Pi on earth, or mathematics in the real world

Erkenntnis 68 (3):421-435 (2008)
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
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DOI 10.1007/s10670-008-9102-5
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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?Y. Rav - 1999 - Philosophia Mathematica 7 (1):5-41.
Two Applications of Logic to Mathematics.Gaisi Takeuti - 1978 - Princeton University Press.
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.

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Citations of this work BETA
Mathematical Arguments in Context.Jean Paul van Bendegem & Bart van Kerkhove - 2009 - Foundations of Science 14 (1-2):45-57.

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