5.5301 Identity is patently not a relation between objects. This becomes very clear if one considers, e.g., the proposition: “(x) : fx. [if…then] . x = a”. What this proposition says, is simply that only a satisfies the function f, and not that only such things satisfy the function f as have a certain relation to a.

One could of course say that in fact only a has this relation to a, but in order to express this we would need the identity sign itself.

And why is that a problem? Because we are trying to explain the meaning of the identity sign, I take it. To say that one thing is identical to another is to say something about the symbolism in use, not the objects in question. “A = A” tells you nothing about A. And a = b tells you nothing about a or b, only that these signs are used for the same thing.