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Ontology and mathematical practice
Philosophia Mathematica 12 (3):244-267 (2004)
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.My notes
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Citations of this work
Philosophy of Mathematical Practice — Motivations, Themes and Prospects†.Jessica Carter - 2019 - Philosophia Mathematica 27 (1):1-32.
International Handbook of Research in History, Philosophy and Science Teaching.Michael R. Matthews (ed.) - 2014 - Springer.
Social constructivism in mathematics? The promise and shortcomings of Julian Cole’s institutional account.Jenni Rytilä - 2021 - Synthese 199 (3-4):11517-11540.
Mathematics Dealing with 'Hypothetical States of Things'.Jessica Carter - 2014 - Philosophia Mathematica 22 (2):209-230.
Handling mathematical objects: representations and context.Jessica Carter - 2013 - Synthese 190 (17):3983-3999.
References found in this work
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton 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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