Wednesday, November 28, 2007

6.232 Frege says the two expressions have the same meaning [Bedeutung] but different senses [Sinn].

But the essence of an equation is that it is not necessary in order to show that the two expressions that the equals sign combines have the same meaning [Bedeutung], since this can be seen from the two expressions themselves.

The distinction between meaning and sense (and hence between senselessness and nonsense?) breaks down, because, roughly speaking at least, meaning is use. The notion of sense is seemingly treated here as unnecessary or irrelevant. If 1+1 = (1+1) then this should be manifest in all sorts of ways within mathematics. We do not need to be told it, as if it were an axiom or first principle. To know what (1+1) means is to know, among other things perhaps, that it means (is substitutable for) 1+1. The substitutability of these expressions for each other is not an additional fact, additional to the meaning of each.

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