Philosophia Scientiae 9 (2):295-304 (2005)

Denis Bonnay
Université Paris Nanterre
Hintikka and Sandu have developed IF logic as a genuine alternative to classical first-order logic : liberalizing dependence schemas between quantifiers, IF would carry out all the ideas already underlying classical logic. But they are alternatives to Hintikka’s game-theoretic approach; one could use instead Henkin quantifiers. We will present here some arguments of both technical and philosophical nature in favor of IF. We will show that its notion of independence, once extended to connectives, can indeed claim to be fully general, and that IF logic provides an analysis of independence patterns. This last point will be argued for thanks to an explanation of the epistemic content of IF, through a partial translation into modal logic.RésuméLa logique IF prétend constituer une alternative à la logique classique du premier ordre : en libéralisant les schémas de dépendance entre quantificateurs, elle mènerait à leur terme les idées sous-jacentes à la logique classique. Mais les jeux de Hintikka ne constituent pas la seule manière possible de fournir une sémantique pour l’indépendance : on pourrait au contraire vouloir le faire dans le cadre d’une sémantique récursive avec des quantificateurs de Henkin. Nous présentons ici quelques arguments techniques et philosophiques en faveur de IF, en montrant pourquoi son concept d’indépendance, élargi aux connecteurs, peut prétendre être pleinement général, et en montrant en quel sens la logique IF traite l’indépendance de manière analytique. Ce dernier point est réalisé à travers une explicitation du contenu épistémique de IF, sous la forme d’une traduction partielle dans la logique modale
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DOI 10.4000/philosophiascientiae.547
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