Inferential Role and the Ideal of Deductive Logic

Abstract

Although there is a prima facie strong case for a close connection between the meaning and inferential role of certain expressions, this connection seems seriously threatened by the semantic and logical paradoxes which rely on these inferential roles. Some philosophers have drawn radical conclusions from the paradoxes for the theory of meaning in general, and for which sentences in our language are true. I criticize these overreactions, and instead propose to distinguish two conceptions of inferential role. This distinction is closely tied to two conceptions of deductive logic, and it is the key, I argue, for understanding first the connection between meaning and inferential role, and second what the paradoxes show more generally.

References

Armour-Garb, B. 2007. ‘Consistent inconsistency theories’. Inquiry 50(6): 639–654.

Azzouni, J. 2006. Tracking Reason: proof, consequence and truth. Oxford University Press.

Azzouni, J. 2007. ‘The inconsistency of natural languages: how to live with it’. Inquiry 50(6): 590–605.
http://dx.doi.org/10.1080/00201740701698530

Beall, J. (ed.). 2007. Revenge of the Liar: New Essays on the Paradox. Oxford University Press.

Bueno, O. 2007. ‘Troubles with trivialism’. Inquiry 50(6): 655–667.
http://dx.doi.org/10.1080/00201740701698670

Eklund, M. 2002. ‘Inconsistent languages’. Philosophy and Phenomenological Research 64(2): 251–276.
http://dx.doi.org/10.1111/j.1933-1592.2002.tb00001.x

Field, H. (ed.). 2008. Saving truth from paradox. Oxford University Press.

Hofweber, T. ‘The ideal of deductive logic’. Unpublished manuscript.

Hofweber, T. 2008. ‘Validity, paradox, and the ideal of deductive logic’. In J. Beall (ed.) ‘Revenge of the Liar: New Essays on the Paradox’, 145–158. Oxford University Press.

Patterson, D. 2008. ‘Understanding the liar’. In J. Beall (ed.) ‘Revenge of the Liar: New Essays on the Paradox’, Oxford University Press.

Patterson, D. 2009. ‘Inconsistency theory of semantic paradox’. Philosophy and Phenomenological Research LXXIX(2): 387–422.
http://dx.doi.org/10.1111/j.1933-1592.2009.00283.x

Pettit, D. 2002. ‘Why knowledge is unnecessary for understanding language’. Mind 111: 519–550.
http://dx.doi.org/10.1093/mind/111.443.519

Priest, G. 1979. ‘The logic of paradox’. The Journal of Philosophical Logic 8: 219–241.

Scharp, K. 2007. ‘Replacing truth’. Inquiry 50(6): 606–621.
http://dx.doi.org/10.1080/00201740701698589

Schiffer, S. (ed.). 1987. Remnants of Meaning. MIT Press.

Tarski, A. 1983. ‘The concept of truth in formalized languages’. In ‘Logic, Semantics, Metamathematics’, Hackett.