Problemas para a Explicação Matemática

Problemas para a Explicação Matemática

Tags:

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

Notes:

• 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.