The material below represents a brief summary of a much lengthier criticism of Trotsky's 'analysis' of the 'Law of Identity' [LOI], where I enter into this topic in greater detail.
[If you visit my site directly, or by using the links I have inserted below, and are using Internet Explorer 10 (or later), you will find some of the links I have used won't work properly unless you switch to 'Compatibility View' (in the Tools Menu); for IE11 select 'Compatibility View Settings' and then add my site: anti-dialecitcs.co.uk.]
Although I am severely critical of Trotsky's defective analysis of the LOI, comrades who aren't Trotskyists should find little comfort in what follows, since Trotsky did at least try to defend this aspect of Dialectical Materialism [DM]. I know of no other DM-theorist/supporter (non-Trotskyist, Stalinist, Maoist, or, indeed, academic Marxist) who has attempted to do this (except they simply quote Trotsky), indeed, to the extent to which he endeavoured to do it. His arguments are original to him, even if they are still defective. He at least gave this some thought.
In which case, the material presented below (but more specifically, that which has been presented in the above Essay) represents a complete refutation of this aspect of DM, and that includes the even more lamentable 'analysis' found in Hegel.
Equality And Identity Not Identical
Unfortunately, the 'definition' Trotsky used (viz., "A is equal to A" ) -- which has been copied and reproduced identically by his followers ever since (irony intended) -- doesn't actually relate to Identity; it is in fact an example of the principle of equality:
So: Trotsky attacked the wrong target!"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 -- 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.]
It could be objected that this is just a minor, 'semantic' quibble, and hardly worth mentioning. But, as we will see, dialecticians make mistakes like this all the time. Moreover, if details like this are little more that minor, "semantic quibbles", then Marx ought to be slated for his own minor, "semantic quibbles" concerning the difference between, for example, the "relative" and the "equivalent" form of value in Das Kapital -- and critics of Marx, who ignore such 'pedantic distinctions' (and who think they have thereby refuted Marx) should be praised for their lack of attention to detail. Moreover, Trotsky shouldn't have been quite so 'semantic' (or even 'quibbly') about the minute difference between two bags of sugar (or, a bag of sugar and itself) and two letter "A"s!
Indeed, as Trotsky himself said:
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 we have at least two items (namely these two) that obey the LOI, which in turn means Trotsky was wrong to say no two things are identical. On the other hand, if they aren't identical, then Trotsky attacked the wrong target, after all.
It could be objected that these two principles are approximately identical -- so that the difference between them can be ignored. However, as we will see, this isn't even remotely correct; these two concepts/words are radically different. But, even if it were the case that they are approximately identical, that would still be no help. Unless we possess a clear idea of what would count as absolute identity between these two, we would be in no position to declare they have only approximated to this ideal. An approximation only makes sense if we know with what it is that it approximates; but, for us to know that, we would have to know how the LOI applies absolutely here so that we could say why this is in fact an approximation. [More on this below.]
It could be argued that this is quite clearly an example of abstract identity, which dialecticians don't in fact question; they merely point out the limitations of LOI when it is applied to change. But, the passages above are expressed in very material ink (or they are represented by very material pixels on your screen), so they aren't abstract in the least. If it is now maintained that it is their content (i.e., what they say) that expresses abstract identity then Trotsky's point about those letter "A"s cannot stand either, since these letters are equally material. [Irony intended.] Indeed, his argument depends on these letters not being 'abstract'.
Anyway, 'abstract identity' will be discussed below.
As noted above, identity and equality are relatively easy to distinguish -- 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 (i.e., if x is equal to three), 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 what follows, I have had to use photographs since the software here can't cope with the symbols I have employed.]
[The triple-barred sign used above is the symbol for identity in mathematics and MFL]
[MFL = Modern Formal Logic.]
[Of course, the distinctions we draw in MFL aren't the same as those that feature in ordinary language (no irony intended), nor yet those found in Traditional Philosophy -- more on this below, too. "Truth-functional" is a technical term that describes the logical connection between the truth-values of the constituent propositions of a molecular proposition (such as the one at the end of the second photograph above), the alteration of which changes the truth-value of the compound proposition in a rule-governed way. So, the truth-value of the molecular proposition -- p & q (i.e., "p and q") -- changes from true to false if the truth-value of p, or the truth-value of q, or the truth-values of both p and q, is changed from true to false; hence the molecular proposition -- p & q -- is true if and only if both atomic propositions -- i.e., both p and q -- are true, false otherwise. For more on this, see here.]
Furthermore, in ordinary 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" (which would carry the implication that the said author wasn't in fact Lenin, but was his equal nonetheless; perhaps he was an equally great leader, or writer -- in other words, this would be tantamount to saying someone else wrote the said book!). 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". [If the latter were the case, we could argue that since the number of Moons of the Earth is identical to one, the number of Moons of the Earth must be the author of What is To Be Done?!]
Moreover, since counting objects is just as material a practice as weighing them is, no dialectician can consistently take exception to awkward examples of the difference between identity and equality (like those above) while accepting uncritically Trotsky's point about weighing bags of sugar.
Additionally, two things can be equal even while they fail to be identical, and vice versa. For example, two distinct (non-identical) comrades could be equally first in two separate lists and/or queues; two numerically different horses could be identically placed third in two separate races.
Other things can be equal and identical, or not, as the case may be. For instance, the letter "T" can be situated identically in first place in two different words (such as "Trotsky" and "teamster") even though neither letter nor word is equal or identical in shape and/or size. And, two letter "A"s, for example, which are identically placed first in the alphabet can be non-identically positioned in two words of unequal length (such as "target" and "Antarctic"). Indeed, careful optical examination (along the lines Trotsky suggested) will fail to show that those two "T"s aren't identically-positioned at the front of the two quoted words (i.e., "Trotsky" and "teamster"), nor yet that those two numerically different "A"s aren't both identically situated as the opening letter of the alphabet. This sort of identity clearly isn't sensitive to empirical test, eyeglass or no.
We needn't concentrate, either, on examples that some might still consider "abstract"; two (physical) ink marks on a page (two letter "A"s, again) which aren't even 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 sandwiched identically between two other non-identical letters (i.e., both are in the middle). Large or small physical differences between these letters, and any other incidental changes they might experience (which don't affect their position) -- such as a change of colour on your screen -- wouldn't alter the fact that they are identically placed between two other letters. Indeed, the spacing of these letters could be grossly unequal, but that wouldn't affect the fact that these letters are placed identically in the middle.
[By "middle" I mean "having one letter either side", not "located at or near the geometric centre".]
Now the position of ink marks on a page (or even those electronically produced as pixels on your screen) isn't abstract, it is manifestly material --, so much so that one or both can be obliterated by the non-dialectical use either of some Tipp-ex, or the delete key.
And, deletion isn't the removal of an abstraction.
[Alternatively, just try deleting an abstraction!]
Ordinary language is in fact almost limitless in the capacity it allows its users to express sameness, equality, identity and difference -- that is, if they refuse to be led astray by the obscure jargon bequeathed to us by Idealist Philosophers (like Hegel). It is a pity that Trotsky's otherwise brilliant mind failed to notice familiar facts such as these about the vernacular.
I have listed many more examples of the complexities that ordinary language allows in this and other respects, here.
Some Things Can Change Even While Remaining The Same!
[Again, I have had to use a photograph from my site.]
[There is a minor typo in the above photograph, the "=" sign used near the top should in fact be a triple-barred identity sign.]
Several more examples of genuinely material objects that change while remaining the same, are given in the above Essay.
The triteness of these 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 argued that the above counter-examples do not address the classical problem of identity, which concerns the entire set of predicates "true of" an object, or of some 'substance'. That is undeniable, but DM-theorists themselves fail to consider "the classical problem of identity" -- fixated as they are on "A is equal to A" --, and neither did Hegel.
As soon as they do, I will, of course, address what they have to say.
Finally, someone might object that despite several earlier responses, these examples are all "abstract". But even if that were so, there is still 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, Leibniz's), and subsequent Trotskyists appear to be blithely unaware of more recent technical, but more precise, definitions of this 'law'. Clearly, these major defects and interpretive blunders fatally compromise the claim that DM is a science, let alone a philosophical theory that merits serious attention. [See also the comments I have added to Essay Six on this topic.]
Of course, Trotskyists aren't alone in this; the same is true of DM-theorists in general (irony intended, again).
Trotsky Refutes Himself -- In Practice
Even if Trotsky's criticism of the LOI had have been carefully worded and had been correctly targeted, it would still have backfired.
That 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 are weights. In that case, Trotsky can't 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 when it is applied to bags of sugar!
If time can be measured (just as sugar can be weighed), the above argument can't be neutralised by claiming that time and/or temporal moments are "abstractions". Weighing and timing are both practical activities, and are thus subject to the same constraints over variability.
But, even if they weren't, Trotsky can't argue that a bag of sugar changes in the same instant, for there could be no such thing if he were right, and that is because, according to him, nothing can be the same. So, even if moments in time are abstractions, Trotsky would still have to refer to the same 'abstract moment' during which a bag of sugar supposedly changed.
Trotsky also referred his readers to the same weight of one of these bags; and yet, if no two bags ever weigh the same, or no bag ever weighs the same as itself, then no two moments could be the same either. And if that is so, Trotsky can't legitimately refer to the "same moment" during which such weights may vary. Once again, his criticism fails.
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 well below the water-line, declaring that all things are never the same:
Hence, if objects and processes are never the same, they can't be "the same, yet different", they can only be "different yet different". On the other hand, if it is true that they are "the same, yet different" then it can't be true that they are never the same. Either way, Trotsky's criticism backfires, once more."Again one can object: but a pound of sugar is equal to itself. Neither is true -- all bodies change uninterruptedly in size, weight, colour etc. They are never equal to themselves." [Ibid., p.64. Emphasis added.]
'Abstract' And Approximate Identity
Again, someone might object that the points made above ignore the fact that dialecticians aren't attacking the abstract version of the LOI, merely pointing out that when applied to changing reality it is only approximately true.
However, dialecticians certainly have to use identically the same words/concepts as one another (or as they themselves have done from day-to-day) if they want to make the same point, and/or communicate with each other (irony intended).
Consider just one example of the difficulties this now creates for DM-supporters: 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 or is expressed somewhere in their central nervous systems, or is written on the page in one of Trotsky's essays, say) applies to these 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.
Any response from the DM-community to the effect that the above aren't doing what is alleged of them (since all they need appeal to is approximate identity) must suffer the same fate; that is because any dialectician who says this must mean exactly the same as any other dialectician who also says it, or admit they are not talking about the same thing.
Furthermore, the idea that identity only really approximates to abstract identity (so that no two concrete objects in the material world are exactly the same -- even if they are approximately identical --, or that any one particular thing is only approximately self-identical), is equally misconceived.
That is because we are 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 are empty notions.
In order to underline this point, consider an analogy: let us suppose that someone introduces a word into the language -- say "schmidentity" -- but can give no examples of anything in reality that might possibly exhibit "schmidentity". If we were then told that certain things were "approximately schmidentical" (or "schmidentical only within certain limits", or even that they exhibited "schmidentity-in-difference") we would still have no clear idea what was being maintained. If we don't know what "schmidentity" is, we certainly don't know what "approximate schmidentity", or what "schmidentity-in-difference" is, either. And calling this new 'concept' "abstract schmidentity", "absolute schmidentity", or even "relative schmidentity" would be equally pointless.
In that case, when dialecticians presume to tell us that a word (or set of words) in ordinary language connected with sameness and identity, which we all know how to use in our daily lives, doesn't mean what we usually take it to mean, then the onus is on dialecticians to tell us what they do mean by their novel use of it. Until they do, they might as well be talking about 'schmidentity'.
[And it is little help referring to Hegel's criticisms of the LOI; as I have demonstrated here, he badly misconstrued this 'law', compounding his folly with a series of egregious errors over the nature of propositions.]
For example, how do DM-fans know that their notion of identity isn't absolutely identical with schmidentity? Or, indeed with nothing? The fact that I haven't defined "schmidentity" is no objection. They have yet to tell us what they mean by their use of words for identity. In fact, as we have seen, they mis-identify this word right from the start; and, to cap it all, they have inherited an exact copy of this misidentification from Trotsky! [Irony intended, again.]
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, and that is because their idea of abstract identity must be materially identical to abstract identity itself (otherwise they would once again be talking about the wrong thing!).
Alternatively, if this idea of theirs isn't identical with 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, or maybe to some other concept) -- then what they have to say about identity (ordinary or abstract) can safely be ignored, for it won't be about identity, but about something different. [Irony intended, once more.]
Furthermore, Trotsky's appeal to the hypothetical weight of bags of sugar is no less misconceived. That is because weighing scales are just as susceptible to change as are bags of sugar. Hence, Trotsky had no way of knowing whether the different weights he predicted were genuine effects (because only the weight of the sugar had altered), or whether they were merely artefacts of changes in the machinery that had been used -- or whether it was the result of a locally variable gravitational field, the changing eyesight of the experimenter, or, indeed, the consequence a host of other capricious factors.
Plainly, the above objection can only be neutralised if weighing machines, the bodies of experimenters, and the rest of the universe (other than bags of sugar) are all exempted from this as changeless beings. Only in such circumstances would it be safe to assume that the differing measurements predicted by Trotsky 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 if he asserted this as an a priori stipulation.
In that case, Trotsky would have imposed dialectics on nature, contrary to what he elsewhere said should never be done:
On the other hand, if Trotsky had been faced with someone who claimed that at least two of their weighings were identical, he could only have responded in one or more of the following ways:"Dialectics cannot be imposed on facts; it has to be deduced from facts, from their nature and development…." [Trotsky (1973), p.233.]
(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 and to the letter.
(4) Arguing that identically the same experiment 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 would be able to 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 bags of sugar, confirming this 'law'!
In which case, Trotsky's predictions would end up being refuted by anyone who adopted this diluted/'dialectical' version of the LOI applied to his instructions!
Such experimenters would thus succeed in confirming the absolute form of this 'law' by adopting and then applying a weaker version of it!
Conversely, the more precisely these experimenters adhered to Trotsky's instructions, the more likely it would be that they reported non-identical weights. In that case, they would succeed in disconfirming the absolute form 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 his instructions in order to disconfirm it when applied to bags of sugar!
Some might think all this is irrelevant; if things change, who cares what causes it? But, Trotsky is here appealing to the results of an experiment -- one that he clearly didn't carry out himself -- to substantiate a claim about all objects everywhere in the universe, and for all of time. It now turns out that because of that thesis itself, it might not be possible to verify some (any?) of his claims. If so, we are still owed an explanation why Trotsky thought it correct to say that everything changes all the time, when this cannot be confirmed. And that isn't 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 don't have access to most regions of space and time, and never will!
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.
Indeed, he failed to account for even so much a simple bag of sugar!
More to follow...