David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 113 (2):265-284 (1997)
Certain anti-realisms about mathematics are distinguished by their taking proof rather than truth as the central concept in the account of the meaning of mathematical statements. This notion of proof which is meaning determining or canonical must be distinguished from a notion of demonstration as more generally conceived. This paper raises a set of objections to Dummett's characterisation of the notion via the notion of a normalised natural deduction proof. The main complaint is that Dummett's use of normalised natural deduction proofs relies on formalisation playing a role for which it is unfit. Instead I offer an alternative account which does not rely on formalisation and go on to examine the relation of proof to canonical proof, arguing that rather than requiring an explicit characterisation of canonical proofs we need to be more aware of the complexities of that relation.
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
|Through your library||Configure|
Similar books and articles
Maria Luisa Bonet & Samuel R. Buss (1993). The Deduction Rule and Linear and Near-Linear Proof Simulations. Journal of Symbolic Logic 58 (2):688-709.
Carlo Cellucci (2008). Why Proof? What is a Proof? In Giovanna Corsi & Rossella Lupacchini (eds.), Deduction, Computation, Experiment. Exploring the Effectiveness of Proof, pp. 1-27. Springer.
James Franklin (1996). Proof in Mathematics. Quakers Hill Press.
Dag Prawitz (1965/2006). Natural Deduction: A Proof-Theoretical Study. Dover Publications.
Mathieu Marion (2009). Radical Anti-Realism, Wittgenstein and the Length of Proofs. Synthese 171 (3):419 - 432.
Paolo Gentilini (1999). Proof-Theoretic Modal PA-Completeness III: The Syntactic Proof. Studia Logica 63 (3):301-310.
Gerard Renardel de Lavalette, Barteld Kooi & Rineke Verbrugge (2008). Strong Completeness and Limited Canonicity for PDL. Journal of Logic, Language and Information 17 (1):291-292.
Andrew Aberdein (2006). Proofs and Rebuttals: Applying Stephen Toulmin's Layout of Arguments to Mathematical Proof. In Marta Bílková & Ondřej Tomala (eds.), The Logica Yearbook 2005. Filosofia. 11-23.
Added to index2009-01-28
Total downloads20 ( #70,333 of 1,004,690 )
Recent downloads (6 months)1 ( #64,743 of 1,004,690 )
How can I increase my downloads?