So, I feel the need to defend the uses of of “=” and ““. Mainly because I am differentiating uses of but not differentiating uses of “=”. If I differentiated, say the identity “A=A” from the identity “B=B” it would mean not that these were different identities, but that there were two kinds of identity. That is a can of worms I am not ready to open yet. But the choice makes more sense if you think of the concept of equals, including identity, as being the opposite of making distinctions, which is what identifying kinds of identity is. This is what makes equals universal, while not-equals is always special, even though I am aware that this undermines the concept of difference, making (allowable) inconsistencies in my previous post.
We can say, for example that 1+2=3 and 2+3 = 5 and then that 1+2 2+3 which in effect means that the two equals signs are for different equalities. No problem there, and the difference is kept with the symbol , which is the way it should be. But how can I defend that there shouldn’t be different kinds of identity, where there should be different kinds of distinctions? Well, is the way that “A=A” any different from the way “B=B”? I would say no. And, again appealing to the intuition: There is a big difference between the way a question is different from a neutron star and the way an lemon is different from a lime. So I am committed to the idea that there are different kinds of differences, but there is only one kind of sameness.