Logical Pluralism and Logical Form

Gillman Payette, Nicole Wyatt

Abstract


Disputes about logic are commonplace and undeniable. It is sometimes argued that these disputes are not genuine disagreements, but are rather merely verbal ones. Are advocates of different logics simply talking past each other? In this paper we argue that pluralists (and anyone who sees competing logics as genuine rivals), should reject the claim that real disagreement requires competing logics to assign the same meaning to logical connectives, or the same logical form to arguments. Along the way we argue that ascriptions of logical form, as well as connective meaning, are always theory-relative.


References


Baaz, M., Fermüller, C. G. and Zach, R. (1993), Systematic construction of nat- ural deduction systems for many-valued logics, in ‘Proceedings of the 23rd International Symposium on Multiple-Valued Logic’, IEEE Press, pp. 208–13.

Béziau, J.-Y., ed. (2007), Logica Universalis: Toward a General Theory of Logic, 2 edn, Birkhauser Verlag, Basel.

Cargile, J. (2010), Logical form, in J. Lear and A. Oliver, eds, ‘The Force of Argu- ment: Essays in Honour of Timothy Smiley’, Routledge Studies in Contem- porary Philosophy, Routledge, New York, chapter 3, pp. 48–67.

Church, A. (1956), Introduction to Mathematical Logic, 1 edn, Princeton University Press, Princeton, NJ.

Cook, R. T. (2010), ‘Let a thousand flowers bloom: a tour of logical pluralism’, Philosophy Compass 5/6, 492–504.

Dummett, M. (1991), The Logical Basis of Metaphysics, Harvard University Press, Cambridge, MA.

Dutilh Novaes, C. (2011), ‘The different ways in which logic is (said to be) formal’, History and Philosophy of Logic 32(4), 303–332.

Etchemendy, J. (1990), The Concept of Logical Consequence, Harvard University Press, Cambridge, MA.

Field, H. (2008), Saving Truth From Paradox, Oxford University Press, Oxford, UK.

Frege, G. (1952/1980), Begriffsschift (Chapter I) 1879, 3 edn, Basil Blackwell and Rowman and Littlefield, New Jersey, chapter 1, pp. 1–20. 1988 reprint by Barnes and Noble.

Haack, S. (1978), Philosophy of Logics, Cambridge University Press, Cambridge, UK.

Hjortland, O. (2013), ‘Logical pluralism, meaning-variance, and verbal disputes’, Australasian Journal of Philosophy 91(2), 355–73.

Jenkins, C. S. I. (2014), ‘Merely verbal disputes’, Erkenntnis 79, 11–30.

Keenan, E. (1979), ‘On surface form and logical form’, Studies in Linguistic Science 8(2), 163–204.

Paoli, F. (2003), ‘Quine and Slater on paraconsistency and deviance’, Journal of Philosophical Logic 32(5), 531–548.

URL: http://dx.doi.org/10.1023/A:1025648722188

Paoli, F. (2007), ‘Implicational paradoxes and the meaning of logical constants’, Australasian Journal of Philosophy 85(4), 553–579.

URL: http://dx.doi.org/10.1080/00048400701728574

Payette, G. and Schotch, P. K. (2007), ‘On preserving’, Logica Universalis 1(2), 295–310.

Payette, G. and Wyatt, N. (forthcoming), ‘How do logics explain?’, Australasian Journal of Philosophy 0(0), 1–11.

URL: http://dx.doi.org/10.1080/00048402.2017.1342674

Priest, G. (2014), Revising logic, in P. Rush, ed., ‘The Metaphysics of Logic’, Cambridge University Press, pp. 211–223. Cambridge Books Online.

URL: http://dx.doi.org/10.1017/CBO9781139626279.016

Putnam, H. (1979), The Logic of Quantum Mechanics, 2 edn, Cambridge Univer- sity Press, Cambridge, UK, pp. 174–197.

Quine, W. V. O. (1986), Philosophy of Logic, 2 edn, Harvard University Press, Cambridge, MA.

Restall, G. (2002), ‘Carnap’s tolerance, language change, and logical pluralism’, Journal of Philosophy 99(8), 426–43.

Restall, G. (2014), ‘Pluralism and proofs’, Erkenntnis 79, 279–291.

Russell, B. (1905), ‘On denoting’, Mind 114(456), 479–493.

Sagi, G. (2014), ‘Formality in logic: From logical terms to semantic constraints’, Logique et Analyese 57(227), 259–76.


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