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Negation in Logic and in Natural Language

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Abstract

In game-theoretical semantics, perfectlyclassical rules yield a strong negation thatviolates tertium non datur when informationalindependence is allowed. Contradictorynegation can be introduced only by a metalogicalstipulation, not by game rules. Accordingly, it mayoccur (without further stipulations) onlysentence-initially. The resulting logic (extendedindependence-friendly logic) explains several regularitiesin natural languages, e.g., why contradictory negation is abarrier to anaphase. In natural language, contradictory negationsometimes occurs nevertheless witin the scope of aquantifier. Such sentences require a secondary interpretationresembling the so-called substitutionalinterpretation of quantifiers.This interpretation is sometimes impossible,and it means a step beyond thenormal first-order semantics, not an alternative to it.

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  1. Department of Philosophy, Boston University, 745 Commonwealth Avenue, Boston, Massachusets, 02215

    Jaakko Hintikka

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  1. Jaakko Hintikka
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Hintikka, J. Negation in Logic and in Natural Language. Linguistics and Philosophy 25, 585–600 (2002). https://doi.org/10.1023/A:1020895229197

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