The square of opposition and the paradoxes

Logica Universalis 2 (1):87-105 (2008)
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Abstract

Can an appeal to the difference between contrary and contradictory statements, generated by a non-uniform behaviour of negation, deal adequately with paradoxical cases like the sorites or the liar? This paper offers a negative answer to the question. This is done by considering alternative ways of trying to construe and justify in a useful way (in this context) the distinction between contraries and contradictories by appealing to the behaviour of negation only. There are mainly two ways to try to do so: i) by considering differences in the scope of negation, ii) by considering the possibility that negation is semantically ambiguous. Both alternatives are shown to be inapt to handle the problematic cases. In each case, it is shown that the available alternatives for motivating or grounding the distinction, in a way useful to deal with the paradoxes, are either inapplicable, or produce new versions of the paradoxes, or both.

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Teresa Marques
Universitat de Barcelona

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References found in this work

Speaker’s Reference and Semantic Reference.Saul Kripke - 1977 - Midwest Studies in Philosophy 2 (1):255-276.
Speaker's reference and semantic reference.Saul A. Kripke - 1977 - In Peter A. French, Theodore Edward Uehling & Howard K. Wettstein (eds.), Studies in the philosophy of language. Morris: University of Minnesota, Morris. pp. 255-296.
Presupposition and the Delimitation of Semantics.R. M. Kempson - 1975 - Linguistics and Philosophy 2 (3):437-446.
On 'the denial of bivalence is absurd'.F. J. Pelletier & R. J. Stainton - 2003 - Australasian Journal of Philosophy 81 (3):369 – 382.

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