Thursday, November 08, 2007

5.521 I separate the concept all from the truth-function.

Frege and Russell introduced generality in connection with the logical product or the logical sum. So it would be hard to understand the propositions “(Ex). fx” and “(x). fx”, in which both ideas are contained.

My translation of the last sentence is not very literal.

See Anscombe pp. 141-143 on this. She says that Frege and Russell did not at all explicitly do what Wittgenstein says here. The relevant Frege paper is “Function and Concept,” and Russell offers similar explanations of generality in his work. Frege explains his sign for generality in terms of what it means, and specifically in terms of when it means what he calls “the true.” Wittgenstein believes that the truth of a general proposition is the truth of a logical product. Hence his claim here about what he takes to be implicit in Frege and Russell. Universal propositions (For all x, …), he thinks, each say that some logical product is true, and particular propositions (For some x, …) each say that some logical sum is true.

White (p. 94) says that Wittgenstein’s target here seems mainly to be what Russell says in Principia Mathematica.

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