Mathematical Proof – Argumentation or Derivation? – Part II
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Nov 19, 2011
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Abstract
In the first part of the paper, Azzouni’s derivation–indicator view was presented. In the second part it is analyzed in a detailed way. It is shown, that many problems arise, which cannot be explained in a satisfactory way in Azzouni’s theory, in particular the problem of the explanatory role of proof, of its epistemic role; the relationship between first–order and second–order versions of proofs is also not clear. It is concluded, that Azzouni’s theory does not provide a satisfactory account of mathematical proof, but inspires an interesting discussion. In the article, some of the mentioned problems are discussed.
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Wójtowicz, K. (2011). Mathematical Proof – Argumentation or Derivation? – Part II. Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce), (49), 81–97. Retrieved from https://zfn.edu.pl/index.php/zfn/article/view/121
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References
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Boolos G., [1987] “A curious inference”, Journal of Philosophical Logic, 16, 1 -12
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Mancosu P., [2001] “Mathematical Explanation: problems and prospects”, Topoi , 20, pp. 97–117.
Rav Y., [1999] „Why do we prove theorems?” Philosophia Mathematica, 7, 1999, 5-41
Rav Y., [2007] “A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians’ Proof Practices”, Philosophia Mathematica (III) 15, 291–320.
Rota G.C., [1997] “The phenomenology of mathematical proof”, Synthese, 111, 183-196
Stannett. M., [2006] “The case for hypercomputation”, Applied Mathematics and Computation, 178, 8-24
Tymoczko T., [1979] „The four-color problem and its philosophical significance”, The Journal of Philosophy, 76 (2), 57-83.,
Wójtowicz K., [2011] „Dowód matematyczny - argumentacja czy derywacja? (I)”, Zagadnienia Filozoficzne w Nauce
Boolos G., [1987] “A curious inference”, Journal of Philosophical Logic, 16, 1 -12
Brown J., [1999] Philosophy of Mathematics. An Introduction to the World of Proofs and Pictures. Routledge, New York.
Copeland B.J., [2002] “Hypercomputation”, Minds and Machines, 12, 461-502
Ketland J., [2005] „Some More Curious Inferences” Analysis 65 (285), 18–24.
Mancosu P., [2001] “Mathematical Explanation: problems and prospects”, Topoi , 20, pp. 97–117.
Rav Y., [1999] „Why do we prove theorems?” Philosophia Mathematica, 7, 1999, 5-41
Rav Y., [2007] “A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians’ Proof Practices”, Philosophia Mathematica (III) 15, 291–320.
Rota G.C., [1997] “The phenomenology of mathematical proof”, Synthese, 111, 183-196
Stannett. M., [2006] “The case for hypercomputation”, Applied Mathematics and Computation, 178, 8-24
Tymoczko T., [1979] „The four-color problem and its philosophical significance”, The Journal of Philosophy, 76 (2), 57-83.,
Wójtowicz K., [2011] „Dowód matematyczny - argumentacja czy derywacja? (I)”, Zagadnienia Filozoficzne w Nauce