Objects and Processes in Mathematical Practice

Foundations of Science 16 (4):337-351 (2011)
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Abstract

In this paper it is argued that the fundamental difference of the formal and the informal position in the philosophy of mathematics results from the collision of an object and a process centric perspective towards mathematics. This collision can be overcome by means of dialectical analysis, which shows that both perspectives essentially depend on each other. This is illustrated by the example of mathematical proof and its formal and informal nature. A short overview of the employed materialist dialectical approach is given that rationalises mathematical development as a process of model production. It aims at placing more emphasis on the application aspects of mathematical results. Moreover, it is shown how such production realises subjective capacities as well as objective conditions, where the latter are mediated by mathematical formalism. The approach is further sustained by Polanyi’s theory of problem solving and Stegmaier’s philosophy of orientation. In particular, the tool and application perspective illuminates which role computer-based proofs can play in mathematics

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References found in this work

The Tacit Dimension. --.Michael Polanyi & Amartya Sen - 1966 - Chicago, IL: University of Chicago.
Personal Knowledge: Towards a Post-Critical Philosophy.Michael Polanyi - 1958 - Chicago: University of Chicago Press. Edited by Mary Jo Nye.
Proofs and refutations: the logic of mathematical discovery.Imre Lakatos (ed.) - 1976 - New York: Cambridge University Press.
Why Do We Prove Theorems?Yehuda Rav - 1999 - Philosophia Mathematica 7 (1):5-41.
Proofs and Refutations. The Logic of Mathematical Discovery.I. Lakatos - 1977 - Tijdschrift Voor Filosofie 39 (4):715-715.

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