Apostolado da Oração


Problemas para a Explicação Matemática

Problemas para a Explicação Matemática

Eduardo Castro, “Problemas para a Explicação Matemática,” Revista Portuguesa de Filosofia 73, no. 3–4 (2017): 1437–62, DOI 10.17990/RPF/2017_73_3_1437.

Mais detalhes

À venda À venda!
10,00 €


Disponível apenas on-line

Problemas para a Explicação Matemática

Type Journal Article
Author Eduardo Castro
Rights © 2018 Aletheia - Associação Científica e Cultural | © 2018 Revista Portuguesa de Filosofia
Volume 73
Issue 3-4
Pages 1437-1462
Publication Revista Portuguesa de Filosofia
ISSN 0870-5283; 2183-461X
Date 2017
DOI 10.17990/RPF/2017_73_3_1437
Language Portuguese
Abstract Mathematical proofs aim to establish the truth of mathematical propositions by means of logical rules. Some recent literature in philosophy of mathematics alleges that some mathematical proofs also reveal why the proved mathematical propositions are true. These mathematical proofs are called explanatory mathematical proofs. In this paper, I present and discuss some salient problems around mathematical explanation: the existence problem, the normative problem, the explanandum problems of truth value and psychological value, the logical structure problem, the regress problem and the modelling problem. At the end, I sum up two contemporary models for mathematical explanation – the deductive-nomological model and the model of Steiner. I analyse these models against the previous problems.
Date Added 17/01/2018, 17:51:14
Modified 18/01/2018, 10:41:58


  • explanation,
  • logic,
  • mathematics,
  • models,
  • proof,
  • Science


  • Aristotle. The Complete Works of Aristotle the Revised Oxford Translation. Edited by Jonathan Barnes. Princeton, NJ: Princeton University Press, 1984.
    Armstrong, David. What Is a Law of Nature? Cambridge: Cambridge University Press, 1983.
    Avigad, Jeremy. ‘Mathematical Method and Proof’. Synthese 153, no. 1 (2006): 105–59. doi:10.1007/s11229-005-4064-5.
    Baker, Alan. ‘Are There Genuine Mathematical Explanations of Physical Phenomena?’ Mind 114, no. 454 (2005): 223–38. doi:10.1093/mind/fzi223.
    Burgess, John. Rigor and Structure. Oxford: Oxford University Press, 2015.
    Colyvan, Mark. An Introduction to the Philosophy of Mathematics. Cambridge: Cambridge University Press, 2012.
    Colyvan, Mark. The Indispensability of Mathematics. New York: Oxford University Press, 2001.
    Dennett, Daniel. ‘Higher-Order Truths about Chmess’. Topoi 25, no. 1–2 (2006): 39–41. doi:10.1007/s11245-006-0005-2.
    Ellis, Brian. Scientific Essentialism. Cambridge: Cambridge University Press, 2001.
    Fraassen, Bas van. Laws and Symmetry. Oxford: Oxford University Press, 1989.
    Fraassen, Bas van. The Scientific Image. New York: Oxford University Press, 1980.
    Frege, Gottlob. Der Grundlagen Die Arithmetik. Breslau: W. Koebner, 1884.
    Frege, Gottlob. Grundgesetze Der Arithmetik. Vol. 1. Jena: Pohle, 1893.
    Gale, David. ‘Proof as Explanation, Letters to the Editor’. Mathematical Intelligencer 12, no. 1 (1990): 4.
    Hanna, Gila. ‘Some Pedagogical Aspects of Proof’. Interchange 21, no. 1 (1990): 6–13. doi:10.1007/BF01809605.
    Hempel, Carl. Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. New York: The Free Press, 1965.
    Kitcher, Philip. ‘Bolzano’s Ideal of Algebraic Analysis’. Studies in History and Philosophy of Science Part A 6, no. 3 (1975): 229–69. doi:10.1016/0039-3681(75)90024-2.
    Lange, Marc. ‘Aspects of Mathematical Explanation: Symmetry, Unity, and Salience’. Philosophical Review 123, no. 4 (2014): 485–531. doi:10.1215/00318108-2749730.
    Lange, Marc. ‘Depth and Explanation in Mathematics’. Philosophia Mathematica 23, no. 2 (2015): 196–214. doi:10.1093/philmat/nku022.
    Lange, Marc. ‘Why Proofs by Mathematical Induction Are Generally Not Explanatory’. Analysis 69, no. 2 (2009): 203–11. doi:10.1093/analys/anp002.
    Maddy, Penelope. ‘Naturalizing Mathematical Methodology’. In The Philosophy of Mathematics Today, edited by Matthias Schirn, 175–93. Oxford: Clarendon Press, 1998.
    Maddy, Penelope. ‘Three Forms of Naturalism’. In The Oxford Handbook of Philosophy of Mathematics and Logic, edited by Stewart Shapiro, 437–59. New York: Oxford University Press, 2005.
    Mancosu, Paolo. ‘Mathematical Explanation: Problems and Prospects’. Topoi 20, no. 1 (2001): 97–117. doi:10.1023/A:1010621314372.
    Mancosu, Paolo, and Johannes Hafner. ‘The Varieties of Mathematical Explanation’. In Visualization, Explanation and Reasoning Styles in Mathematics, edited by Paolo Mancosu, Klaus Frovin Jørgensen, and Stig Andur Pedersen, 215–50. Springer Science & Business Media, 2006.
    Molinini, Daniele. ‘Deductive Nomological Model and Mathematics: Making Dissatisfaction More Satisfactory’. THEORIA. An International Journal for Theory, History and Foundations of Science 29, no. 2 (2014): 223. doi:10.1387/theoria.6464.
    Nicole, Pierre, and Antoine Arnauld. Logic; or the Art of Thinking. London: William Taylor, 1717.
    Quine, Willard. ‘Five Milestones of Empiricism’. In Theories and Things, 67–72. Cambridge, MA: Harvard University Press, 1981.
    Salmon, Wesley. Four Decades of Scientific Explanation. Pittsburgh: University of Pittsburgh Press, 1989.
    Sandborg, David. ‘Mathematical Explanation and the Theory of Why-Questions’. The British Journal for the Philosophy of Science 49, no. 4 (1998): 603–24. doi:10.1093/bjps/49.4.603.
    Steiner, Mark. ‘Mathematical Explanation’. Philosophical Studies 34, no. 2 (1978): 135–151. doi:10.1007/BF00354494.
    Weber, Erik, and Joachim Frans. ‘Is Mathematics a Domain for Philosophers of Explanation?’ Journal for General Philosophy of Science 48, no. 1 (2017): 125–42. doi:10.1007/s10838-016-9332-1.
    Zelcer, Mark. ‘Against Mathematical Explanation’. Journal for General Philosophy of Science 44, no. 1 (2013): 173–92. doi:10.1007/s10838-013-9216-6.


Sem produtos

Envio 0,00 €
Total 0,00 €

Carrinho Encomendar