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EXCEPTIONAL LOGIC

Published online by Cambridge University Press:  21 July 2020

BRUNO WHITTLE*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF WISCONSIN–MADISON MADISON, WI 53706, USA E-mail: bwhittle@wisc.edu

Abstract

The aim of the paper is to argue that all—or almost all—logical rules have exceptions. In particular, it is argued that this is a moral that we should draw from the semantic paradoxes. The idea that we should respond to the paradoxes by revising logic in some way is familiar. But previous proposals advocate the replacement of classical logic with some alternative logic. That is, some alternative system of rules, where it is taken for granted that these hold without exception. The present proposal is quite different. According to this, there is no such alternative logic. Rather, classical logic retains the status of the ‘one true logic’, but this status must be reconceived so as to be compatible with (almost) all of its rules admitting of exceptions. This would seem to have significant repercussions for a range of widely held views about logic: e.g., that it is a priori, or that it is necessary. Indeed, if the arguments of the paper succeed, then such views must be given up.

Type
Research Article
Copyright
© Association for Symbolic Logic, 2020

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References

Barwise, J., & Etchemendy, J. (1987). The Liar: An Essay on Truth and Circularity. Oxford: Oxford University Press.Google Scholar
Beall, J. (2009). Spandrels of Truth. Oxford: Clarendon Press.CrossRefGoogle Scholar
Burge, T. (1979). Semantical paradox. Journal of Philosophy, 76, 169198.CrossRefGoogle Scholar
Field, H. (2008). Saving Truth from Paradox. Oxford: Oxford University Press.CrossRefGoogle Scholar
Gaifman, H. (1992). Pointers to truth. Journal of Philosophy, 89, 223261.CrossRefGoogle Scholar
Gaifman, H. (2000). Pointers to propositions. In Chapuis, A., & Gupta, A., editors. Circularity, Definition, and Truth. New Delhi, India: Indian Council of Philosophical Research, pp. 79121.Google Scholar
Glanzberg, M. (2001). The liar in context. Philosophical Studies, 103, 217251.CrossRefGoogle Scholar
Gupta, A. (2001). Truth. In Goble, L., editor. The Blackwell Guide to Philosophical Logic. Oxford: Blackwell, pp. 90114.Google Scholar
Hansen, C. S. (2014). Grounded ungroundedness. Inquiry, 57, 216243.CrossRefGoogle Scholar
Hofweber, T. (2008). Validity, paradox and the ideal of deductive logic. In Beall, J., editor. Revenge of the Liar: New Essays on the Paradox . Oxford: Oxford University Press, pp. 145158.Google Scholar
Hofweber, T. (2010). Inferential role and the ideal of deductive logic. The Baltic International Yearbook of Cognition , Logic and Communication, 5, pp. 126.Google Scholar
Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690716.CrossRefGoogle Scholar
Maudlin, T. (2004). Truth and Paradox: Solving the Riddles. Oxford: Clarendon Press.CrossRefGoogle Scholar
Parsons, C. (1974). The liar paradox. Journal of Philosophical Logic, 3, 381412.CrossRefGoogle Scholar
Priest, G. (2006). In Contradiction. Oxford: Clarendon Press.CrossRefGoogle Scholar
Simmons, K. (1993). Universality and the Liar: An Essay on Truth and the Diagonal Argument. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Skyrms, B. (1984). Intensional aspects of self-reference. In Martin, R. L., editor. Recent Essays on Truth and the Liar Paradox. Oxford: Clarendon Press, pp. 119131.Google Scholar
Soames, S. (1999). Understanding Truth. Oxford: Oxford University Press.CrossRefGoogle Scholar
Szabó, Z. G. (2017). Compositionality. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy. Summer 2017 edition. http://plato.stanford.edu/archives/sum2017/entries/compositionalityplato.stanford.edu/archives/.Google Scholar
Whittle, B. (2017). Self-referential propositions. Synthese, 194, 50235037.CrossRefGoogle Scholar
Yablo, S. (1993). Paradox without self-reference. Analysis, 53, 251252.CrossRefGoogle Scholar

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