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

All propositions are the result of truth operators applied to elemental propositions.

A truth operation is how a truth function originates from elemental propositions. According to the nature of truth operations, a truth function turns into a new truth-function just as an elemental proposition turns into its own truth function. Every application of a truth operator to truth functions of elemental propositions generates another truth function of elemental propositions, another proposition. Whenever a truth operator is applied to the results of truth operations on elemental propositions, there is always a single operation on elemental propositions that has the same result. Thus, every proposition is the result of truth operations on elemental propositions.

Truth value tables have a meaning even when 'p', 'q', 'r', etc. are not elemental propositions. And it is easy to see that a propositional sign in truth table form expresses a single truth-function of elemental propositions even when 'p' and 'q' are themselves truth-functions of other propositions. So all truth functions are the result of successive application of a finite number of truth operations to elemental propositions.

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