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||No keywords specified (fix it)|
|Categories||No categories specified (fix it)|
|Through your library||Configure|
Similar books and articles
Bart Van Kerkhove & Jean Paul Van Bendegem (2008). Pi on Earth, or Mathematics in the Real World. Erkenntnis 68 (3).
Jean Paul Van Bendegem (2005). Proofs and Arguments: The Special Case of Mathematics. Poznan Studies in the Philosophy of the Sciences and the Humanities 84 (1):157-169.
Jarosław Mrozek (1997). Matematyka i świat. Filozofia Nauki 4.
Edwin Coleman (2009). The Surveyability of Long Proofs. Foundations of Science 14 (1-2):27-43.
Mark McEvoy (2013). Experimental Mathematics, Computers and the a Priori. Synthese 190 (3):397-412.
Bart van Kerkhove, Jean Paul van Bendegem & Jonas de Vuyst (eds.) (2010). Philosophical Perspectives on Mathematical Practice. College Publications.
James Franklin (2009). Aristotelian Realism. In A. Irvine (ed.), The Philosophy of Mathematics (Handbook of the Philosophy of Science series). North-Holland Elsevier.
Jean Paul Van Bendegem (1989). Foundations of Mathematics or Mathematical Practice: Is One Forced to Choose? Philosophica 43.
Jean Paul Van Bendegem (1988). Non-Formal Properties of Real Mathematical Proofs. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:249 - 254.
Uwe Riss (2011). Objects and Processes in Mathematical Practice. Foundations of Science 16 (4):337-351.
Bart Van Kerkhove (ed.) (2009). New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics. [REVIEW] World Scientific.
Ken Dennis (1995). A Logical Critique of Mathematical Formalism in Economics. Journal of Economic Methodology 2 (2):181-200.
Sorry, there are not enough data points to plot this chart.
Added to index2011-05-29
Recent downloads (6 months)0
How can I increase my downloads?