Creativity, Freedom, and Authority: A New Perspective On the Metaphysics of Mathematics

Australasian Journal of Philosophy 87 (4):589-608 (2009)
Authors
Julian Cole
Buffalo State College
Abstract
I discuss a puzzle that shows there is a need to develop a new metaphysical interpretation of mathematical theories, because all well-known interpretations conflict with important aspects of mathematical activities. The new interpretation, I argue, must authenticate the ontological commitments of mathematical theories without curtailing mathematicians' freedom and authority to creatively introduce mathematical ontology during mathematical problem-solving. Further, I argue that these two constraints are best met by a metaphysical interpretation of mathematics that takes mathematical entities to be constitutively constructed by human activity in a manner similar to the constitutive construction of the US Supreme Court by certain legal and political activities. Finally, I outline some of the philosophical merits of metaphysical interpretations of mathematical theories of this type
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DOI 10.1080/00048400802598629
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References found in this work BETA

Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.

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Citations of this work BETA

Deflationary Nominalism and Puzzle Avoidance†.David Mark Kovacs - 2019 - Philosophia Mathematica 27 (1):88-104.
Mathematical Structuralism Today.Julian C. Cole - 2010 - Philosophy Compass 5 (8):689-699.
The Semantics of Social Constructivism.Shay Allen Logan - 2015 - Synthese 192 (8):2577-2598.

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