Could experience disconfirm the propositions of arithmetic?
Canadian Journal of Philosophy 30 (1):55--84 (2000)
| 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. | |||||||||
| Keywords | philosophy of mathematics epistemology | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,705 |
| External links |
  Try with proxy. |
| Through your library | Configure |
Similar books and articlesAlistair H. Lachlan & Robert I. Soare (1998). Models of Arithmetic and Subuniform Bounds for the Arithmetic Sets. Journal of Symbolic Logic 63 (1):59-72.
M. Krynicki & K. Zdanowski (2005). Theories of Arithmetics in Finite Models. Journal of Symbolic Logic 70 (1):1-28.
Mirosław Kutyłowski (1988). Finite Automata, Real Time Processes and Counting Problems in Bounded Arithmetics. Journal of Symbolic Logic 53 (1):243-258.
J. Michael Dunn (1980). Quantum Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Charles Sayward (2005). Why Axiomatize Arithmetic? Sorites 16:54-61.
Wojciech Krysztofiak (2012). Indexed Natural Numbers in Mind: A Formal Model of the Basic Mature Number Competence. Axiomathes 22 (4):433-456.
Matthew Nudds (2004). The Significance of the Senses. Proceedings of the Aristotelian Society 104 (1):31-51.
Kristina Engelhard & Peter Mittelstaedt (2008). Kant's Theory of Arithmetic: A Constructive Approach? Journal for General Philosophy of Science 39 (2):245 - 271.
C. S. Jenkins (2005). Knowledge of Arithmetic. British Journal for the Philosophy of Science 56 (4):727-747.
Jessica M. Wilson (2000). Could Experience Disconfirm the Propositions of Arithmetic? Canadian Journal of Philosophy 30 (1):55-84.
Analytics
Monthly downloads |
Added to index2009-03-14Total downloads69 ( #12,635 of 549,316 )Recent downloads (6 months)1 ( #63,397 of 549,316 )How can I increase my downloads? |
My notes
Discussion
