This log was inspired by "How to Read Wittgenstein" and "Ludwig Wittgenstein: the duty of genius" by Ray Monk. It is based on reading Tractatus Logico-Philosophicus by Ludwig Wittgenstein translated by D. F. Pears & B. F. McGuinness (Routledge and Kegan Paul:1963)

Thursday, April 3, 2008

Occam's rule points out that unnecessary signs mean nothing.

Logic must provide for itself, so if a sign is possible it must be able to signify. In logic, whatever can be done is also allowed. ('Socrates is identical' is absurd because 'identical' is not a property. The proposition makes no sense because we have not made an arbitrary assignment and not because the symbol itself is invalid.) In a certain sense, we cannot err in logic. Self-evidence can only be dispensed with in logic because language itself prevents every logical mistake. So logic is a priori because illogical thought is not possible: We cannot give a sign the wrong sense.

Occam's maxim is, of course, not an arbitrary rule, nor is it one justified by practice: It points out that unnecessary signs mean nothing. So signs that serve one purpose are logically equivalent, and signs that serve none are logically meaningless.

Frege says: any legitimately constructed proposition must make sense. Wittgenstein says: Any possible proposition is legitimately constructed, and can only be absurd because we have not given some of its constituents a meaning. (Even if we think that we have done so.) Thus 'Socrates is identical' says nothing because we gave the word 'identical' no meaning as an adjective. For when it appears as a sign for identity, the signifying relation is an entirely different one, so the symbols also are entirely different. In the two cases, the symbols have only the sign in common and that by chance.

The number of necessary fundamental operations depends only on our notation. We need only construct a system of signs with a particular number of dimensions - with a definite mathematical multiplicity. It is clear that this is not a matter of some primitive ideas that need a sign, but rather of expressing a rule.

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