The law of identity

[Apex_Predator]

Below is written by Leon Trotsky. While of course the Law of Identity is an axiom, beyond its base truthiness, what good is it? How does Ayn Rand build a philosophy from this Law? It's because she assumes that we can all know what an object is, we can all perceive things objectively. But that has nothing to do with the law. Trotsky explains the futility of taking this law any further as Ayn Rand did around the same time as this was written.


"Dialectic is neither fiction nor mysticism, but a science of the forms of our thinking insofar as it is not limited to the daily problems of life but attempts to arrive at an understanding of more complicated and drawn-out processes. The dialectic and formal logic bear a relationship similar to that between higher and lower mathematics.

I will here attempt to sketch the substance of the problem in a very concrete form. The Aristotelian logic of the simple syllogism starts from the proposition that ‘A’ is equal to ‘A’. This postulate is accepted as an axiom for a multitude of practical human actions and elementary generalizations. 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 of 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 this 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”.

Aside from the extremely dubious practical value of this “axiom”, it does not withstand theoretical criticism either. 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.

At first glance it could seem that these “subtleties” are useless. In reality they are of decisive significance. 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. To make use of the axiom of ‘A’ is equal to ‘A’ with impunity is possible only within certain limits. When quantitative changes in ‘A’ are negligible for the task at hand then we can presume that ‘A’ is equal to ‘A’. This is, for example, the manner in which a buyer and a seller consider a pound of sugar. We consider the temperature of the sun likewise. Until recently we consider the buying power of the dollar in the same way. But quantitative changes beyond certain limits become converted into qualitative. A pound of sugar subjected to the action of water or kerosene ceases to be a pound of sugar. A dollar in the embrace of a president ceases to be a dollar. To determine at the right moment the critical point where quantity changes into quality is one of the most important and difficult tasks in all the spheres of knowledge including sociology.

Every worker knows that it is impossible to make two completely equal objects. In the elaboration of baring-brass into cone bearings, a certain deviation is allowed for the cones which should not, however, go beyond certain limits (this is called tolerance). By observing the norms of tolerance, the cones are considered as being equal. (‘A’ is equal to ‘A’). When the tolerance is exceeded the quantity goes over into quality; in other words, the cone bearings become inferior or completely worthless.

Our scientific thinking is only a part of our general practice including techniques. For concepts there also exits “tolerance” which is established not by formal logic issuing from the axiom ‘A’ is equal to ‘A’, but by the dialectical logic issuing from the axiom that everything is always changing. “Common sense” is characterized by the fact that it systematically exceeds dialectical “tolerance”.

Vulgar thought operates with such concepts as capitalism, morals, freedom, workers’ state, etc as fixed abstractions, presuming that capitalism is equal to capitalism. Morals are equal to morals, etc. 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.

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. Dialectical thinking gives to concepts, by means of closer approximations, corrections, concretisation, a richness of content and flexibility; I would even say “a succulence” which to a certain extent brings them closer to living phenomena. Not capitalism in general, but a given capitalism at a given stage of development. Not a workers’ state in general, but a given workers’ state in a backward country in an imperialist encirclement, etc.

Dialectical thinking is related to vulgar 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. Dialectics does not deny the syllogism, but teaches us to combine syllogisms in such a way as to bring our understanding closer to the eternally changing reality. Hegel in his Logic established a series of laws: change of quantity into quality, development through contradictions, conflict of content and form, interruption of continuity, change of possibility into inevitability, etc., which are just as important for theoretical thought as is the simple syllogism for more elementary tasks.

Hegel wrote before Darwin and before Marx. Thanks to the powerful impulse given to thought by the French Revolution, Hegel anticipated the general movement of science. But because it was only an anticipation, although by a genius, it received from Hegel an idealistic character. Hegel operated with ideological shadows as the ultimate reality. Marx demonstrated that the movement of these ideological shadows reflected nothing but the movement of material bodies.

We call our dialectic materialist, since its roots are neither in heaven nor in the depths of our “free will”, but in objective reality, in nature. Consciousness grew out of the unconscious, psychology out of physiology, the organic world out of the inorganic, the solar system out of the nebulae. On all the rungs of this ladder of development, the quantitative changes were transformed into qualitative. Our thought, including dialectical thought, is only one of the forms of the expression of changing matter. There is place within this system for neither God nor Devil, nor immortal soul, nor eternal norms of laws and morals. The dialectic of thinking, having grown out of the dialectic of nature, possess consequently a thoroughly materialist character.

Darwinism, which explained the evolution of species through quantitative transformations passing into qualitative, was the highest triumph of the dialectic in the whole field of organic matter. Another great triumph was the discovery of the table of atomic weights of chemical elements and further the transformation of one element into another.

With these transformations (species, elements, etc.) is closely linked the question of classification, equally important in the natural as in the social sciences. Linnaeus’ system (18th century), utilising as its starting point the immutability of species, was limited to the description and classification of plants according to their external characteristics. The infantile period of botany is analogous to the infantile period of logic, since the forms of our thought develop like everything that lives. Only decisive repudiation of the idea of fixed species, only the study of the history of the evolution of plants and their anatomy prepared the basis for a really scientific classification.

Marx, who in distinction from Darwin was a conscious dialectician, discovered a basis for the scientific classification of human societies in the development of their productive forces and the structure of the relations of ownership which constitute the anatomy of society. Marxism substituted for the vulgar descriptive classification of societies and states, which even up to now still flourishes in the universities, a materialistic dialectical classification. Only through using the method of Marx is it possible correctly to determine both the concept of a workers’ state and the moment of its downfall.

All this, as we see, contains nothing “metaphysical” or “scholastic”, as conceited ignorance affirms. Dialectic logic expresses the laws of motion in contemporary scientific thought. The struggle against materialist dialectics on the contrary expresses a distant past, conservatism of the petit-bourgeoisie, the self-conceit of university routinists and … a spark of hope for an after-life."

[From A Petit-bourgeois Opposition in the Socialist Workers Party, by Leon Trotsky, December 15, 1939.]

[Renee]

While of course the Law of Identity is an axiom, beyond its base truthiness, what good is it? How does Ayn Rand build a philosophy from this Law? It's because she assumes that we can all know what an object is, we can all perceive things objectively. But that has nothing to do with the law. Trotsky explains the futility of taking this law any further as Ayn Rand did around the same time as this was written.

Well, well, well. A=A, the first tenet of the Law of Identity, is useful in practical terms, but not in the same way as Trotsky states or derives.

"All two-legged people are two-legged people." Here we are not saying how much they weigh, how many atoms make up their content. Here we count their legs, and there is no margin of error possible there. Here the Law of Identity is not defeated.

Valid corollaries ensue from this different way of looking at A=A.

-- Updated October 20th, 2016, 9:50 am to add the following --

Below is written by Leon Trotsky. While of course the Law of Identity is an axiom, beyond its base truthiness, what good is it? How does Ayn Rand build a philosophy from this Law? It's because she assumes that we can all know what an object is, we can all perceive things objectively. But that has nothing to do with the law. Trotsky explains the futility of taking this law any further as Ayn Rand did around the same time as this was written.

Another way of defeating Trotsky's argument is identifying ranges, not individual instances.

"A" is not identified as an object, person, or concept, but a group of objects, persons, or concepts, which has a lower and upper limit.

Thus:

Given a group of people that weighs between 2009 kg and 2011 kg, then this is the same weight of people who also weigh between 2009 and 2011 kgs as a group. Whether the group is itself or some other group.

-- Updated October 21st, 2016, 2:22 am to add the following --

I believe I made mistakes just like the author. A=A is not the first rule of identity; it is the first rule of identicality.

Big difference.

[Apex_Predator]

Yet Ayn Rand uses the law of identity to assume they can know the identity of A, and that their perception of A is perfect in so much as it is objective, building a philosophically nonsensical religion.

[Cuthbert]

Ayn Rand confused these two statements:

"Ayn Rand thinks that everything is just what it is."

and

"Everything is just what Ayn Rand thinks it is."

The first is probably true, but uninteresting. The second is very interesting and almost certainly false.

Trotsky's argument is similar to Heraclitus's idea that the river you step into twice is the same and yet not the same. Panta rhei - all things are in flux. The formal objection is that, if A does not equal A, then it follows that A does not equal not-A. So we can say nothing true about either A or about not-A. This was a big problem for some other ancient Greeks but really we'd got over it by the time of Trotsky, surely.