Monday, November 12, 2007

5.5321 Instead of “(x): fx [if…then] x = a” we therefore write, e.g., “(Ex) .fx. [if…then]. fa: ~ (Ex, y) .fx .fy”.

And the proposition “only one x satisfies f( )” reads: “(Ex) . fx: ~(Ex, y) .fx .fy”.

All this does is eliminate (the need for) the sign “=”. OK. Clearly, it can be dispensed with.

Anscombe points out (p. 149) that he is here allowing a way of saying that only one thing has f. But in that case, “it is difficult to see how he could avoid a way of admitting formulae which say ‘There are only n things and m functions’ without using either ‘thing’ or ‘function’ as a function.” Yet at 5.535 the number of objects is supposed to be shown by the number of names with different references, not by some statement of how many objects there are. And what can be shown cannot be said. Supposedly. Looks like a problem, as Anscombe notes.

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