Naturalizing the Applicability of Mathematics

Journal title PARADIGMI
Author/s Carlo Cellucci
Publishing Year 2015 Issue 2015/2
Language Italian Pages 20 P. 25-44 File size 90 KB
DOI 10.3280/PARA2015-002004
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In order to deal with the question of the applicability of mathematics to the world, this article distinguishes between natural mathematics, that is, innate mathematics, and artificial mathematics, that is, mathematics as a discipline. It argues that natural mathematics is applicable to the world because the systems of core knowledge upon which it is based, being a result of biological evolution, fit in certain mathematical properties of the world. On the other hand, the basis for the applicability of artificial mathematics to the world is Galileo’s philosophical revolution, the decision to confine physics to the study of some properties of the world mathematical in character. But, like the applicability of natural mathematics, also the applicability of artificial mathematics depends on our makeup, and hence ultimately on biological evolution.

Keywords: Applicability, conceptualizations, evolution, mathematics, simplicity

  1. Abbott D. (2013). The Reasonable Ineffectiveness of Mathematics. Proceedings of the IEEE, 101: 2147-2153.
  2. Atiyah M. (1995). Creation v Discovery. Times Higher Education Supplement, 29 September.
  3. Bueno O. and Colyvan M. (2011). An Inferential Conception of the Application of Mathematics. Noûs, 45: 345-374.
  4. Bueno I. and French S. (2012). Can Mathematics Explain Physical Phenomena? The British Journal for the Philosophy of Science, 63: 85-113.
  5. Cellucci C. (2013). Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method. Berlin: Springer.
  6. Colyvan M. (2012). An Introduction to the Philosophy of Mathematics. Cambridge: Cambridge University Press.
  7. De Cruz H. (2008). An Extended Mind Perspective on Natural Number Representation. Philosophical Psychology, 21: 475-490.
  8. De Cruz H. and De Smedt J. (2013). Mathematical Symbols as Epistemic Actions. Synthese, 190: 3-19.
  9. Diels H.A. and Krantz W. (1964). Die Fragmente der Vorsokratiker. Berlin: Weidmann.
  10. Dirac P.A.M. (1963). The Evolution of the Physicists’ Picture of Nature. Scientific American, 208, 5: 43-53.
  11. Dirac P.A.M. (1978). Directions in Physics. New York: Wiley.
  12. Galilei G. (1968). Opere, a cura di A. Favaro. Firenze: Barbera.
  13. Grattan-Guinness I. (2008). Solving Wigner’s Mystery: The Reasonable (Though Perhaps Limited) Effectiveness of Mathematics in the Natural Sciences. The Mathematical Intelligencer, 30: 7-17.
  14. Hersh R. (2014). Experiencing Mathematics. What do we do, when we do mathematics? Providence: American Mathematical Society.
  15. Hilbert D. (1996a). The Knowledge of Nature. In: Ewald W.B., ed., From Kant to Hilbert. A Source Book in the Foundations of Mathematics, vol. 2. Oxford: Oxford University Press: 1157-1165.
  16. Hilbert D. (1996b). From Mathematical Problems. In: Ewald W.B., ed., From Kant to Hilbert. A Source Book in the Foundations of Mathematics, vol. 2. Oxford: Oxford University Press: 1096-1105.
  17. Hooker C., ed. (2011). Philosophy of Complex Systems. Amsterdam: North Holland.
  18. Husserl E. (1970). The Crisis of European Sciences and Transcendental Phenomenology. Evanston: Northwestern University Press.
  19. Kant I. (2002). Theoretical Philosophy after 1781. Cambridge: Cambridge University Press.
  20. Kepler J. (1937-). Gesammelte Werke, ed. by von Dyck W., Caspar M. and Hammer F. München: Beck.
  21. Leibniz G.W. (1965). Die Philosophischen Schriften. Hildesheim: Olms.
  22. Plantinga A. (2011). Where the Conflict Really Lies: Science, Religion, and Naturalism. Oxford: Oxford University Press.
  23. Poincaré H. (1914). Science and Method. London: Nelson.
  24. Renfrew A.C., Frith C. and Malafouris L. eds. (2008). The Sapient Mind. Archaeology Meets Neuroscience. Philosophical Transaction of the Royal Society B, 363, 1499.
  25. Resnik M.D. (1997). Mathematics as a Science of Patterns. Oxford: Oxford University Press.
  26. Russell B. (1979). The Principles of Mathematics. Cambridge: Cambridge University Press.
  27. Russell B. (1995). An Outline of Philosophy. London: Routledge.
  28. Sarukkai S. (2005). Revisiting the “Unreasonable Effectiveness” of Mathematics. Current Science, 88: 415-423.
  29. Schwartz J. (1992). The Pernicious Influence of Mathematics on Science. In: Kac
  30. M., Rota G.-C. and Schwartz J., eds., Discrete Thoughts. Boston: Birkhäuser: 19-25.
  31. Spelke E. (2011). Natural Number and Natural Geometry. In: Dehaene S. and Brannon E.M., eds., Space, Time and Number in the Brain. London: Elsevier: 287-317.
  32. Starr A., Libertus M.E. and Brannon E.M. (2013). Number Sense in Infancy Predicts Mathematical Abilities in Childhood. Proceedings of the National Academy of Sciences USA, DOI: 10.1073/pnas.1302751110
  33. Steiner M. (1998). The Applicability of Mathematics as a Philosophical Problem. Cambridge (MA): Harvard University Press.
  34. Tegmark M. (2008). The Mathematical Universe. Foundations of Physics, 38: 101-150. Thurston W. (2011). Foreword. In: Pitici M., ed., The Best Writings on Mathematics 2010. Princeton: Princeton University Press: xi-xiii.
  35. Weinberg S. (1986). Lecture on the Applicability of Mathematics. Notices of the American Mathematical Society, 33: 725-728.
  36. Weinberg S. (1993). Dreams of a Final Theory: The Search for the Fundamental Laws of Nature. New York: Vintage.
  37. Wigner E.P. (1960). The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Communications on Pure and Applied Mathematics, 13: 1-14.
  38. Ye F. (2010). Strict Finitism and the Logic of Mathematical Applications. Dordrecht: Springer.

Carlo Cellucci, Naturalizing the Applicability of Mathematics in "PARADIGMI" 2/2015, pp 25-44, DOI: 10.3280/PARA2015-002004