Logicality and Invariance

نویسنده

Denis Bonnay

چکیده

This paper deals with the problem of giving a principled characterization of the class of logical constants. According to the so-called Tarski-Sher thesis, an operation is logical iff it is invariant under permutation. In the model-theoretic tradition, this criterion has been widely accepted as giving a necessary condition for an operation to be logical. But it has been also widely criticized on the account that it counts too many operations as logical, failing thus to provide a sufficient condition. Our aim is to solve this problem of overgeneration by modifying the invariance criterion. We introduce a general notion of invariance under a similarity relation and present the connection between similarity relations and classes of invariant operations. The next task is to isolate a similarity relation well-suited for a definition of logicality. We argue that the standard arguments in favor of invariance under permutation, which rely on the generality and the formality of logic, should be modified. The revised arguments are shown to support an alternative to Tarski’s criterion, according to which an operation is logical iff it is invariant under potential isomorphism. ∗I wish to thank the following for helpful discussions: Johan van Benthem, Serge Bozon, Mikaël Cozic, Jacques Dubucs, Paul Égré, Solomon Feferman, Henri Galinon, John MacFarlane, Gabriel Sandu, Philippe Schlenker, Gila Sher, Jouko Väänänen and Dag Westerståhl. Special thanks to Johan van Benthem, Serge Bozon and Solomon Feferman for very fruitful suggestions. †Département d’Études Cognitives & IHPST, École Normale Supérieure, 29, rue d’Ulm, 75005 Paris, FRANCE. [email protected]

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