Thursday, June 15, 2006

Julius Caesar and substitutions

Brandom's reading of Frege's Grundlagen leads him to an interesting take on the Julius Caesar problem. He thinks that if you have an indirectly defined term fX, like X has the same direction as Y iff X is parallel to Y, then if you hold P(fX) and X=Y, you will be committed to the substitution P(fY). You will not be committed one way or the other to the substitution P(Z). The reason is that he thinks that Frege's requirement on understanding identity statements is too strong. Frege required that the sense of all identity statements be settled, in principle, before you could use a new term like fX where X is an old term of the language.

I'm not sure exactly why, but this leads Brandom to the conclusion that something can't be referred to by a singular term unless it can be referred to by many singular terms. This is a sort of term holism: being able to use one means being able to use many. This one will require a lot more thought on my part.

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