What does the Objectivist "A = A" even mean?

That ”A is A” is one of the fundamental principles of Objectivism. However, it is not terribly unequivocal, or at least not to the degree that proponents would have it be. What exactly does it mean? In propositional logic, the formal definition of ”=” is, roughly, that A = B iff P(A) iff P(B); e.g. A is B if and only if all predicates applied to them result in the same truth value. There’s a pretty important distinction from the Objectivist version here – propositional logic offers a test for when A = B; and A = A is just a trivial case of that. From an objectivist point of view, how would you go about demonstrating that A = B? A = A and B = B are both valid, but there seems to be no chain of operations that can connect them.



As far as I understand, the ”axiom” derives from a Socratic dialogue, where Socrates says something along the lines of, ”Do you agree that everything is the same as itself, and different from another?”. I’m not certain of the context of that line, regardless, the language is hopelessly imprecise and incomplete. ”Is” is infamously one of the most ambiguous words in the English language; it can imply existence, equivalence and attributes.



I understand that the axiom is supposed to be a distancing from epistemological relativism; and yet, it is not a useful principle. How would an objectivist go about to demonstrate that two propositions are equivalent, for instance? Well, I’m not even sure if that sentence, or something like ”A is B” would be meaningful within the framework of Objectivism. The equality seems to be nothing but a symbol with the trivial attribute that x = x is valid for all x.

Anyone care to elaborate on this? I’ve tried to read a few sites attempting to explain the epistemology of Objectivism, but I’ve generally found them sloppy and very ipsedixitous. Surely someone must have attempted to straighten things out properly?

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