Ontology and mathematical practice

Philosophia Mathematica 12 (3):244-267 (2004)
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Abstract

In this paper I propose a position in the ontology of mathematics which is inspired mainly by a case study in the mathematical discipline if-theory. The main theses of this position are that mathematical objects are introduced by mathematicians and that after mathematical objects have been introduced, they exist as objectively accessible abstract objects.

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10.1093/philmat/12.3.244

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Citations of this work

Kneebone and Lakatos: At the Roots of a Dialectical Philosophy of Mathematics.Fenner Stanley Tanswell, Brendan Larvor & Colin Jakob Rittberg - forthcoming - Hopos: The Journal of the International Society for the History of Philosophy of Science.

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References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
Mathematics as a science of patterns.Michael David Resnik - 1997 - New York ;: Oxford University Press.
Objective Knowledge.K. R. Popper - 1972 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 4 (2):388-398.
Platonism and Anti-Platonism in Mathematics.Mark Balaguer - 1998 - Bulletin of Symbolic Logic 8 (4):516-518.

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