Truth, Logic and Invariance

Henri Galinon (1) , Denis Bonnay (1) , Julien Boyer (1)

1 IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques

In the spirit of Klein's Erlanger program logical notions have been characterized as the invariant of some suitably motivated similarity relations S over structures. Not every authors agree on a choice of a similarity relation (e.g., Tarski [3], Feferman [2], Bonnay [1]) but one might argue that any plausible candidate should abide by a constraint of closure under definability: every operator which is definable in a language L whose logical constants are interpreted by S-invariant operators should be S-invariant. If L is a logic, being generated by a similarity relation closed under definability amounts to a kind of functional completeness of L with respect to a target notion of logicality. On the other hand we can define alethic extensions of a given model-theoretic logic L as the logics that one may obtain from L by adding to it the expressive power of an interpreted Tarskian truth predicate. We say that a logic L is truth-complete if every class of structures which is elementary (i.e., definable by one sentence) in an alethic extension of L is elementary in L. Eventually, we prove the following: a logic is truth complete if and only if it is generated by a similarity relation which is closed under definability.

Mots clés: philosophy of science

Domaines: Histoire, Philosophie et Sociologie des sciences

Henri Galinon, Denis Bonnay, Julien Boyer. Truth, Logic and Invariance. Logic Colloquium '08 (2008 European summer meeting of the Association for Symbolic Logic), Jul 2008, Bern, Suisse. ⟨halshs-00792019⟩