Question How do formal logicians respond to Marxist/Leninist/Dialectical logic claims? For example, in "An Introduction to the Logic of Marxism", George Novack explains that the law of identity of formal logic, that "A is equal to A", is always falsified when we try to apply it to reality. Here is a quote from the book, in which he quotes from "In Defense of Marxism" (it is long, I apologize): "... a pound of sugar is equal to itself. Neither is this true -- all bodies change uninterruptedly in size, weight, color, 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; ... 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." He goes on to say that since everything exists in time, the law of identity of formal logic is never applicable to the real world. Presumably at least one reason we use logic is to help us arrive at beliefs that will then guide our actions, so presumably if the law of identity of formal logic were in fact falsified when applied to the real world, that would be a problem. What do you make of all of this?? Thanks.

Accepted:
October 22, 2005

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According to a standard conception of identity, if A is identical to B, then A and B haveall of their properties in common. This principle is commonly known asLeibniz’s law, after the philosopher Gottfried Wilhelm Leibniz, a 17thcentury German philosopher, who articulated this implication of ourconcept of identity. This principle is also referred to as "theprinciple of the indiscernibility of identicals". This law or principlemight seem to imply that if a particular object (say a particularquantity of sugar) changes over time, then it’s not the same thing–after all, the properties of the object at one time are different fromthe properties of that object at another time. However, this reasoningrests on a confusion. Leibniz’s law does not imply that if A at T1 has properties f, g, and h, then A at T2 must have these same properties. Instead, it implies that, if it is true of A that at T1 it has properties f, g, and h, then at T2 it is true of A that at T1 it had properties f, g, and h.