Canadian Journal of Philosophy 30 (1):55--84 (2000)
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Abstract |
Alberto Casullo ("Necessity, Certainty, and the A Priori", Canadian Journal of Philosophy 18, 1988) argues that arithmetical propositions could be disconfirmed by appeal to an invented scenario, wherein our standard counting procedures indicate that 2 + 2 != 4. Our best response to such a scenario would be, Casullo suggests, to accept the results of the counting procedures, and give up standard arithmetic. While Casullo's scenario avoids arguments against previous "disconfirming" scenarios, it founders on the assumption, common to scenario and response, that arithmetic might be independent of standard counting procedures. Here I show, by attention to tallying as the simplest form of counting, that this assumption is incoherent: given standard counting procedures, then (on pain of irrationality) arithmetical theory follows.
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Keywords | philosophy of mathematics epistemology |
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ISBN(s) | 0045-5091 |
DOI | 10.1080/00455091.2000.10717525 |
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References found in this work BETA
Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Philosophy of Mathematics.Paul Benacerraf & Hilary Putnam - 1985 - Philosophy of Science 52 (3):488-489.
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Citations of this work BETA
Fundamental Properties of Fundamental Properties.M. Eddon - 2013 - In Karen Bennett Dean Zimmerman (ed.), Oxford Studies in Metaphysics, Volume 8. pp. 78-104.
In Defense of Countabilism.David Builes & Jessica M. Wilson - forthcoming - Philosophical Studies:1-38.
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