Friday, November 09, 2007

5.522 What is peculiar to the symbolism of generality is first, that it points to a logical prototype, and secondly, that it emphasizes constants.

I follow Black (p. 284) on the translation of hinweist as ‘points to.’

What logical prototype? See 3.315.

What constants? Black (p. 284): “I think the ‘constants’ in question must be the names that could be substituted for the variable in the propositional function to which the quantifier is attached (not the constant formal features of the generalized proposition, i.e. those that show its form).”

Emphasized how? I'm not sure.


Ponder Stibbons said...

My first reaction was that 'constants' refers to the properties ascribed to the things that are represented by the variables in a statement of generality. (So, for example, in 'for all x, Bx', the constant is B.) But then I couldn't figure out what this constancy had to do with symbolism, or how it is emphasized.

DR said...

I find this a bit obscure, but Mounce (pp. 68-69) might be helpful. He says: "To see what he means consider (x) (fx). What Wittgenstein is referring to as the generality sign is not the quantifier but the second x. His point is that generality is already contained in the x of fx."

So "It follows then that fx contains generality; it is, one might say, a prototype for a set of propositions -- fa, fb, fc etc."

If a, b, and c are the constants, it seems odd to say that they are emphasized in (x) (fx), which does not mention them at all. But I suppose one can emphasize something, point attention to it, without mentioning it.