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Abstract

Kripke’s version of Wittgenstein’s rule-following paradox has been influential. My concern is with how it—and Wittgenstein’s views more generally—have been perceived as undercutting the individualistic picture of mathematical practice: the view that individuals—Robinson Crusoes—can, entirely independently of a community, engage in cogent mathematics, and indeed (more generally) have “private languages.” What has been denied is that phrases like “correctly counting” can be applied to such individuals because these normative notions (so the Wittgensteinian analysis is taken to show) can only be applied cogently in a context involving community standards. I attempt to show that this shocking corollary doesn’t follow even if Kripke’s Wittgensteinian objections to dispositional approaches to rule-following are largely right. My reason for claiming this is that there is another (“sceptical”) solution to the rule-following paradox, one that doesn’t favor community standards over individual ones. Furthermore, it doesn’t replace truth conditions with assertability conditions; and this latter maneuver is essential to Kripke’s sceptical solution favoring the community over the individual.

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This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

References

Azzouni, Jody. 1994. Metaphysical myths, mathematical practice: The epistemology and ontology of the exact sciences. Cambridge: Cambridge University Press.
http://dx.doi.org/10.1017/CBO9780511551291

Azzouni, Jody. 2000. Knowledge and reference in empirical science. London: Routledge.

Azzouni, Jody. 2006. Tracking reason: Proof, consequence and truth. Oxford: Oxford University Press.

Azzouni, Jody. forthcoming(a). ‘Deflationist truth’. In Michael Glanzberg (ed.) ‘Handbook on Truth’, London: Blackwell.

Azzouni, Jody. forthcoming(b). Talking about nothing: Numbers, hallucinations and fictions. Oxford: Oxford University Press.

Butterworth, Brian. 1999. The mathematical brain. London: Papermac.

Carey, Susan. 2009. ‘Where our number concepts come from’. Journal of Philosophy 106, no. 4: 220–254.

Gelman, R. & Galistel, C. R. 1986. The child’s understanding of number. Cambridge: Harvard University Press. (originally published in 1978).

Goldfarb, Warren. 1992. ‘Wittgenstein on understanding’. Midwest studies in philosophy 17: 109–122.
http://dx.doi.org/10.1111/j.1475-4975.1992.tb00145.x

Kripke, Saul. 1982. Wittgenstein on rules and private language. Cambridge, Mass.: Harvard University Press.

Lewis, David. 1983. ‘New work for a theory of universals’. In ‘Papers in Metaphysics and Epistemology (1999)’, 56–77. Cambridge: Cambridge University Press.
http://dx.doi.org/10.1017/CBO9780511625343.003

Mandler, G. & Shebo, B. J. 1982. ‘Subilizing: An analysis of its component processes’. Journal of Experimental Psychology: General 11–22.

McDowell, John. 1984. ‘Wittgenstein on following a rule’. Synthese 58: 325–63.
http://dx.doi.org/10.1007/BF00485246

Putnam, Hilary. 1981. Reason, truth and history. Cambridge: Cambridge University Press.

Rosch, E. & Mervis, C. B. 1975. ‘Family resemblances: Studies in the internal structure of categories’. Cognitive Psychology 7: 573–605.
http://dx.doi.org/10.1016/0010-0285(75)90024-9

Rosch, E., Gray, W. D., Johnson, D. M. & Boyes-Braem, P. 1976. ‘Basic objects in natural categories’. Cognitive Psychology 8: 382–439.
http://dx.doi.org/10.1016/0010-0285(76)90013-X

Sider, Theodore. 2009. ‘Ontological realism’. In Chalmers, Manley & Wasserman (eds.) ‘Metametaphysics: New essays on the foundations of ontology’, 384–423. Oxford: Oxford University Press.

Wittgenstein, Ludwig. 1956. Remarks on the foundations of mathematics. Oxford: Basil Blackwell.

Wittgenstein, Ludwig. 1958. Philosophical investigations. Third ed. New York: The Macmillan Company.(trans. G.E.M. Anscombe).

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