Graduate studies at Western
Synthese 153 (1):105 - 159 (2006)
|Abstract||On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria depend on the methods of inference the proofs employ, and that standard models of formal deduction are not well-equipped to support such evaluations. I discuss a model of proof that is used in the automated deduction community, and show that this model does better in that respect|
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
|Through your library||Configure|
Similar books and articles
David S. Henley (1995). Syntax-Directed Discovery in Mathematics. Erkenntnis 43 (2):241 - 259.
Bernhard Weiss (1997). Proof and Canonical Proof. Synthese 113 (2):265-284.
Francis Jeffry Pelletier (1998). Automated Natural Deduction in Thinker. Studia Logica 60 (1):3-43.
Konstantine Arkoudas & Selmer Bringsjord (2007). Computers, Justification, and Mathematical Knowledge. Minds and Machines 17 (2):185-202.
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.
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.
Mateja Jamnik, Alan Bundy & Ian Green (1999). On Automating Diagrammatic Proofs of Arithmetic Arguments. Journal of Logic, Language and Information 8 (3):297-321.
Added to index2009-01-28
Total downloads15 ( #86,079 of 739,207 )
Recent downloads (6 months)1 ( #61,778 of 739,207 )
How can I increase my downloads?