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

Logic must be clearly constructed from its primitive signs.

If there are primitive logical signs, then a valid logic must clearly show how they relate to one another and justify their existence. If logic has fundamental ideas, they must be independent of one another. If a fundamental idea has been introduced, it must have been introduced in all the combinations in which it ever occurs. It cannot, therefore, be introduced first for one combination and later reintroduced for another.

For example, once negation has been introduced, we must understand it both in propositions of the form (~p) and in propositions like (~(p∨q)), ((∃x).~fx), etc. We must not introduce it first for one class of cases and then again for another, since it would then be doubtful whether it means the same thing in both cases, and neither would there be any reason to combine the signs in the same way.

In short, Frege's remarks in The Fundamental Laws of Arithmetic about introducing signs by means of definitions also apply, mutatis mutandis, to the introduction of primitive signs.

The introduction of any new aid into the symbolism of logic is always significant. It should not be introduced in brackets or in a footnote - sneaked in, so to speak. But if a new aid is required at a certain point, place in logic must be explained. We must immediately ask ourselves: Where must it be used?

All numbers in logic need justification; or rather: It must become evident that there are no numbers in logic. Thus, there are no privileged numbers in logic; neither are co-ordination or classification; nor degrees of the general or specific. The solutions of the problems of logic must be simple, since they set the standard of simplicity.

We have always had a presentiment that there must be an area of investigation whose results - a priori - lie combined in a self-consistent system. A realm in which it is valid to assert: Simplex sigillum veri.

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