Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-25T18:03:39.130Z Has data issue: false hasContentIssue false
  • English
  • Français

Problematic Objects between Mathematics and Mechanics

Published online by Cambridge University Press:  31 January 2023

Emily R. Grosholz
Emily R. Grosholz*
Affiliation:
The Pennsylvania State University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The relationship between the objects of mathematics and physics has been a recurrent source of philosophical debate. Rationalist philosophers can minimize the distance between mathematical and physical domains by appealing to transcendental categories, but then are left with the problem of where to locate those categories ontologically. Empiricists can locate their objects in the material realm, but then have difficulty explaining certain peculiar “transcendental” features of mathematics like the timelessness of its objects and the unfalsifiability of (at least some of) its truths. During the past twenty years, the relationship between mathematics and physics has come to seem particularly problematic, in part because of a strong interest in “naturalized epistemology” among American philosophers. The tendency to construe epistemological relations in causal and materialist terms seems to enforce a sharp distinction between mathematical and physical entities, and makes the former seem at best uncomfortably inaccessible and at worst irrelevant.

Type
Part IX. Mathematical and Physical Objects
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1990 , Issue 2: Volume Two: Symposia and Invited Papers 1990 , 1990 , pp. 385 - 395
Copyright
Copyright © Philosophy of Science Association 1991

References

Benacerraf, P. (1965), “What Numbers Could Not Be”, Philosophical Review 74: 47–73.CrossRefGoogle Scholar
Bos, H.J.M. (1988), “fractional Motion and the Legitimation of Transcendental Curves”, Centaurus 31: 9–62.CrossRefGoogle Scholar
Field, H. (1980), Science Without Numbers. Princeton: Princeton University Press.Google Scholar
Gracia, J. (1988), Individuality. Albany: State University of New York Press.Google Scholar
Grosholz, E. (1985), “Two Episodes in the Unification of Logic and Topology”, British Journal for Philosophy of Science 36: 147-57.CrossRefGoogle Scholar
Grosholz, E. (1990/91), Cartesian Method and the Problem of Reduction. Oxford: Oxford University Press.Google Scholar
Grosholz, E. (forthcoming), “Was Leibniz a Mathematical Revolutionary?”, in Revolutions in Mathematics, Gillies, D., ed. Oxford: Oxford University Press.Google Scholar
Hale, S. (forthcoming), “On Intrinsic and Relational Properties.”Google Scholar
Heath, T.L. (1956), Euclid’s Elements. Vol. I. New York: Dover.Google Scholar
Resnik, M. (1981), “Mathematics as a Science of Patterns: Ontology and Reference”, Nous 15: 529-50.CrossRefGoogle Scholar
Resnik, M. (1982), “Mathematics as a Science of Patterns: Epistemology”, Nous 16: 95–105.CrossRefGoogle Scholar
Resnik, M. (1990), “Between Mathematics and Physics”, PSA 1990, Volume II, pp. 369-378.CrossRefGoogle Scholar