Against the Judgment-Dependence of Mathematics and Logic |
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Authors: | Alexander Paseau |
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Institution: | (1) Wadham College, Oxford, OX1 3PN, UK |
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Abstract: | 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. |
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Keywords: | |
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