Realism in Mathematics

Oxford, England and New York, NY, USA: Oxford University Prress (1990)
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Abstract

Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics.

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Chapters

Perception and Intuition

Begins with a presentation and elaboration of Benacerraf's epistemic challenge to realism: how can we gain knowledge of an acausal world of non‐spatio‐temporal abstracts? I then outline a theory of perception based in part on neurological theories of Hebb and developmental evidence from Pi... see more

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Author's Profile

Penelope J. Maddy
University of California, Irvine

Citations of this work

The dynamical hypothesis in cognitive science.Tim van Gelder - 1998 - Behavioral and Brain Sciences 21 (5):615-28.
Location and Mereology.Cody Gilmore - 2013 - Stanford Encyclopedia of Philosophy.
Naturalism.Davidn D. Papineau - 2007 - Stanford Encyclopedia of Philosophy.
Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.

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