Gödel, truth & proof

Does Gödel ’ S Incompleteness Theorem Prove That Truth Transcends Proof ? ∗

Joseph Vidal-Rosset. Does Gödel’s Incompleteness Theorem Prove That Truth Transcends Proof ?. Johan van Benthem, Gerhard Heinzmann, Manuel Rebuschi, Henk Visser The Age of Alternative Logics Assessing Philosophy of Logic and Mathematics Today, 23, Springer Netherlands, pp.51-73, 2006, <10.1007/978-1-4020-50127 5>. . <h...

Portraits of science. Kurt Gödel--separating truth from proof in mathematics.

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’...

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...

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...