Gottlob Frege's On Sense And Reference

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In On Sense and Reference, Gottlob Frege analyzes the concept of identity statements. He aims to figure out what kind of relation equality is and solve an apparent puzzle that results from identity statements. Frege defines and uses the notions of sense and reference to explain the differences two types of identity claims, “a=a” and “a=b.” In this paper I will explain Frege’s puzzle and its application to identity statements and propositional attitude ascriptions. I will then give Frege’s solution to this puzzle and then offer an objection to Frege’s solution. I do not believe Frege’s solution to his puzzle is substantial enough.
Frege begins by putting forward a puzzle that results from two types of identity statements. Frege first dismisses his old view that an identity statement is a relation between names. If one believes that “a=b” expresses a relation between the names “a” and “b”, then one is making a linguistic claim instead of a claim about the objects “a” and “b.” Frege then says
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Frege states that an identity statement must be relations between objects rather than names because it is not a linguistic claim. However, if sense, or the mode of presentation, is what differentiates “a” from “b” in “a=b,” this does not seem to express a relation between objects. Rather, it looks like it expresses a relation between modes of presentation of objects. It is not clear how modes of presentation become manifest. When one uses a proper name, they are referring to an object, not a mode of presentation. It does not seem to follow that due to an identity statement, modes of presentations become significant. The statement “a=b” concerns not the names “a” and “b” nor the modes of presentations of “a” and “b”, but rather the objects “a” and “b”. If two modes of presentations refer to the same object, it does not follow that the identity statement connecting them is about the objects

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