Wittgenstein and the Logic of Inference

The Tractatus first appeared in 1921, the same year that Post's “Introduction to a General Theory of Elementary Propositions” appeared in the American Journal of Mathematics . As the latter is the first piece clearly to present and exploit the distinction between a deductive system and a truth-functional interpretation of such a system, we may conclude that Wittgenstein's views had been arrived at somewhat before a variety of logical concepts had received the clarification and refinement incipient on the now taken-for-granted distinction between proof and model theory. One such concept, of considerable interest to Wittgenstein, was that of inference. The following constitutes an attempt to explicate his notion. In particular, I shall attempt to show that his repudiation of “laws of inference” is closely tied to his rejection of logical constants; and that both can be seen as the product of what might be termed a “metaphysics of completeness”—before, of course, any (presently recognizable) notion of completeness had achieved a measure of precision or currency

Calculus (dental) · Completeness (order theory) · Epistemology · Inference · Interpretation (philosophy) · Linguistics · Logical consequence · Logical truth · Metaphysics · Rule of inference · Variety (cybernetics) · Artificial Intelligence · Computer Science · Logic, Reasoning, and Knowledge · Mathematics · Philosophy · Philosophy and Theoretical Science · Wittgensteinian philosophy and applications

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