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Identity/"is"/analytical/intensional/Mates: it is debatable whether "A is A" must be regarded as formal analytically or analytically because of the sense of "is" - like statements from scheme. Example: If A is warmer than B and B is warmer than C, then A is warmer than C analytically because of the sense of "is warmer than" - the dispute is whether "is" can be regarded as a logical constant such as "not" etc, or as a belonging to the non-logical vocabulary - language L: here was "is" non-logic - that was arbitrary.
if not -logic, then independent theory of identity possible - on the other hand: if "is" logical constant (which means the relation of identity above this area) we construct with that a new language.
Identity/Frege/Mates: "a = a" and "a = b": Difference sense/meaning- E.g. "7 + 5 = 12" does not mean the same as "The expressions" 7 + 5 "and" 12 " refer to the same object "- solution/Frege: the second is a synthetic truth about language ((s) metalinguistically) - the first an analytic truth about numbers - ((s) object language) - identity/Mates: there is not the relation of identity! - They are different from area to area - ((s) intensional/extensional).
Elementare Logik Göttingen 1969