose their abstract schemas on it:
"If some processes have direction and others have not, this depends solely on the particular character of the processes themselves and of the conditions under which they happen." [Cornforth (1976), pp.108-09.]
"Marxism, therefore, seeks to base our ideas of things on nothing but the actual investigation of them.... It does not invent a 'system' as previous philosophers have done, and then try to make everything fit into it." [Ibid., p.15.]
And those who, like me, regard such regimes as State Capitalist, should avoid crowing too loudly at the refutation that history has happily visited upon Stalinism. If, for example, the 1917 revolution has been reversed (in 1921, 1929, 1989, or whenever), then the NON must have made a serious error, and should perhaps be tossed into the trash-can of history (along with the crystalline spheres, humoral theory and Caloric) -- as a bogus 'scientific' concept.
Hence, it is worth asking of the DM-theorists who tell us that the NON only applies to things that "develop": Why saddle DM with such a crazy set of examples (such as "ice contradicts water", and roots 'contradict' powers) if they play no part in understanding the world?
[More on the NON, below.]
Dialectics Meets The Calculus -- And Comes To Nought
Another topic often linked with these 'Laws' is the claim advanced by Engels that Descartes' use of variables introduced dialectics into mathematics.
Despite what Engels said about mathematics, variables had been in use in FL long before they were employed in Algebra. [Cf., Kneale and Kneale (1962), pp.23-297.]
[FL = Formal Logic; AFL = Aristotelian Formal Logic; MFL = Modern Formal Logic.]
Indeed, this is what Professor Nidditch had to say about Aristotle's use of variables:
"One has to give Aristotle great credit for being fully conscious of this [i.e., of the need for a general account of inference -- RL] and for seeing that the way to general laws is by the use of variables, that is letters which are signs for every and any thing whatever in a certain range of things: a range of qualities, substances, relations, numbers or of any other sort or form of existence....
"If one keeps in mind that the Greeks were very uncertain about and very far from letting variables take the place of numbers or number words in algebra, which is why they made little headway in that branch of mathematics...then there will be less danger of Aristotle's invention of variables for use in Syllogistic being overlooked or undervalued. Because of this idea of his, logic was sent off from the very start on the right lines." [Nidditch (1998), pp.8-9. Italic emphasis in the original.]
Of course, that fact alone undermines the idea that traditional FL could not cope with change, and that it had used only "fixed concepts". Moreover, as is pointed out in Essay Four, variables are as widely used in MFL as they are in Mathematics -– in which case, MFL is even more 'change-friendly', as it were, than traditional AFL ever was. [These claims are substantiated in Essay Four.]
A word of warning needs to be interjected at this point: in view of the comments made here, the use of the word "variable" should to be treated with some caution. Indeed, as we will see, there can be no 'variable magnitudes'.
[However, throughout both this Essay and this site I have in general used "variable" in its traditional sense; the complications discussed at the above link would make these Essays more precise but needlessly recondite, for no real gain.]
However, what Engels actually said is worth examining on its own merits:
"The turning point in mathematics was Descartes' variable magnitude. With that came motion and hence dialectics in mathematics, and at once, too, of necessity the differential and integral calculus…." [Engels (1954), p.258.]
Several points need making about this passage and about Engels and Marx's ideas on Mathematics and the foundations of the Calculus in general.
(1) The claim that Descartes's invention of "variable magnitudes" introduced "motion" into Mathematics is as confused as it is inaccurate. A more balanced account from a Marxist perspective can be found in Hadden (1994). As Hadden points out, variables began to be used by mathematicians in the late Middle Ages as a result of the development of ideas connected with the nature of what were taken to be the commensurable values of commodities. For example, Nicholas Oresme had anticipated much of Descartes's analytic Geometry in the fourteenth century, and had already begun to use algebraic ideas to study motion. [On this, see Boyer (1959), pp.60-95, Boyer (1968), pp.288-95, Edwards (1979), pp.81-93, and Katz (1993), pp.292-99. Some of the original papers can be found in Clagett (1959).]
Also worthy of note is the fact that Muslim mathematicians had originally invented the use of algebraic variables long before Descartes. Engels cannot have been unaware of this.
Nevertheless, Engels's point stands or falls on its own merits, irrespective of who actually introduced variables into Mathematics, or when and why this was done.
However, as Frege noted, the idea that variables in mathematics refer to 'varying magnitudes' is confused in the extreme. [Frege (1904). His arguments have been summarised in Note 17a.]17a
(2) As far as Engels's own views on mathematics are concerned, they seem to oscillate between naïve versions of Abstractionism and confused forms of Platonism. Examples of both can be found in Engels (1976): pp.47-50 (naïve Abstractionism), pp.62-63 (naïve Platonism), p.154 (confused Platonism), pp.171-72 (inconsistent Platonism).
In addition, his ideas on the nature of zero are decidedly odd. [Engels (1954), p.261.] Engels fetishises this symbol, attributing to it what seem to be autonomous powers:
"...[Z]ero is richer in content than any other number. Hence, it is part of the nature of zero itself that it finds this application [i.e., that it equals zero] and that it alone can be applied in this way. Zero annihilates every other number with which it is multiplied...." [Engels (1954), p.261.]
Does this mean that if someone tried to calculate, say, "0 x 12", the number "12" would be "annihilated", never to be used by anyone ever again? Are we now to assume that the numeral itself will disappear from the page in a puff of smoke? If not, what precisely is the force of the word "annihilate" here?
As is argued in detail in Essays Two, Three Parts One and Two, and Essay Twelve (summary here), Abstractionism itself is a form of Idealism founded on a syntactically inept misinterpretation of general terms as if they were the names of abstract particulars, in effect conjuring these into existence by the 'power' of naming alone. On any interpretation, this relies on and supports the belief that the underlying structure of reality is abstract, hence rational and mind-like. That accounts for the confused Platonism in Engels's writings, witnessed above.
[In fact, comrades who are overly impressed with Engels's mathematical ideas should consult van Heijenoort (1948) in order to have that unfortunate condition corrected; a copy can be found here.]
(3) Unfortunately, the publication of Marx's Mathematical Manuscripts [Marx (1983)] has revealed the spectacle of a first-rate mind vainly attempting to shoehorn an interpretation of the Calculus into a dialectical boot it will not fit.
As the editors of these manuscripts themselves admit, Marx's analysis of the Calculus was based on his reading of textbooks that were badly out-of-date even in his own day. Marx was clearly unaware of the important work done in Analysis by Cauchy, and of the definitive results obtained by Weierstrass and Riemann –- work that was in fact available in his lifetime (the former having been completed in the 1820s, the latter in the late 1850s).17b
Several of the authors writing in the Appendix to the above work make some attempt to explicate and defend Marx's ideas, as well as outline a few criticisms of their own of subsequent developments in Analysis. As these theorists correctly point out, mathematicians working after Weierstrass found that the development of his results required a much clearer understanding of the nature of real numbers, continuity and the logic of infinity than were apparent at the time. Unfortunately, early Logicist theories in this area foundered when alleged contradictions were uncovered in Frege's classic work. Subsequently, Hilbert's entire foundational program was dealt a severe (but, as it turns out, spurious) blow by Gödel's Theorem.18 Nevertheless, these comrades pointedly failed to show how dialectics could possibly help, or have helped in any way at all here; indeed, it is quite obvious (from considerations aired below) that the opposite is in fact the case.
Despite this several other points arise from the comments the above authors (i.e., Yanovskaya, Kol'man and Smith) make about Marx's unpublished writings on the Calculus.
(A) Smith himself admits that Marx's analysis is technically limited; for example, it only relates to certain types of analytic functions (Smith (1983), pp.265-66). In the intervening years, and to the best of my knowledge, no one has attempted to correct this defect or to extend Marx's method to cover a wider variety of functions.
Moreover, other types of derivatives were not considered by Marx -- for example: dT/dx (the rate of change of temperature with respect to position, where no 'motion' is implied by the variables mentioned); dA/dt or dV/dt (the rate of change of area/volume with respect to time). What sort of 'motion' could these possibly involve? Can an area or a volume be in two places at once, and in one of these and not in it at the same time? What about dr/dt -- the rate of change of a position vector with respect to time? In this particular case, it is even more difficult to see how a changing vector can be given a 'dialectical' make-over; can a magnitude and a direction occupy two places at once, but not be in one of them while being in another at the same moment -- especially if vectors themselves define locations?
Not only that, but higher-order derivatives were ignored by Marx, and it is not at all clear how these can be reconciled with a 'dialectical' account of change. Are we to suppose that, for instance, d2y/dx2 -- or d(dy/dx)/dx -- expresses how the first derivative itself changes, or how the variables themselves undergo more complex sorts of 'motion' -- or what? What then about dny/dxn? [To say nothing of (dy/dx)n.]
And what about several of the more complex (but still rather simple) ways that derivatives can inter-relate? For example, what sort of 'dialectical spin' can be put on the following?
If y = f(u), and u = g(x), then dy/dx = (dy/du).(du/dx).
If y = uv, and u = f(x), v = g(x), then dy/dx = (u.dv/dx) + (v.du/dx).
If y = u/v, and u = f(x), v = g(x), then dy/dx = [(v.du/dx) - (u.dv/dx)]/v2.
Are we to suppose that the 'movement' of all these variables is equal, inter-coordinated -- or even comparable?
[Marx did try to examine these, but as I will show in a later re-write of this Essay, his attempt fails rather badly.]
On top of this, Marx totally ignored partial derivatives. Perhaps this is because it would have involved him in having to consider variables 'changing' in three or more directions at once!
Finally, there seems to have been no consideration at all given to the whole of the Integral Calculus. It is impossible, anyway, to see how the latter can be accommodated within a dialectical framework -- and with that, out would go much of modern Mathematics and Science.
It could be argued that the Integral Calculus is a sort of 'reverse' Differentiation. But that is not so. Quite apart from their different proof structures, there are functions that cannot be differentiated which can be integrated, and vice versa.
(B) Independently of the above, Marx's approach is badly flawed. This is because it requires a variable, x (taking values in the domain of a function, f(x)), to 'change' into x1, and that this be represented as part of the factorisation of f(x), i.e., g(x)(x1 – x) -- where g(x) and (x1 – x) are both factors of f(x).
Now, in order to avoid well-known problems (notoriously outlined by Bishop Berkeley in The Analyst) that had plagued earlier attempts to make the Calculus rigorous, Marx set the value of x1 such that x1 = x (or, rather, he allowed it to 'move' back!) This manoeuvre was justified by an appeal to appropriately vague 'dialectical principles' (to be examined presently), the upshot of which is that unless the meanings of "=" and "–" have themselves changed, the factor (x1 – x) must equal zero! But, that just leaves the Calculus in the same state it had been in the 18th century, with all the problems that had bedevilled it since Newton and Leibniz's day.
[Several commentators have tried to blow away the chaff surrounding Marx's argument, leaving behind the 'rational core', so to speak. Their arguments will be examined in a later re-write of this Essay.]
Hence, despite the obvious genius he displayed in other areas, Marx's ideas on the Calculus are entirely worthless.
In fact, there is little evidence anyone has ever made any serious use of his ideas -- including mathematicians working in the old Stalinist USSR, where lip-service had at least to paid to them (for career and/or neck-saving reasons). Sure, Marx's ideas in this area were extensively studied [Dauben (2003)], but there is no evidence they were put to any use. And, as far as can be ascertained, no one since has bothered to develop Marx's ideas into a rigorous system, or ironed-out its fatal weaknesses. [However, on more recent attempts to rehabilitate Marx's re-interpretation of these symbols, see below.]
(C) Even if the above criticisms are misguided in some way -- and Engels's point about variables introducing dialectics into Mathematics was correct, and Marx's analysis was flawless -- it would still be of no use. This is because it is a serious mistake to redirect ones attention away from motion itself onto the symbols depicting it in an attempt to explain how the Calculus handles movement and change. Marx made just such an error when he confused the alleged 'motion' of variables with motion itself in the real world. This can be seen by his use of 'dialectical reasoning' to justify the 'change' of x into x