Tuesday, September 18, 2007

4.1273 If we want to express in the concept-script the general proposition: “b is a successor of a,” then we need for this an expression for the general term of the formal series: aRb, (Ex):aRx. xRb, (Ex,y):aRx. xRy. yRb, … The general term for a formal series can be expressed only by a variable, because the concept ‘term for this formal series’ is a formal concept. (This has been overlooked by Frege and Russell: because of this the way they want to express general propositions like the one above is false; it contains a vicious circle.)

We can determine the general term of a formal series by giving its first term and the general form of the operation that produces the next term from the proposition that goes before it.

Black (p. 203) points out that Wittgenstein seems to be attacking “Frege and Russell’s definition of the so-called ‘ancestral’ of a relation, which they use in their definition of a natural number.”

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