David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Leon Horsten (1998). In Defense of Epistemic Arithmetic. Synthese 116 (1):1-25.
Wojciech Krysztofiak (2012). Indexed Natural Numbers in Mind: A Formal Model of the Basic Mature Number Competence. [REVIEW] Axiomathes 22 (4):433-456.
Ann Dowker, Sheila Bala & Delyth Lloyd (2008). Linguistic Influences on Mathematical Development: How Important is the Transparency of the Counting System? Philosophical Psychology 21 (4):523 – 538.
C. S. Jenkins (2005). Knowledge of Arithmetic. British Journal for the Philosophy of Science 56 (4):727-747.
Mirosław Kutyłowski (1988). Finite Automata, Real Time Processes and Counting Problems in Bounded Arithmetics. Journal of Symbolic Logic 53 (1):243-258.
Gottlob Frege (1964). The Basic Laws of Arithmetic. Berkeley, University of California Press.
Emil Jeřábek (2007). Approximate Counting in Bounded Arithmetic. Journal of Symbolic Logic 72 (3):959 - 993.
Rochel Gelman (2008). Counting and Arithmetic Principles First. Behavioral and Brain Sciences 31 (6):653-654.
Emil Jeřábek (2009). Approximate Counting by Hashing in Bounded Arithmetic. Journal of Symbolic Logic 74 (3):829-860.
Jessica M. Wilson (2000). Could Experience Disconfirm the Propositions of Arithmetic? Canadian Journal of Philosophy 30 (1):55--84.
Added to index2009-01-28
Total downloads42 ( #96,229 of 1,792,259 )
Recent downloads (6 months)15 ( #53,685 of 1,792,259 )
How can I increase my downloads?