proof theory

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The study of the relations of deducibility among sentences in a logical calculus. Deducibility is defined purely syntactically, that is, without reference to the intended interpetation of the calculus. The subject was founded by the mathematician David Hilbert (1862–1943) in the hope that strictly finitary methods would provide a way of proving the consistency of classical mathematics, but the ambition was torpedoed by Godel's second incompleteness theorem. See also model theory.

Subjects: Philosophy.

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