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Negation in Logic and in Natural Language

Jaakko Hintikka
Linguistics and Philosophy
Vol. 25, No. 5/6 (Dec., 2002), pp. 585-600
Published by: Springer
Stable URL: http://www.jstor.org/stable/25001865
Page Count: 16
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Negation in Logic and in Natural Language
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Abstract

In game-theoretical semantics, perfectly classical rules yield a strong negation that violates tertium non datur when informational independence is allowed. Contradictory negation can be introduced only by a metalogical stipulation, not by game rules. Accordingly, it may occur (without further stipulations) only sentence-initially. The resulting logic (extended independence-friendly logic) explains several regularities in natural languages, e.g., why contradictory negation is a barrier to anaphase. In natural language, contradictory negation sometimes occurs nevertheless witin the scope of a quantifier. Such sentences require a secondary interpretation resembling the so-called substitutional interpretation of quantifiers. This interpretation is sometimes impossible, and it means a step beyond the normal first-order semantics, not an alternative to it.

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