Abstract
This chapter discusses the relation of mathematics to the world considering two questions: What is the relation of mathematical objects to the world? Why is mathematics applicable to the world? As to the first question, the chapter maintains that mathematical objects are not obtained by abstraction from sensible things, or by idealization from our operations of collecting objects. They are hypotheses we make to solve mathematical problems by the analytic method, several of which have an extra-mathematical origin. As to the second question, the chapter maintains, on the one hand, that the applicability of natural mathematics to the world is due to the fact that natural mathematics fits in certain mathematical properties of the world. On the other hand, the applicability of artificial mathematics to the world is due to several factors, starting with the decision of modern science to confine itself to dealing only with some phenomenal properties of the world, mathematical in kind.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abbott, Derek. 2013. The reasonable ineffectiveness of mathematics. Proceedings of the IEEE 101: 2147–2153.
Atiyah, Michael. 1995. Creation v. discovery. Times Higher Education Supplement, 29 September.
Balaguer, Mark. 1998. Platonism and anti-platonism in mathematics. Oxford: Oxford University Press.
Bangu, Sorin. 2016. On ‘The unreasonable effectiveness of mathematics in the natural sciences’. In Models and inferences in science, ed. Emiliano Ippoliti, Fabio Sterpetti, and Thomas Nickles, 11–29. Cham: Springer.
Bourbaki, Nicholas. 1949. Foundations of mathematics for the working mathematician. The Journal of Symbolic Logic 14 : 1–8.
———. 1950. The architecture of mathematics. The American Mathematical Monthly 57 : 221–232.
Bueno, Otávio, and Mark Colyvan. 2011. An inferential conception of the application of mathematics. Noûs 45 : 345–374.
Bueno, Otávio, and Steven French. 2012. Can mathematics explain physical phenomena? The British Journal for the Philosophy of Science 63 : 85–113.
Chace, Arnold Buffum, ed. 1927. The Rhind mathematical papyrus. Vol. 1. Oberlin: Mathematical Association of America.
Dieudonné, Jean. 1964. Recent developments in mathematics. The American Mathematical Monthly 71 : 239–248.
Dirac, Paul Adrien Maurice. 1963. The evolution of the physicist’s picture of nature. Scientific American 208 : 43–53.
———. 1978. Directions in physics. New York: Wiley.
Dyson, Freeman John. 1999. Foreword. In Michael Monastyrsky, Riemann, topology, and physics, ix–ix, Boston: Birkhäuser.
Eddington, Arthur. 1939. The philosophy of physical science. Cambridge: Cambridge University Press.
Frege, Gottlob. 1960. The foundations of arithmetic: A logico-mathematical enquiry into the concept of number. New York: Harper.
———. 1984. Collected papers on mathematics, logic, and philosophy. Oxford: Blackwell.
Galilei, Galileo. 1968. Opere.Florence: Barbera.
Grattan-Guinness, Ivor. 2008. Solving Wigner’s mystery: The reasonable (though perhaps limited) effectiveness of mathematics in the natural sciences. The Mathematical Intelligencer 30 (3): 7–17.
Hamming, Richard. 1980. The unreasonable effectiveness of mathematics. The American Mathematical Monthly 87 : 81–90.
Hardy, Godfrey Harold. 1992. A mathematician’s apology. Cambridge: Cambridge University Press.
Hilbert, David. 1980a. Letter to Frege, 29 December 1899. In Gottlob Frege, Philosophical and mathematical correspondence, 38–41. Oxford: Blackwell.
———. 1996f. Logic and the knowledge of nature. In From Kant to Hilbert: A source book in the foundations of mathematics, II, ed. William Ewald, 1157–1165. Oxford: Oxford University Press.
———. 2000. Mathematical problems. Appendix to Jeremy Gray, The Hilbert challenge, 240–282. Oxford: Oxford University Press.
Hooker, Cliff, ed. 2011. Philosophy of complex systems. Amsterdam: North Holland.
Kant, Immanuel. 1992. Lectures on logic. Cambridge: Cambridge University Press.
Kepler, Johannes. 1937–. Gesammelte Werke. München: Beck.
Kitcher, Philip. 1983. The nature of mathematical knowledge. Oxford: Oxford University.
Kline, Morris. 1972. Mathematical thought from ancient to modern times. Oxford: Oxford University Press.
Leibniz, Gottfried Wilhelm. 1965. Die Philosophischen Schriften. Hildesheim: Olms.
Parsons, Charles. 1983. Mathematics in philosophy: Selected essays. Ithaca: Cornell University Press.
Pincock, Christopher. 2012. Mathematics and scientific representation. Oxford: Oxford University Press.
Russell, Bertrand. 1995a. An outline of philosophy. London: Routledge.
Schwartz, Jack. 1992. The pernicious influence of mathematics on science. In Discrete thoughts, ed. Mark Kac, Gian-Carlo Rota, and Jack Schwartz, 19–25. Boston: Birkhäuser.
Steiner, Mark. 1998. The applicability of mathematics as a philosophical problem. Cambridge: Harvard University Press.
von Neumann, John. 1961. The mathematician. In John von Neumann, Collected works, vol. 1, 1–9. Oxford: Pergamon Press.
Weinberg, Steven. 1986. Lecture on the applicability of mathematics. Notices of the American Mathematical Society 33 : 725–728.
———. 1993. Dreams of a final theory: The search for the fundamental laws of nature. New York: Vintage.
Wigner, Eugene Paul. 1960. The unreasonable effectiveness of mathematics in the natural sciences. Communications on Pure and Applied Mathematics 13 : 1–14.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Cellucci, C. (2017). Mathematics and the World. In: Rethinking Knowledge. European Studies in Philosophy of Science, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-53237-0_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-53237-0_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-53236-3
Online ISBN: 978-3-319-53237-0
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)