Against the Judgment-Dependence of Mathematics and Logic
- 98 Downloads
Although the case for the judgment-dependence of many other domains has been pored over, surprisingly little attention has been paid to mathematics and logic. This paper presents two dilemmas for a judgment-dependent account of these areas. First, the extensionality-substantiality dilemma: in each case, either the judgment-dependent account is extensionally inadequate or it cannot meet the substantiality condition (roughly: non-vacuous specification). Second, the extensionality-extremality dilemma: in each case, either the judgment-dependent account is extensionally inadequate or it cannot meet the extremality condition (roughly: absence of independent explanation). The paper concludes with a moral concerning the judgment-dependence of a posteriori areas of discourse that emerges from consideration of these two a priori cases.
This paper was written in 2005 under the welcoming roof of the New York Public Library. I am grateful to audiences at the 2005 Bristol Logic Colloquium, the Oxford Philosophy of Mathematics Seminar and the Oxford Philosophical Society for subsequent discussion, and to Mark Sprevak and Ralph Wedgwood for comments.
- Boolos, G., Burgess, J. P., & Jeffrey, R. (2007). Computability and logic (5th ed.). New York: Cambridge University Press.Google Scholar
- Gödel, K. (1946). Remarks before the Princeton bicentennial conference on problems in mathematics. In S. Feferman, et al. (Eds.), Collected works, Vol. 2 (pp. 150–153). Oxford: Oxford University Press.Google Scholar
- Johnston, M. (1989). Dispositional theories of value. Proceedings of the Aristotelian Society Supplementary, 63, 139–174.Google Scholar
- Johnston, M. (1993). Objectivity refigured: Pragmatism without verificationism. In J. Haldane & C. Wright (Eds.), Reality, representation and projection (pp. 85–130). Oxford: Oxford University Press.Google Scholar
- McDowell, J. (1985). Values and secondary qualities. In T. Honderich (Ed.), Morality and objectivity (pp. 110–129). London: Routledge.Google Scholar
- Pettit, P. (1991). Realism and response-dependence. Mind, 100, 587–626.Google Scholar
- Shapiro, S. (1991). Foundations without foundationalism. Oxford: Clarendon Press.Google Scholar
- Tarski, A. (1951). A decision method for elementary algebra and geometry (2nd ed.). Berkeley and Los Angeles: University of California Press.Google Scholar
- Wright, C. (1992). Truth and objectivity. Cambridge, MA: Harvard University Press.Google Scholar
- Wright, C. (1993). Realism: the contemporary debate: W(h)ither now? In J. Haldane & C. Wright (Eds.), Reality, representation and projection (pp. 63–84). Oxford: Oxford University Press.Google Scholar