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.
|Keywords||philosophy of mathematics epistemology|
|Categories||categorize this paper)|
References found in this work BETA
Necessity, Certainty, and the a Priori.Albert Casullo - 1988 - Canadian Journal of Philosophy 18 (1):43 - 66.
Mathematics and the World.D. A. T. Gasking - 1940 - Australasian Journal of Psychology and Philosophy 18 (2):97-116.
Citations of this work BETA
No citations found.
Similar books and articles
Models of Arithmetic and Subuniform Bounds for the Arithmetic Sets.Alistair H. Lachlan & Robert I. Soare - 1998 - Journal of Symbolic Logic 63 (1):59-72.
Theories of Arithmetics in Finite Models.M. Krynicki & K. Zdanowski - 2005 - Journal of Symbolic Logic 70 (1):1-28.
Finite Automata, Real Time Processes and Counting Problems in Bounded Arithmetics.Mirosław Kutyłowski - 1988 - Journal of Symbolic Logic 53 (1):243-258.
Quantum Mathematics.J. Michael Dunn - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Indexed Natural Numbers in Mind: A Formal Model of the Basic Mature Number Competence. [REVIEW]Wojciech Krysztofiak - 2012 - Axiomathes 22 (4):433-456.
The Significance of the Senses.Matthew Nudds - 2004 - Proceedings of the Aristotelian Society 104 (1):31-51.
Kant's Theory of Arithmetic: A Constructive Approach? [REVIEW]Kristina Engelhard & Peter Mittelstaedt - 2008 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 39 (2):245 - 271.
Added to index2009-01-28
Total downloads189 ( #21,557 of 2,132,865 )
Recent downloads (6 months)13 ( #57,171 of 2,132,865 )
How can I increase my downloads?
There are no threads in this forum
Nothing in this forum yet.