16-06: Summary Of Essay Six: Trotsky And Hegel -- Or, How To Misconstrue The 'Law Of Identity', 101




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The difference between Dialectical Materialism [DM] and HM, as I see it, is explained here.


Phrases like "ruling-class theory", "ruling-class view of reality", "ruling-class ideology" (etc.) used at this site (in connection with Traditional Philosophy and DM), aren't meant to suggest that all or even most members of various ruling-classes actually invented these ways of thinking or of seeing the world (although some of them did -- for example, Heraclitus, Plato, Cicero, and Marcus Aurelius). They are intended to highlight theories (or "ruling ideas") that are conducive to, or which rationalise the interests of the various ruling-classes history has inflicted on humanity, whoever invents them. Up until recently this dogmatic approach to knowledge had almost invariably been promoted by thinkers who either relied on ruling-class patronage, or who, in one capacity or another, helped run the system for the elite.**


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[**Exactly how this applies to DM will, of course, be explained in the other Essays published at this site (especially here, here, and here). In addition to the three links in the previous paragraph, I have summarised the argument (but this time aimed at absolute beginners!) here.]


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1) Trotsky Screws Up, But He's Not the Only One


a) Equality And Identity Not Identical


b) An Everyday Example Of Absolute Identity


c) Some Things Can Change Even While Remaining The Same


d) Trotsky In Fact Ignores Identity


2) Trotsky Ends Up Refuting Himself


3) Abstract Vs Approximate Identity


4) Sugar-Coated Error


5) Physicists Discover Identical Particles


6) Identity Is No Enemy Of Change


Summary Of My Main Objections To Dialectical Materialism


Abbreviations Used At This Site


Return To The Main Index Page


Contact Me


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


[Although I am severely critical of Trotsky's defective analysis of the 'Law of Identity' [LOI], readers 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), or 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 this Essay, Trotsky's radically misconceived criticisms of the LOI will be analysed and shown to be misguided at best, incomprehensible at worst.


[A comprehensive demolition of Hegel's 'analysis' of Identity will be published in Essay Twelve Part Five. However, many of the comments below apply equally well to Hegel's work. (No pun intended.)]


Equality And Identity Not Identical


Unfortunately, the 'definition' Trotsky used (viz., "'A' is equal to 'A'" -- when I use or mention letters like this I will highlight them in bold to distinguish them from the ordinary employment of such letters ), which has been reproduced identically by his followers ever since (irony intended), doesn't actually concern Identity; it is in fact an example of the principle of equality:


"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.]


So: Trotsky attacked the wrong target!


It could be objected that this is merely a minor, semantic quibble, and hardly worth mentioning. But, as we will see, dialecticians make mistakes like this all the time. Indeed, if details like this are little more than 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 characteristically ignore these 'pedantic distinctions' (and who think they have thereby refuted Marx) should be praised for their lack of attention to detail. Indeed, Trotsky shouldn't have been quite so 'semantic' (or 'quibbly') about the difference between two bags of sugar and two letter "A"s!


[The "pedantry" objection has been neutralised here.]


As Trotsky himself said:


"It is necessary to call things by their right names." [Trotsky (1971), p.56.]


Unfortunately, this is something Trotsky himself failed to do.


Others might 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 terms (namely these two) that obey the LOI, which 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 -- to such an extent that any 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. Until we possess a clear idea of what would count as absolute identity between these two, we are 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 what it would be for the LOI to apply absolutely in this case so that we could say how and why this is merely an approximation. [More on this below.]


It could be argued that the above is plainly an example of abstract identity, which dialecticians don't in fact question; they merely wish to point out the limitations of LOI when it is applied to change in the real world. 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. If it is now objected that it is their content that expresses abstract identity, then Trotsky's point about those letter "A"s can't stand either, since these A"s 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. 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).


Contrast the above with the "º" sign, as it appears in, say, 2sinxcosx º sin2x, where it expresses an identity -- this trigonometric rule yields the value "true" for all defined values of x. [On this sign, see here.]


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 -- in other words identically the same number (zero) is equal to two typographically different but nonetheless mathematically identical expressions -- or, rather, to what they yield (i.e., 0 + 0 and 0 x 0), and this is so even though it is also true that neither 0 + 0 nor 0 x 0 are identical to 0.


[MFL = Modern Formal Logic.]


In MFL, the distinction between these two symbols is even more pronounced. The "=" sign  is used as a relational expression, flanked only by Proper Names (or other singular terms, such as "The 43rd President of the United States"), as in "a = b", where "a" could stand for, say, "Cicero", and "b" could stand for, say, "Tully" (the latter was Cicero's other name). On the other hand, in logic, "º", is a truth-functional operator, which can be flanked only by propositions (indicative sentences), as in (p & q) º ¬(¬p v ¬q), (where "¬" is the sign for negation, and "v" is the inclusive "or" -- i.e., it stands for "and/or", and "p" is a propositional variable).


[It should be pointed out, however, that grammarians in general understand the indicative mood differently from logicians.]


Of course, the distinctions we draw in MFL aren't the same as those that are found in ordinary language (no irony intended), nor yet those drawn by Traditional Philosophers (more on this below, too). "Truth-functional" is a technical term that describes the logical (functional) connection between the truth-values of the constituent, 'atomic' propositions of a 'molecular'/compound proposition (such as, "p & q", which is molecular, comprised of atomic propositions, "p" and "q"), the alteration to which changes the truth-value of that 'molecular'/compound proposition in a rule-governed way. So, the truth-value of the latter -- p & q -- will change from true to false if (i) the truth-value of p, (ii) the truth-value of q, or (iii) the truth-values of both p and q are changed from true to false. Hence, for example, p & q itself is true if and only if the truth-value of p and the truth-value of q are both true; it is false otherwise.


The above can be summarised neatly in what has come to be known as a 'Truth Table':




p & q














Table One: Truth-Table For P & Q


So, when the atomic propositions, p and q, are severally true, the molecular proposition, p & q, is true -- shown in line one; otherwise p & q is false -- shown by lines 2 to 4.


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 to Lenin" (which is often shortened to "The author of What is To Be Done? is 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 identical with Lenin (i.e., he/she 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 "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, and the number of authors of What is To Be Done? is identical to one, therefore the number of Moons of the Earth is the author of What is To Be Done?!]


Moreover, since counting objects is just as material a practice as weighing them, no dialectician can consistently take exception to awkward examples that illustrate 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) individuals could be equally first in two separate lists 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 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 not.


We needn't concentrate, either, on examples that some might still consider "abstract"; two (physical) ink marks on a page or screen (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 undergo (which don't affect their relative position) -- such as a change of colour on your screen, or on the page -- won'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.


[To be sure, the gap between the letters might be different, but that wouldn't alter the fact that both are identically placed in the middle. And by "middle" is meant "having one letter either side", but 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 express sameness, equality, identity and difference -- that is, if they refuse to be led astray or hoodwinked by the obscure jargon dialecticians have imported from 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.


[Many more examples of the complexities that ordinary language allows are given in Essay Six.]


An Everyday Example Of Absolute Identity


Consider the following scenario: two individuals, NN and NM, board the same train at the same time and remain on it for two hours. While these two are still on that train, whatever changes it experiences or undergoes as it speeds along (and this includes changes to all its contents and its relations with the entire universe in this two hours), this will always be true: NN and NM are on an absolutely identical train as each other.


More precisely:


A1: During time interval, T, (lasting m hours), the following set of predicates is true of, or can be used to form true propositions about, (a) train, L, (b) all on board, and (c) L and its contents' relation with everything in the universe: {P1, P2, P3,..., Pn} -- where n is indefinitely large --, abbreviated to, P.


A2: NN and NM are both passengers on L during any sub-interval, tk, of T, of arbitrary length.


A3: During tk, a subset of P, namely {Pi..., Pk}, can be used to form true propositions about (a) L, (b) all on board, and (c) L and its contents' relation with everything in the universe, including any changes that occur during tk.


A4: So, during tk, NN and NM are on absolutely identically the same train as one another, since, while they are on L, {Pi,..., Pk}, remains the case throughout.


Now, every element of {Pi,..., Pk} -- i.e., these predicates, or what they 'reflect' -- can change 'dialectically' all the time, but that won't alter the result, since any changed element of {Pi,..., Pk} will also be an element of that set, by the above definitions.


So, here we have an example of absolute identity that would remain such even in a Heraclitean universe.


[I have tried to use DM-phraseology here wherever possible (e.g., "reflect", "dialectically", and "L's relation with everything in the universe") so that this argument doesn't become obscured by the presence of too much non-DM terminology. Its use, however, doesn't imply I accept its validity; it is merely being employed in order to assist in its long-overdue demise.]


Finally, what applies to passengers on trains applies in like manner (irony intended) to those in or on ships, boats, aeroplanes, spacecraft, buses, taxis, rickshaws, and cars at the same time. Indeed, it applies in equal measure (more irony intended) to those in the same cinema, theatre, café, restaurant, hotel, hostel, house, hospital, waiting room, stadium, palace, mansion, igloo, cave, tree house and graveyard, at the same time -- just as it applies to all of us on the same planet, at the same time. And if we go for broke, it applies to everything in the universe at the same time.


So, far from being a rather rare occurrence (or even an impossibility according to DM-fans) absolute identity like this is as common as sand in the Sahara.


Of course, it could be objected that this sort of identity isn't the sort that interests dialecticians, so the above comments are beside the point. But, as we will see as this Essay unfolds, we don't yet know what DM-theorists mean by the odd things they say in this area, so not even they could consistently advance this (i.e., identically this) objection -- yet more irony intended.


One thing is for certain, neither Trotsky's nor Hegel's criticisms of the LOI are successful against this sort of identity.


Some Things Can Change Even While Remaining The Same!


Worse still, some things can change even while they remain the same. For example, it is easy to transform 1/√n into √n/n thus:


1/√n x √n/√n º √n/n


But, 1/√n doesn't even look like √n/n, although the two are identical; i.e., 1/√n º √n/n.


So, here we have change with no change!


[Recall: the signs used here are manifestly material. Note also that I am using the "º" sign mathematically here, not logically. Several more examples of genuinely material objects that change while remaining the same are given in Essay Six.]


The triteness of these examples should provide no reason for anyone to cavil (but are mathematical examples really "trite"?); 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 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. [Anyway, the train example above does address this.]


Again, 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' only deteriorates further. 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 interpretative blunders fatally compromise the claim that DM is a science, let alone a philosophical theory that merits serious attention.


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.


"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." [Ibid. Bold added.]


That is because his argument depends on the LOI being true of "moments" 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 (or as he puts it "a pound of sugar is subjected during the course of that 'moment' to inevitable changes"). But, moments in time are just as capable of being measured as are the weights of bags of sugar. In that case, Trotsky can't consistently appeal to the "same moment" while criticising the "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, 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 "moment", for there could be no such thing if he were right, since, 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 appeal to the fall-back defence 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:


"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.]


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.


'Abstract' Versus 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, or communicate with each other (irony intended).


Consider just one example of the difficulties this now creates for DM: 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, for 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 -- or even approximately 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 they don't 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 only "approximately schmidentical" (or "only schmidentical 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 (irony intended).


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 them to tell us what they do mean by their novel employment 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 at all? 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 copied this misidentification exactly from Trotsky ever since! [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 actually approximates to the right concept -- or, indeed, whether it approximates 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.]


Sugar-Coating Error


Furthermore, Trotsky's appeal to the hypothetical weight of certain bags of sugar was 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, indeed, whether it was the result of a locally variable gravitational field, the changing eyesight of the experimenter, or was even a consequence of 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 as changeless objects. 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 a dogmatic stipulation.


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 weighings were identical, he could only have responded in one or more of the following ways:


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


(2) Pointing out that the machines used weren't accurate enough.


(3) Maintaining that his instructions hadn't been carried out exactly and to the letter.


(4) Arguing that identically the same experiment hadn't 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 these 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 detected 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.


"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." [Loc cit. Bold added.]


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 why Trotsky thought it correct to say that everything in existence changes all the time when this cannot be confirmed. And that isn't just because many of the above complications might cancel each other out -- or even mask a temporary lack of change in other things --, it is because we don't have access to the vast bulk 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, to everything in existence; not least because he evidently performed no experiments himself.


Indeed, he failed to account for a simple bag of sugar!


Physicists Discover Identical Particles!


Trotsky also argued as follows:


"Every worker knows that it is impossible to make two completely equal objects. In the elaboration of a bearing-brass into cone bearings, a certain deviation is allowed for the cones which should not, however, go beyond certain limits…. By observing the norms of tolerance, the cones are considered as being equal. ('A' is equal to 'A')…. Every individual is a dialectician to some extent or other, in most cases, unconsciously." [Trotsky (1971), pp.65, 106.]


However, contrary to what Trotsky says, it is very easy to make two identical objects -- everyone manages to do so when they throw a light switch!


Physicists tell us that every photon, for example, is identical to every other photon. Indeed, every electron is also identical with every other electron. This is how Philosopher of Science, Stephen French, puts things:


"It should be emphasised, first of all, that quantal particles are indistinguishable in a much stronger sense than classical particles. It is not just that two or more electrons, say, possess all intrinsic properties in common but that -- on the standard understanding -- no measurement whatsoever could in principle determine which one is which. If the non-intrinsic, state-dependent properties are identified with all the monadic or relational properties which can be expressed in terms of physical magnitudes associated with self-adjoint operators that can be defined for the particles, then it can be shown that two bosons or two fermions in a joint symmetric or anti-symmetric state respectively have the same monadic properties and the same relational properties one to another. [French and Redhead (1988); see also Butterfield (1993).] This has immediate implications for Leibniz's Principle of the Identity of Indiscernibles which, expressed crudely, insists that two things which are indiscernible, must be, in fact, identical." [French (2019). Bold emphases and links added. Referencing altered to conform to the conventions adopted at this site.]


The above passage has now been replaced by the following in the new, 2019, edition of this article:


"Now, of course, both quantum and classical objects of the same kind -- such as electrons, say -- are indistinguishable in the sense that they possess all intrinsic properties -- charge, spin, rest mass etc. -- in common. However, quantum objects are indistinguishable in a much stronger sense in that it is not just that two or more electrons possess the same intrinsic properties but that -- on the standard understanding -- no measurement whatsoever could in principle determine which one is which. If the non-intrinsic, state-dependent properties are identified with all the monadic or relational properties which can be expressed in terms of physical magnitudes standardly associated with self-adjoint operators that can be defined for the objects, then it can be shown that two bosons or two fermions in a joint symmetric or anti-symmetric state respectively have the same monadic properties and the same relational properties one to another (French and Redhead 1988; see also Butterfield 1993). This has immediate implications for the Principle of the Identity of Indiscernibles which, expressed crudely, insists that two things which are indiscernible, must be, in fact, identical." [Ibid. Bold added.]


Of course, French offers his own solution to this difficulty, but it isn't one that challenges the identity of quantal particles, just their lack of individuality. And, Nobel Laureate, Paul Dirac, made a similar point:


"If a system in atomic physics contains a number of particles of the same kind, e.g., a number of electrons, the particles are absolutely indistinguishable. No observable change is made when two of them are interchanged…." [Dirac (1967), p.307. Bold emphasis added.]


However, one might wonder how anyone could possibly know that two particles had been interchanged if they are "absolutely indistinguishable". On the other hand, Pure Mathematician that he was, Dirac might merely be making a theoretical point on a par with the following: "If we swap one number in this equation with another (identical) number, no change will be observed: 2 + 3 = 5". We can see this perhaps more clearly with this example: "Two plus three equals five" is mathematically indistinguishable from "2 + 3 = 5" even though "2" and "Two", for instance, are plainly different.


In that case, every time a worker turns on a light, he or she generates countless trillion identical objects per second -- which must mean that such workers are "unconscious" anti-dialecticians, if we employ the same sort fractured of reasoning here as Trotsky.


Naturally, contentious claims like these can only be neutralised by an a priori stipulation to the effect that every photon in existence (past, present and future) must be non-identical -- despite what scientists tell us and in abeyance of the impossibly large (finite) amount of data that would be needed to substantiate such a cosmically ambitious claim. At this point, perhaps, even hardnosed dialecticians might be able to see in this a blatant attempt to impose DM on reality.


[A recent discussion of these issues can be found in Brading and Castellani (2003), and Castellani (1998). An even more recent discussion can be found in Saunders (2006) [this links to a PDF], and French and Krause (2006). See also, Hilborn and Yuca (2002), Ladyman and Bigaj (2010), and the Wikipedia entry here.]


It could be objected that Trotsky would surely have been unaware of developments in Physics after he died, but, as the references given show, such facts were largely true of classical particles; quantum particles merely present a more extreme form of strict identity. And Lenin it was who reminded us that science is ever revisable; hence, no dialectician (who agrees with Lenin) could consistently rule out the possibility that scientists would one day discover identical particles -- as indeed they have.


Again, Trotsky was quite happy to impose his views on nature before all (or even most) of the evidence was in, in defiance of what he said elsewhere:


"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. [b] 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.]


Identity Is No Enemy Of Change


Finally, and perhaps most damningly, Trotsky (and Hegel) failed to notice that the LOI doesn't preclude change -- for if an object changes, then anything identical to it will change equally quickly. Moreover, if something changes, it will no longer be identical with its former self.


So, far from denying change, this 'law' allows us to determine if and when it has occurred.


With that observation, much of Dialectical Materialism falls apart.


Latest Update: 17/01/20


Word Count: 7,350


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