Abstract
If mathematical realism - whether Platonist or Aristotelian - is true, then mathematics is a scientific study of a world ‘out there’. In that case, in addition to methods special to mathematics such as proof, there ought to be a role for ordinary scientific methods such as experiment, conjecture and the confirmation of theories by observations. Those methods should work in mathematics just as well as in science. Mathematics has extra and more certain methods of its own, but that should not prevent ordinary scientific methods from working.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes and Bibliography
J. Franklin, Non-deductive logic in mathematics, British Journal for the Philosophy of Science 38 (1987), 1–18.
C. Chandler, Hello, I Must Be Going: Groucho Marx and His Friends (Doubleday, Garden City, New York, 1978), 560.
C. Fadiman, The American Treasury (Harper, New York, 1955), 794.
J.M. Borwein and D. Bailey, Mathematics by Experiment: Plausible Reasoning in the 21st Century (A.K. Peters, Natick, MA, 2004).
D. Zeilberger, Theorems for a price: tomorrow’s semi-rigorous mathematical culture, Notices of the American Mathematical Society 46 (1993), 978–981.
J. Derbyshire, Prime obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (Joseph Henry Press, Washington, DC, 2003).
R.P. Brent, J. van de Lune, H.J.J. Te Riele, and D.T. Winter, On the zeros of the Riemann Zeta Function in the critical strip (II), Mathematics of Computation, 39 (1982), 681–688.
A. Weil, Variétés abéliennes et courbes algébriques (Hermann, Paris, 1948).
G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory (Cambridge University Press, Cambridge, 1995).
A. Ivić, On some reasons for doubting the Riemann Hypothesis, in P. Borwein et al., eds, The Riemann Hypothesis: A resource for the aficionado and virtuoso alike (Springer, New York, 2008), 131–160.
Y. Wang, ed., Goldbach Conjecture (World Scientific, River Edge, NJ, 2002).
W. Feit, and J. Thompson, Solvability of groups of odd order, Pacific Journal of Mathematics, 13 (1963), 775–1029.
R. Solomon, A brief history of the classification of the finite simple groups, Bulletin of the American Mathematical Society 38 (2001), 315–352.
D. Gorenstein, Finite Simple Groups (Plenum, New York, 1982).
Z. Janko, A new finite simple group with abelian 2-Sylow subgroups and its characterization, Journal of Algebra 3 (1966), 147–186.
M. Aschbacher, The Finite Simple Groups and Their Classification (Yale University Press, New Haven, CT, 1980), 6–7.
R. Lyons, Evidence for a new finite simple group, Journal of Algebra, 20 (1972), 540–569.
M. O’Nan, Some evidence for the existence of a new finite simple group, Proeedings of the London Mathematical Society 32 (1976), 421–479.
D. Gorenstein, The classification of finite simple groups (I), Bulletin of the American Mathematical Society New Series, 1 (1979), 43–199.
M.J. Collins, ed., Finite Simple Groups II (London Mathematical Society, London, 1980), 21.
M. Aschbacher, The status of the classification of the finite simple groups, Notices of the American Mathematical Society 51 (2001), 736–740.
J.M. Keynes, A Treatise on Probability (Macmillan, London, 1921).
E.T. Jaynes, Probability Theory: The logic of science (Cambridge University Press, Cambridge, 2003).
J. Williamson, In Defence of Objective Bayesianism (Oxford University Press, Oxford, 2010).
J. Franklin, Resurrecting logical probability, Erkenntnis 55 (2001), 277–305.
J. Franklin, What Science Knows: And How It Knows It (Encounter Books, New York, 2009).
J. Franklin, The objective Bayesian conceptualisation of proof and reference class problems, Sydney Law Review 33 (2011), 545–561.
H. Bender, On the uniqueness theorem, Illinois Journal of Mathematics 14 (1970), 376–384.
A.L. Ruhkin, Testing randomness: a suite of statistical procedures, Theory of Probability and Its Applications 45 (2001), 111–132.
Author information
Authors and Affiliations
Copyright information
© 2014 James Franklin
About this chapter
Cite this chapter
Franklin, J. (2014). Non-Deductive Logic in Mathematics. In: An Aristotelian Realist Philosophy of Mathematics. Palgrave Macmillan, London. https://doi.org/10.1057/9781137400734_16
Download citation
DOI: https://doi.org/10.1057/9781137400734_16
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-48618-2
Online ISBN: 978-1-137-40073-4
eBook Packages: Palgrave Religion & Philosophy CollectionPhilosophy and Religion (R0)