Method developed independently by Post (1921) and Wittgenstein (1922) of defining logical connectives on the basis of truth values. Since the truth value of complex propositions connected by constants (such as and, or) is dependent on the truth values of the component propositions and on the meaning of their constants, these relations can be represented in a matrix. In the first vertical column the different possible combinations for the individual component propositions are entered: t=‘true,’ f=‘false’; the number of the horizontal lines is 2n, whereby n is the number of actual component propositions (=atomic sentences) in the propositional connection: two component propositions yield four, five component propositions yield thirty-two lines. The far-right line indicates the truth value applied to the distribution of the truth values by the constants (cf. the examples shown in conjunction, disjunction,implication, and others).
The following table provides an overview of the most important two-place sentence operators and the distribution of their truth values.
References
Post, E. 1921. Introduction to a general theory of elementary propositions. AJM 43.163–85.
Wittgenstein, L. 1922. Tractatus logicophilosophicus. London.
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