The recent Ayn Rand entry at the Mises Institute Blog got me thinking about A=A. One commenter asks, "What if I say A=B?" This, of course, was part of a broader point that if one perceives A to be B, then for that person A=B even though it might be A=A for you. I'm going to side-step the polylogism argument for now so that I can focus on what A=A actually means.
A=A means that A is something that we know, that it exists outside of our perception, that it is what it is. Simple, right?
A=B is nonsense. The statement A=B used in the capacity to describe an alternate scenario to A=A means that one is aware of two things: A, and B, and that upon closer inspection they are in fact the same thing.
In the context of a philosophical debate, the assertion A=B doesn't mean that A could be something else other than A, it means that what you mistook for two things is actually one.
To put it the way Rand might have, in order to assert that A=B, you'd have to first know that A and B are two separate things, and choose to pretend otherwise. This is very definitely nonsense. When people make assertions like these, they don't just misunderstand Rand - they misunderstand logic and philosophy themselves.
That's all I have to say for now. I told you this one would be brief. ;)