Neil Tennant

I propose an anti-realist account of truth and paradox according to which the logico-semantic paradoxes are not genuine inconsistencies. The ‘global’ proofs of absurdity associated with these paradoxes cannot be brought into normal form. The account combines epistemicism about truth with a proof-theoretic diagnosis of paradoxicality. The aim is to combine a substantive philosophical account of truth with a more rigorous and technical diagnosis of the source of paradox for further consideration by logicians. Core Logic plays a central role in the account on offer. It is shown that the account is not prey to the problem of revenge paradox

SummaryI defend a conventionalist view of logical and mathematical truths against the criticisms of Quine and Stroud. Conventionalism is best formulated by appealing to sense‐conferring rules governing important logical and mathematical expressions. Conventional necessity can be understood as arising from these rules in a way that is immune to Quine's and Stroud's criticisms of the earlier formulation of conventionalism, in which stress was incorrectly laid on axiomatic systems of logic.RésuméJe soutiens, en dépit des critiques de Quine et de Stroud, une conception conventionnaliste des vérités logiques et de vérités mathématiques. La meilleure façon de formuler le conventionnalisme est de faire appel à des règies conférant un sens à?on;importantes expressions logiques et mathématiques. La nécessité conventionnelle peut être comprise comme provenant de ces règies par des voies qui ne donnent pas prise aux critiques de Quine et de Stroud ag ľégard de ľancienne formulation du conventionnalisme, dans laquelle ľaccent était mis, a tort, sur les systèmes axiomatiques de la logique.ZusammenfassungGegen Quines und Strouds Kritiken verteidige ich eine konventionalistische Auffassung der logischen und mathematischer Wahrheiten. Der Konventionalismus wird am besten durch Berufung auf bedeutungsstiftende Regeln, die den Gebrauch wichtiger logischer und mathematischer Ausdrücke bestimmen, formuliert. Konventionelle Notwendigkeit kann als von diesen Regeln hervorgebracht verstanden werden – und das zwar auf eine Art, die sie vor Quines und Strouds Anfechtungen schützen. In der von diesen kritisierten, früheren Fassung wurde zu unrecht das Gewicht auf axiomatische Systeme der Logik gelegt

This is a reply to Timothy Williamson ’s paper ‘Tennant’s Troubles’. It defends against Williamson ’s objections the anti-realist’s knowability principle based on the author’s ‘local’ restriction strategy involving Cartesian propositions, set out in The Taming of the True. Williamson ’s purported Fitchian reductio, involving the unknown number of books on his table, is analyzed in detail and shown to be fallacious. Williamson ’s attempt to cause problems for the anti-realist by means of a supposed rigid designator generates a contradiction with arithmetic right away, upon instantiating the obviously relevant theorem that every natural number is provably odd or provably even. The paper also explains and formulates a globally restricted knowability principle, which likewise blocks the attempted reductio

We define a system IR of first-order intuitionistic relevant logic. We show that intuitionistic mathematics (on the assumption that it is consistent) can be relevantized, by virtue of the following metatheorem: any intuitionistic proof of A from a setX of premisses can be converted into a proof in IR of eitherA or absurdity from some subset ofX. Thus IR establishes the same inconsistencies and theorems as intuitionistic logic, and allows one to prove every intuitionistic consequence of any consistent set of premisses.