Erkenntnis 68 (3):421-435 (2008)

Authors
Jean Paul Van Bendegem
Vrije Universiteit Brussel
Abstract
We explore aspects of an experimental approach to mathematical proof, most notably number crunching, or the verification of subsequent particular cases of universal propositions. Since the rise of the computer age, this technique has indeed conquered practice, although it implies the abandonment of the ideal of absolute certainty. It seems that also in mathematical research, the qualitative criterion of effectiveness, i.e. to reach one’s goals, gets increasingly balanced against the quantitative one of efficiency, i.e. to minimize one’s means/ends ratio. Our story will lead to the consideration of some limit cases, opening up the possibility of proofs of infinite length being surveyed in a finite time. By means of example, this should show that mathematical practice in vital aspects depends upon what the actual world is like.
Keywords Philosophy   Logic   Ethics   Ontology   Epistemology   Philosophy
Categories (categorize this paper)
DOI 10.1007/s10670-008-9102-5
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 51,304
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Unreasonable Effectiveness of Mathematics in the Natural Sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.
Why Do We Prove Theorems?Yehuda Rav - 1999 - Philosophia Mathematica 7 (1):5-41.
What is Cantor's Continuum Problem?Kurt Gödel - 1947 - In Solomon Feferman, John Dawson & Stephen Kleene (eds.), Journal of Symbolic Logic. Oxford University Press. pp. 176--187.
Two Applications of Logic to Mathematics.Gaisi Takeuti - 1978 - Princeton University Press.

View all 12 references / Add more references

Citations of this work BETA

Non-Deductive Logic in Mathematics.James Franklin - 1987 - British Journal for the Philosophy of Science 38 (1):1-18.
Mathematical Arguments in Context.Jean Paul Van Bendegem & Bart Van Kerkhove - 2009 - Foundations of Science 14 (1-2):45-57.

Add more citations

Similar books and articles

How to Apply Mathematics.Ulrich Meyer - 2004 - Erkenntnis 61 (1):17-28.
John McDowell, Mind and World.Monika Betzler - 1998 - Erkenntnis 48 (1):117-122.
Visualizations in Mathematics.Kajsa Bråting & Johanna Pejlare - 2008 - Erkenntnis 68 (3):345 - 358.
Experimental Mathematics.Alan Baker - 2008 - Erkenntnis 68 (3):331-344.
On Ontology Being a Philosophy Tendency.Cheng Long - 2008 - Proceedings of the Xxii World Congress of Philosophy 17:275-296.

Analytics

Added to PP index
2009-01-28

Total views
47 ( #198,866 of 2,330,106 )

Recent downloads (6 months)
1 ( #584,494 of 2,330,106 )

How can I increase my downloads?

Downloads

My notes