Necessary truth and proof

Necessary Truth and Proof

What makes necessary truths true? I argue that all truth supervenes on how things are, and that necessary truths are no exception. What makes them true are proofs. But if so, the notion of proof needs to be generalized to include verification-transcendent proofs, proofs whose correctness exceeds our ability to verify it. It is incumbent on me, therefore, to show that arguments, such as Dummett’...

Truth and Proof

T he subject of this article is an old one. It has been frequently dis­ cussed in modern logical and phil­ osophical literature, and it would not be easy to contribute anything original to the discussion. To many readers, I am afraid, none of the ideas put forward in the article will appear essentially novel ; nonetheless , I hope they may find some interest in the way the material has been arr...

Necessary Truth and Grammatical Propositions

Truth Values and Proof Theory

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic s5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic ...

Proof interpretations with truth

This article systematically investigates so-called “truth variants” of several functional interpretations. We start by showing a close relation between two variants of modified realizability, namely modified realizability with truth and q-modified realizability. Both variants are shown to be derived from a single “functional interpretation with truth” of intuitionistic linear logic. This analys...