the identity property is pretty central to a lot of endeavors. if there's one thing our logical proofs, self-congratulatory objectivism and philosophical arguments rest on, it's the fact that "A is A."
of course, this is a perfect example of why traditional logical assumptions and standards shouldn't be applied wholesale to the study of language. in philosophy of language "A is A" is the foundation for the idea that any statement is identical to itself. this works alright for physical objects, but when it comes to language, there are never two identical statements. there are never two identical statements. there are never two identical statements.
the first A is not the same as the second A. in the most trivial sense, they're in different places on the page. they're articulated at different times, drawn slightly differently or pronounced slightly differently. the fact that these types of differences don't count as differences is the most primary function of language. as derrida says, language is repetition and difference. language is, by pretty much anyone's definition, made of repeating elements. but each repetition involves a difference. it's that whole can't-step-in-the-same-river-twice thing.
to say "A is A" is true is not a tautology. it's not a definition handed down by god or a self-evident truth about the universe. it should be seen as a statement of our most basic assumptions about language. assumptions probably isn't even the right word because it's something even stronger than an assumption. it's the nature of language's functioning to flatten out certain differences, especially the differences that context and repetition throw into the works.
i'm not saying "A is A" is not true. it IS true precisely because we understand two separate tokens of the same bit of language (two of the same statement, two "A"s) to be the same thing. and we have this understanding because of the nature of language. and that's a shaky place to build your logic!