smee again
9th May 2009, 19:05
this is really adressed at trotskyists, who would know best... I'm kind of doing a survey like i've read one by bakunin, one by benjamin tucker, several by lenin, one by mao, miscilaneous letters and pamphlets by all types of leftist, plan on reading 1 althusser, 1 gramsci, etc.,...
it can be a large book.
Rosa Lichtenstein
10th May 2009, 00:58
YS
In Defence of Marxism
This is, perhaps, Trotsky's worst book. His 'analysis' of the so-called 'law of identity' (and what he takes to be 'formal logic') is lamentably poor. Here is part of what I have written elsewhere about it:
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 (http://homepage.ntlworld.com/rosa.l/page%2004.htm), dialecticians make such mistakes all the time.
Morever, this sort of attitude would not be tolerated for one second in the sciences, or in any other branch of genuine knowledge. Can you imagine the fuss if someone were to argue that it does not matter what the Magna Carta said, or when the Battle of the Nile was fought, or what the Declaration of Independence actually contained, or what the exact wording of Newton's Second Law was, or whether "G", the Gravitational Constant, was 6.6742 x 10^-11 or 6.7642 x 10^-11 Mm^2kg^-2, or indeed something else? Would we accept this sort of excuse from someone who said it did not matter what the precise wording of a contract in law happened to be? Or, that it did not really matter what Marx meant by "variable capital", or that he "pedantically" distinguished use-value from exchange-value -- or more pointedly, the "relative form" from the "equivalent form" of value --, we should be able to make do with anyone's guess? And how would we react if someone said, "Who cares if there are serious mistakes in that policeman's evidence against those strikers"? Or if someone else retorted "Big deal if there are a few errors in this or that e-mail address/web page URL, or in that mathematical proof! And who cares whether there is a difference between rest mass and inertial mass in Physics! What are you, some kind of pedant?"
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, after all!
[LOI = Law of Indentity.]
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 be able to say why this is a mere approximation.
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.
Anyway, abstract identity is discussed here (http://homepage.ntlworld.com/rosa.l/page%2006.htm).
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 "≡" sign which appears in, say, 2sinxcosx ≡ 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.
[MFL = Modern Formal Logic.]
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 "≡" 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.]
Furthermore, in ordinary material language the difference between equality and identity is even clearer. So, we can say things like "The author of [I]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 (http://homepage.ntlworld.com/rosa.l/page%2006.htm).]
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 ≡ √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 "≡" 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 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.
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, as we are constantly being told (by DM-fans).
With that observation alone, much of dialectics completely falls apart.
More details here:
http://homepage.ntlworld.com/rosa.l/page%2006.htm
This means that, since Trotsky uses such defective reasoning to defend his analysis of the former USSR, the latter is flawed from beginning to end (and I say that as a Trotskyist myself).
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