Skip to main content
SpringerLink
Log in

Mathematics, Indispensability And Scientific Progress

  • Published:
Erkenntnis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

REFERENCES

  • Adler, S.: 1995, Quaternionic Quantum Mechanics and Quantum Fields, Oxford University Press, Oxford.

    Google Scholar 

  • Anderson, R. and G. Joshi: 1993, ‘Quaternions and the Heuristic Role of Mathematical Structures in Physics’, Physics Essays 6(2), 308–319.

    Google Scholar 

  • Baruk, A. (ed.): 1983, Quantum Theory, Groups, Fields, and Particles, Kluwer, Boston.

    Google Scholar 

  • Becker, H. and F. Piper: 1982, Cipher Systems, Northwood.

  • Bell, J.: 1998, A Primer of Infinitesimal Analysis, Cambridge University Press, Cambridge.

    Google Scholar 

  • Bold and Wayne: 1972, Number Systems, Litton.

  • Boyer, C.: 1949, The History of the Calculus and Its Conceptual Development, Dover, New York.

    Google Scholar 

  • Burgess, J.: 1983, ‘Why I Am Not a Nominalist’, Notre Dame Journal of Formal Logic 24, 93–105.

    Google Scholar 

  • Burgess, J.: 1990, ‘Epistemology and Nominalism’, in Irvine (1990), pp. 1–15.

  • Burgess, J. and G. Rosen: 1997, A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics, Clarendon Press, Oxford.

    Google Scholar 

  • Cornwell, J.: 1984, Group Theory in Physics, London Academic Press, London.

    Google Scholar 

  • Crowe, M.: 1985, A History of Vector Analysis, Dover, New York.

    Google Scholar 

  • Dauben, J.: 1988, ‘Abraham Robinson and Nonstandard Analysis: History, Philosophy, and Foundations of Mathematics’, in Asprey and Kitcher (1980), pp. 177–200.

  • De Leo, S.: 1996a, ‘Quaternions and Special Relativity’, Journal of Mathematical Physics 37, 2955–2968.

    Google Scholar 

  • De Leo, S.: 1996b, ‘Quaternions for GUTs’, International Journal of Theoretical Physics 35(9), 1821–1837.

    Google Scholar 

  • Dixon, G.: 1994, Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics, Kluwer, Dordrecht.

    Google Scholar 

  • Eves, H.: 1955, An Introduction to the History of Mathematics, Rinehart, New York.

    Google Scholar 

  • Feferman, S.: 1978, The Logic of Mathematical Discovery vs. the Logical Structure of Mathematics, in Asquith and Hacking (1978), pp. 309–327.

  • Field, H.: 1980, Science without Numbers: A Defense of Nominalism, Blackwell, Oxford and Princeton University PressPrinceton.

    Google Scholar 

  • Finkelstein, D., J. Jauch, S. Schiminovich, and D. Speiser: 1962, ‘Foundations of Quaternion Quantum Mechanics’, Journal of Mathematical Physics 3(2), 207–220.

    Google Scholar 

  • French, S.: 1999, ‘Models and Mathematics in Physics: the Role of Group Theory’, in J. Butterfield and C. Pagonis (eds.), From Physics to Philosophy, Cambridge University Press, Cambridge.

    Google Scholar 

  • Gödel, K.: 1983, ‘What is Cantor's Continuum Problem?’, in Benacerraf and Putnam, 2nd edition (1983), pp. 470–485.

  • Grattan-Guinness, I.: 1972, Joseph Fourier: 1768–1830, MIT Press, Cambridge, MA.

    Google Scholar 

  • Grattan-Guinness, I.: 1990, Convolution in French Mathematics, 1800–1840, Birkhäuser Verlag, Basel and Boston.

    Google Scholar 

  • Lakatos, I.: 1976, Proofs and Refutations: The Logic of Mathematical Discovery, Cambridge University Press, Cambridge.

    Google Scholar 

  • Leibniz, G.: 1702, ‘Mémoire de Mr. Leibniz Touchant son Sentiment sur le Calcul Differential’, Journal de Trévoux 270–272.

  • Maddy, P.: 1992, ‘Indispensability and Practice’, Journal of Philosophy 89, 275–289.

    Google Scholar 

  • Mancosu, P.: 1996, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, Oxford University Press, Oxford.

    Google Scholar 

  • Millard, A.: 1997, Non-Commutative Methods in Quantum Mechanics, Ph.D. Dissertation: Princeton University.

  • O'Neill, J.: 1986, ‘Formalism, Hamilton and Complex Numbers’, Studies in the History and Philosophy of Science 17, 351–372.

    Google Scholar 

  • Quine, W.: 1960, Word and Object, MIT Press, Cambridge and New York.

    Google Scholar 

  • Quine, W.: 1966, The Ways of Paradox and Other Essays, Random House, New York.

    Google Scholar 

  • Reichenbach, H.: 1938, Experience and Prediction, University of Chicago Press, Chicago.

    Google Scholar 

  • Robinson, A.: 1974, Non-standard Analysis, North-Holland, Amsterdam.

  • Rosen, G.: 1992, Remarks on Modern Nominalism, Ph.D. Dissertation: Princeton University.

  • Salanski, J.-M. and H. Sinaceur (eds.): Le Labyrinthe du Continu, Springer-Verlag.

  • Torricelli, E.: 1644, ‘De Solido Hyperbolico Acuto’, in Opera Geometrica, Florentiae.

  • van Fraassen, B.: 1980, The Scientific Image, Clarendon Press, Oxford.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wolfson College, University of Cambridge, Cambridge, CB3 9BB, U.K.

    Alan Baker

Authors
  1. Alan Baker
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baker, A. Mathematics, Indispensability And Scientific Progress. Erkenntnis 55, 85–116 (2001). https://doi.org/10.1023/A:1011977604848

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011977604848

Keywords

Search

Navigation