Proof-theoretic semantics for classical mathematics

Synthese 148 (3):603 - 622 (2006)
We discuss the semantical categories of base and object implicit in the Curry-Howard theory of types and we derive derive logic and, in particular, the comprehension principle in the classical version of the theory. Two results that apply to both the classical and the constructive theory are discussed. First, compositional semantics for the theory does not demand ‘incomplete objects’ in the sense of Frege: bound variables are in principle eliminable. Secondly, the relation of extensional equality for each type is definable in the Curry-Howard theory.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
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