16-06 -- Summary Of Essay Six: Trotsky -- Seriously Confused About Identity

These are Introductory Essays, which have been written for those who find the main Essays either too long, or too difficult. They do not pretend to be comprehensive since they are simply summaries of the core ideas presented at this site. Most of the supporting evidence and argument found in each of the main Essays has been omitted. Anyone wanting more details, or who would like to examine my arguments and evidence in full, should consult the Essay for which each is a précis. [In this particular case, that can be found here.]

Trotsky Screws-Up -- but He's not The Only One

In this Essay, Trotsky's radically misconceived criticisms of the LOI are analysed in detail and shown to be patently wrong at best, incomprehensible at worst.

[A demolition of Hegel's 'analysis' of Identity, which is only marginally better than Trotsky's, will appear in Essay Twelve. However, many of the comment below apply equally to Hegel's work. (No irony intended.)]

[LOI = Law Of Identity; DM = Dialectical Materialism.]

Equality and identity Not Identical

Now, the 'definition' Trotsky uses (viz., "A is equal to A" ) -- and one reproduced identically by his followers -- is in fact an example of the principle of equality, not of identity:

"The Aristotelian logic of the simple syllogism starts from the proposition that 'A' is equal to 'A'…. But in reality 'A' is not equal to 'A'. This is easy to prove if we observe these two letters under a lens -- they are quite different from each other. But, one can object, the question is not the size or the form of the letters, since they are only symbols for equal quantities, for instance, a pound of sugar. The objection is beside the point; in reality a pound of sugar is never equal to a pound of sugar -- a more delicate scale always discloses a difference. Again one can object: but a pound of sugar is equal to itself. Neither is true (sic) -- all bodies change uninterruptedly in size, weight, colour etc. They are never equal to themselves. A sophist will respond that a pound of sugar is equal to itself at 'any given moment'…. How should we really conceive the word 'moment'? If it is an infinitesimal interval of time, then a pound of sugar is subjected during the course of that 'moment' to inevitable changes. Or is the 'moment' a purely mathematical abstraction, that is, a zero of time? But everything exists in time; and existence itself is an uninterrupted process of transformation; time is consequently a fundamental element of existence. Thus the axiom 'A' is equal to 'A' signifies that a thing is equal to itself if it does not change, that is if it does not exist." [Trotsky (1971), pp.63-64.]

Some might object that this is a minor 'semantic' point, but, as was noted in Essay Four, dialecticians make such mistakes all the time. Moreover, if this were a minor 'semantic' issue, then Marx should not have been quite so 'semantic' over the difference between the "relative form of value" and the "equivalent form of value" in Das Kapital, and critics of Marx, who ignore these distinctions, but who think they have thereby refuted Marx, should be praised for their lack of attention to detail. [The "pedantry" alternative to this objection is neutralised here.]

Others might want to argue that this is unfair since the principle of equality is in fact the same as the principle of identity, but if that is so, then plainly at least two items (namely these) obey the LOI, and Trotsky was wrong. On the other hand, if they are not identical, then Trotsky attacked the wrong target.

It could be objected that these two principles are approximately identical, so much so that the difference between them can be ignored. However, as we will see, this is not even remotely correct; these two concepts/words are totally different. But, even if it were the case that they were approximately identical, that would be no help. Unless we had a clear idea what would count as absolute identity between these two, we would be in no position to declare they are only approximately identical. An approximation only makes sense if we know with what it is that it approximates, and for us to know that, we would have to know how the LOI applies absolutely to these two, to b able to say why this is a mere approximation. [More on this below.]

It could be argued that the above is just an example of abstract identity, which dialecticians do not query, they merely wish to point out the limitations of LOI applied to changing reality. But, the passages above are expressed in very material ink (or are represented by very material pixels), so they are not abstract. On the other hand, if they are still to be rejected as abstract then Trotsky's point about the letter "A"s he refers to cannot stand, for they are equally material. [Irony intended.]

Anyway, abstract identity is discussed below.

As noted above, identity and equality are relatively easy to distinguish (such that even the children of workers can tell them apart). For example, in elementary mathematics the equation 2x + 1 = 7 is true if and only if x = 3, but no one supposes that x is identical to 3, otherwise it could never equal any other number (as it does in, say, 3x – 2 = 19).

In contrast, the "º" sign which appears in, say, 2sinxcosx º sin2x expresses identity, for this rule yields the true for all defined values of x. Worse still: two or more identicals can be equal to, but different from the same identical. For instance, even though 0 = 0, it is also true that 0 + 0 = 0, and 0 x 0 = 0 -- even though it is also true that neither 0 + 0 nor 0 x 0 are identical to 0.

In MFL (i.e., outside of mathematics), the distinction between these two is even more pronounced. The "=" sign  is used as a relational expression (and can be flanked only by names (or other singular terms)), whereas "º" and is a truth-functional operator (and can be flanked only by propositions, and the like).

[Of course, these distinctions are not the same as those which feature in ordinary language (no irony intended), nor yet those found in traditional Philosophy -- more on this below.]

[MFL = Modern Formal Logic.]

Furthermore, in ordinary material language the difference between equality and identity is even clearer. So, we can say things like "The author of What is To Be Done? is identical with Lenin" (whereas, it would be decidedly odd to say "The author of What is To Be Done? is equal to Lenin"), just as we can say that "The number of authors of What is To Be Done? is equal to one" (but not, "The number of authors of What is To Be Done? is identical to one"). And, since counting objects is just as material a practice as weighing them, no dialectician can consistently take exception to these and other such awkward material examples of the difference between identity and equality, while accepting uncritically Trotsky's point about weighing bags of sugar.

Not only that, two things can be equal even while they fail to be identical, and vice versa. For example, two distinct comrades could be equal first in two separate lists and/or queues. Now, the material embodiment of such facts could alter either greatly (or hardly at all) without affecting their status; so, for example, the names of the said comrades could be written in neon signs that flashed on and off every second, and out of sequence -- or, one could do handstands while the other reads a book --, but they would still both be equal first, and non-identical for all that.

And some things can be equal and identical, or not, as the case may be. For example, the letter "T" can occur identically in first place in two different words (such as "Trotsky" and "teamster") even though neither letter nor word is equal or identical in size or shape. And, two letters, which are identically first in the alphabet (namely two "A"s) can be non-identically positioned in two unequal words (such as "target" and "Antarctic"). Indeed, careful optical examination will fail to show that those two "T"s were not identically-positioned at the front of the two quoted words (nor that they are not equally first in each), or that the two numerically different "A"s are not identically the opening letter of the alphabet. This sort of identity is clearly not sensitive to empirical test, eyeglass or no.

And we needn't concentrate on examples that some might still consider "abstract"; two physical ink marks on a page (two letter "A"'s, say) which are not identical in shape or size (i.e., "a" and "A") could be identically positioned between other non-identical letters. So, in "pat" and "PAT" each letter "A" is identically sandwiched between two other non-identical letters. Now the physical position of material ink marks on a page, or even that of these electronically produced pixels on your screen, is not abstract, it is eminently material --, so much so that one or both can be obliterated by the non-dialectical application either of Tippex or the delete key.

This non-dialectical deletion would not be removing an abstraction.

Finally, large or small differences in these letters, and any other incidental changes they undergo (that do not alter their position) will not affect the fact that they are identically positioned between two other letters.

Ordinary material language is in fact almost limitless in the capacity it allows its users to express sameness, equality, identity and difference if they refuse to be led astray by the obscure jargon employed by Idealist philosophers (like Hegel). It is a pity that Trotsky's otherwise brilliant mind failed to notice such familiar facts about the vernacular. [Many more examples of the complexities ordinary language allows are given in Essay Six.]

The triteness of some of the above examples should provide no reason for anyone to cavil; after all, Trotsky it was who advised his readers to consider bags of sugar and letter "A"s.

It could be objected that the above examples do not address the classical problem, which concerns the entire set of predicates "true of" an object, or indeed of some 'substance'. This is undeniable, but then DM-theorists do not consider "the classical problem" either (fixated as they are on "A = A"), and neither did Hegel. As soon as they do, I will address what they have to say.

Worse still, some things can change even while they stay the same. For example, it is easy to transform 1/√n into √n/n thus: 1/√n x √n/√n = √n/n. But, 1/√n does not even look like √n/n, although the two are identical: 1/√n º √n/n. So, here we have change with no change!

[Recall: the signs used here are eminently material. Note also that I am using the "º" sign mathematically here, not logically.]

Finally, someone might object that despite the above, all these examples are "abstract". But even if that were so, there would still be a clear difference between abstract identity and abstract equality, something Trotsky also failed to notice.

Trotsky Ignores Identity

However, from this poor start, Trotsky's 'analysis' deteriorates rapidly. As noted above, neither he nor his epigones quote any of the classical versions of the LOI (for example, that constructed by Leibniz), and the latter seem to be unaware of more recent, technical definitions. Clearly, these major interpretive blunders fatally compromise the claim that DM is a science, let alone a philosophical theory that merits serious attention.

Trotsky Refutes Himself -- In Practice

Even if it had have been correctly worded and targeted, Trotsky's attack on the LOI would still backfire. This is because his argument depends on the LOI being true of instants in time so that he can criticise it when it is applied to bags of sugar. Hence, his criticism relies on, say, a bag of sugar being non-self-identical during the same moment in time. But, moments in time are just as capable of being measured as bags of sugar are. In that case, Trotsky cannot consistently use "same moment" while criticising "same weight"; both are legitimate examples of identity (as he interprets it). In that case, Trotsky needs the LOI to be true of instants in time so that he can criticise it as false when it is applied to bags of sugar!

Again, if time can be measured (just as sugar can be weighed), the above objection (of mine to Trotsky's 'analysis') cannot be neutralised by claiming that time and/or temporal moments are "abstractions". Weighing and timing are both material activities, and thus subject to the same constraints over variability.

But, even if they weren't, Trotsky cannot argue that a bag of sugar changes in the same instant, for there could be no such thing (if he were right, since nothing can be the same, according to him) -- unless the LOI can be applied validly to such instants (as abstractions). So, even if moments in time are abstractions, Trotsky would have to be able to refer to the same 'abstract moment'. But then, he has also referred to the same weight; but if the latter can never be ascertained in this world (if no two bags ever weigh the same), then no two moments can be the same either. And if that is so, then Trotsky cannot refer to the "same moment" during which weights may vary --, in which case, his criticism collapses.

Moreover, Trotsky (or one of his epigones) can't use the fall-back option that bags of sugar are the same, yet different (employing the "identity-in-difference" gambit) since Trotsky had already torpedoed that response way below the water-line, declaring that all things are never the same:

"Again one can object: but a pound of sugar is equal to itself. Neither is true (sic) -- all bodies change uninterruptedly in size, weight, colour etc. They are never equal to themselves." [Ibid., p.64. Emphasis added.]

Hence, if objects and processes are never the same, they cannot be "the same, yet different", they can only be "different, yet different". Of course, if it is true that they are "the same, yet different" then it cannot be true that they are never the same. Either way, Trotsky's criticism backfires.

'Abstract' And Approximate Identity

Again, some might complain that the above ignores the fact that dialecticians are not attacking the abstract version of the LOI, merely pointing out that when applied to changing reality, this Law is only approximately true.

However, dialecticians certainly have to use identically the same words/concepts as one another (or as they themselves from day to day) if they want to make this point, and/or communicate with each other. Just to consider one example of the difficulties this now creates: any two dialecticians who fancy they have the same idea of "abstract identity" must either accept that a material version of the LOI (if it exists in their central nervous system somewhere, or written on the page, in one of Trotsky's essays, say) applies to their two distinct ideas of "abstract identity" (so that they can confirm they are talking about exactly the same thing), or they must concede that they are talking about two different things, and stop their blather.

[And any response from the DM-community to the effect that the above two both are and are not doing the what is outlined above must suffer the same fate, for any dialectician who says this today must mean exactly the same as any other dialectician who says this today (or as he/she meant it yesterday), or admit they are not talking about the same thing, once more.]

Furthermore, the idea that ordinary identity (or even the misconstrued version of it that Trotsky used) only really approximates to abstract identity (so that no two concrete things in material reality are exactly the same, even if they are approximately (abstractly) identical, or that any one particular thing is only approximately (abstractly) self-identical), is equally misconceived.

We are surely no further forward unless we can be told with what it is that our ordinary terms for identity are supposed to approximate, for if these terms do not approximate to anything specifiable, they must be empty notions.

In order to underline this point, consider an analogy: let us suppose that someone introduced a word into the language -- say "schmidentity" -- but could give no examples of anything in reality that could possibly exhibit "schmidentity". If we were then told that certain things were "approximately schmidentical" (or even "schmidentical only within certain limits") we would still have no clear idea of what this new word meant; if we do not know what "schmidentity" is, we certainly do not know what "approximate schmidentity" is. And calling this new 'concept' "abstract schmidentity", "absolute schmidentity", or even "relative schmidentity" would be equally useless.

In that case, when dialecticians presume to tell us that a word (or set of words) in ordinary material language connected with sameness and identity, which we all know how to use, does not mean what we usually take it to mean, then the onus is on them to tell us what they do mean by their new word (or set of words). Until they do, they might as well be talking about schmidentity.

On the other hand, if DM-apologists can say with what it is that our words for identity do in fact approximate, then they must have a clear idea of abstract identity which cannot itself be subject to Trotsky's criticisms, since their idea of abstract identity must be materially identical to abstract identity itself. On the other hand, if this idea is not identical to abstract identity (or to put this better, if they haven't got a clue what abstract identity is so they are in no position to say that their idea of approximate identity approximates to the right concept), then what they say about identity (ordinary or abstract) can be safely ignored, for it won't be about identity, but about something different.

Sugar-Coated Error

Furthermore, Trotsky's appeal to the hypothetical weighing of bags of sugar is no less misconceived. Since weighing devices are just as susceptible to change as are bags of sugar, Trotsky had no way of knowing whether the different weights he predicted were genuine effects (because only the weight of the sugar (etc.) alters), or whether they were merely artefacts of changes in the machinery used, the result of a locally variable gravitational field, the changing eyesight of the experimenter, or, indeed, were a consequence a host of other factors.

In fact, this latest objection can only be neutralised if weighing machines, experimenters and the rest of the universe (other than bags of sugar) are all exempted from consideration as changeless beings. Only in such circumstances would it be safe to assume that differing measurements were solely the result of changes in the items being weighed. Short of that, Trotsky could only be 100% confident that subsequently detected differences were always and only the result of changes to the weight of the sugar because of an a priori stipulation to that effect. In that case, Trotsky would have imposed dialectics on nature, contrary to what he elsewhere said should never be done:

"Dialectics cannot be imposed on facts; it has to be deduced from facts, from their nature and development…." [Trotsky (1973), p.233.]

On the other hand, if Trotsky had been faced with someone who claimed that at least two of their results were identical, he could only have responded in one or more of the following ways:

(1) Insisting that this experimenter must have been mistaken.

(2) Pointing out that the machines used were not accurate enough.

(3) Maintaining that his instructions had not been carried out exactly to the letter.

(4) Arguing that identically the same experiments had not been performed each time.

In other words, in the absence of a mistake (and if the same results were recorded on more accurate scales) -- i.e., ruling out (1) and (2) above --, Trotsky would only be able to criticise the above reported experimental verification of the LOI by an appeal to that very same 'law', but now applied to his own instructions! Hence, in order to counter results that would disconfirm his forecast (about varying weights) he would have to argue that only those who followed his instructions identically and to the letter could disprove the LOI!

The irony is thus quite plain: identically performed experiments are required to prove that nothing is identical with anything else -- including experiments!

To be sure, anyone who only roughly followed instructions (who was perhaps content with a wishy-washy, "approximate-within-certain-limits" dialectical-sort-of-equality) would probably find that many (if not most) of their measurements gave identical results for the weights of bags of sugar, confirming this 'law'!

In which case, Trotsky's predictions about such objects would end up being refuted by anyone who adopted this diluted/'dialectical' version of the LOI!

Such experimenters would succeed in confirming the absolute version of the 'law' by adopting a weaker variant of it!

Conversely, the more exactly the experimenters adhered to Trotsky's instructions, the more likely it would be that they detected non-identical weights. In that case, they would succeed in disconfirming the absolute version of this 'law' by applying an exact copy of Trotsky's instructions! So, by reverse irony, they would refute Trotsky in practice by doing exactly as he instructed, using the LOI applied to instructions to disconfirm it as applied to bags of sugar!

Some might think all this irrelevant; if things change, who cares what causes it? But, Trotsky is here appealing to the results of an experiment -- one that he clearly did not carry out -- to substantiate a claim about all objects everywhere in the universe. It now turns out that because of that thesis itself, it might not be possible to verify some of his claims. If so, we are still owed an explanation as to why Trotsky thought it correct to say everything changes all the time, when this cannot be confirmed. And this is not just because many of the above complications could cancel each other out or mask a temporary lack of change in other things, it is because we do not have access to most regions of space and time!

Relying on evidence alone, therefore, Trotsky was certainly not justified in projecting his conclusions as far as he thought he could --, i.e., across the entire universe, and for all of time; not least because he evidently performed no experiments himself.

No Enemy Of Change

Finally, and most damningly, Trotsky (and Hegel) failed to notice that if anything changes then whatever it is identical with must change equally quickly. In that case, identity is no enemy of change.

With that observation, dialectics completely falls apart.

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