THE LAW OF IDENTITY - a discussion article
by Roger Blackwell
The law of identity is usually considered to be the first law of thought. In its positive expression it may be put as A = A.
As Trotsky said (In Defence of Marxism, New Park, p63) "This postulate is accepted as an axiom for a multitude of practical human actions and elementary generalisations...."
We'll examine his further comments later.
What are the problems for understanding if this abstract law is not true? If A did not equal A then all the words in the last sentence, for example, could be different to the ones written here and so how could we understand anything? Let us leave aside, for the moment, A being approximately equal to A and consider what Hegel said in his 'Science of Logic' (trans. A.V.Miller, p413)
"This proposition in its positive expression A = A is, in the first instance, nothing more than the expression of an empty tautology. It has been rightly remarked that this law of thought has no content and leads no further. It is thus the empty identity that is rigidly adhered to by those who take it, as such, to be something true and are given to saying that identity is not difference, but that identity and difference are different. They do not see that in this very assertion they are themselves saying that identity is different....."
Hegel elaborated more on page 414 of the same work:
"It is admitted that the law of identity expresses only a one-sided determinateness, that it contains only formal truth, a truth which is abstract, incomplete. In this correct judgement, however, it is immediately implied that truth is complete only in the unity of identity with difference, and hence consists only in this unity."
Engels further developed this proposition in a materialist way in his book 'Dialectics of Nature' (7th printing 1976, p214/215)
"The fact that identity contains difference within itself is expressed in every sentence where the predicate is necessarily different from the subject; the lily is a plant, the rose is red where, either in the subject or in the predicate, there is something that is not covered by the predicate or the subject."
Let us return to the original abstract law of identity, A = A, and see what Trotsky said further in his remark (In Defence of Marxism, New Park p63)
".....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."
After answering objections to this and further elaborating his method, Trotsky said: (p64)
"At first glance it could seem that these 'subtleties' are useless.
In reality they are of decisive significance."
In more remarks about the abstract law of identity Trotsky continued (p64)
"The axiom 'A' is equal to 'A' appears on one hand to be the point of departure for all our knowledge, on the other hand the point of departure for all the errors in our knowledge."
This is most important. What did Trotsky mean by this? As we said earlier if 'A' does not equal 'A' then how do we understand the meaning of words? On the other hand if we take 'A' to equal 'A' we fall into error because no two 'A's are exactly equal and 'A' is not even equal to itself because everything is always changing.
Trotsky again put the problem concretely (p65) "The fundamental flaw of vulgar thought lies in the fact that it wishes to content itself with motionless imprints of a reality which consists of eternal motion," and further (p66) "Dialectical thinking is related to vulgar thinking in the same way that a motion picture is related to a still photograph. The motion picture does not outlaw the still photograph but combines a series of them according to the laws of motion."
Despite all the advances made in science and technology since the middle ages, modern bourgeois philosophers still teach medieval logic. They even retreat from Hegel back to Kant, Hume and Berkeley, because they are afraid of the revolutionary implications of dialectical logic. It is only dialectical materialism that can assimilate all these advances in science and incorporate them into its world outlook. Bourgeois philosophers remain trapped in the logic of the Middle Ages even though they may partially incorporate scientific advances in their general philosophy.
Let us return again to the abstract law of identity, A equals A. When we know that A is constantly changing, how do we understand anything in the light of these changes? Engels shows the way forward in 'Dialectics of Nature'(1976 ed p215)
"Abstract identity, like all metaphysical categories, suffices for everyday use, where small dimensions or brief periods of time are in question; the limits within which it is useable differ in almost every case and are determined by the nature of the object...."
This was further elaborated by Trotsky (In Defence of Marxism p65) "Dialectical thinking analyses all things and phenomena in their continuous change, while determining in the material conditions of those changes that critical limit beyond which "A" ceases to be "A", a workers' state ceases to be a workers' state."
In contrast to Hegel, who started with the movement of concepts, Trotsky said that it was the material conditions that determined when "A" ceased to be "A". It is those conditions that produce the changes in our logic and although this can in turn lead us to new practices to change those conditions, it is still the material world which predominates over our thought.
It was in the differences between the materialist outlook of Trotsky and the idealist outlook of Hegel that gave us the means to solve the problem of the law of identity.
Hegel used concepts in an exact manner with an idealist rigidity even though he was a brilliant dialectician. However, for the dialectical materialist method, concepts are used flexibly as they reflect the material world in its constant change and motion.
If we examine Lenin's study of Hegel in his Philosophical Notebooks (Vol38, p110) he said "All sided, universal flexibility of concepts, a flexibility reaching to the identity of opposites - that is the essence of the matter. This flexibility applied subjectively, equals electicism and sophistry. Flexibility applied objectively, i.e. reflecting the all-sidedness of the material process and its unity, is dialectics, is the correct reflection of the eternal development of the world."
For Hegel 'A' being approximately equal to 'A' was not an issue that he considered. It wouldn't make much sense in an idealist framework. However, we do use this concept, but we should be aware of the contradiction implied by it. To be approximately equal means to be almost the same, but it also implies being different.
Here we have a real unity of identity with difference which we usually take for granted every day. In this case contradiction is at the centre of our everyday thinking, but we overlook it.
As Lenin said ...... dialectics is a property of all human knowledge in general" (Vol38, p362)
It is up to us to use dialectical logic as a guide to action in the coming World Revolution.