David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Canadian Journal of Philosophy 30 (1):55-84 (2000)
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. 1.
|Keywords||epistemology arithmetic empiricism counting mathematical knowledge|
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References found in this work BETA
Albert Casullo (1988). Necessity, Certainty, and the a Priori. Canadian Journal of Philosophy 18 (1):43 - 66.
D. A. T. Gasking (1940). Mathematics and the World. Australasian Journal of Psychology and Philosophy 18 (2):97-116.
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