Wednesday, March 07, 2007

3.24 A proposition that deals with a complex stands in an internal relation to a proposition that deals with a component of the complex.

A complex can only be given through its description, and this will match it or not match it. A proposition, in which there is mention of a complex, will, if this complex does not exist, be not nonsensical [unsinnig] but simply false.

One can see that a propositional element signifies a complex by a vagueness in the propositions in which it occurs. We know by this proposition that something is not yet definite [determinate]. (The notation for generality indeed contains a prototype.)

The abbreviation of the symbol of a complex in the form of a simple symbol can be expressed by a definition.

See 4.123 for the meaning of ‘internal.’ See 4.241 for the meaning of ‘definition.’ There is a logical relation between propositions about complexes and propositions about parts of complexes, presumably taking these propositions to be about complexes qua complexes and propositions about complex-parts to be about them qua complex parts (see my comment on 2.0201). In the next paragraph of 3.24 Wittgenstein seems to agree with Russell about the (non-existent) King of France. To say that the King of France is bald, when there is no King of France, is to say something that is simply false, not nonsensical. There can indeed be vagueness in propositions, something corresponding to indeterminacy. There is a sort of implication here that this vagueness might be eliminable, but there is certainly no claim that this will be so. Indeed, if the notation for generality (for all x, if x etc., I suppose) already contains a prototype for indeterminacy, then perhaps it is not dispensable from logic.

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