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Realism in Mathematics

Penelope Maddy

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240358
eISBN:
9780191597978
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/019824035X.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Many mathematicians understand their work as an effort to describe the denizens and features of an abstract mathematical world or worlds. Most philosophers of mathematics consider views of this sort ... More


Monism and Beyond

Penelope Maddy

in Realism in Mathematics

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240358
eISBN:
9780191597978
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019824035X.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

Outlines a physicalistic version of set theoretic realism (a sort of monism), and compares and contrasts it with Field's nominalism, with structuralism, and with modalism. I conclude that, despite ... More


Realism

Penelope Maddy

in Realism in Mathematics

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240358
eISBN:
9780191597978
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019824035X.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

The early sections describe the pre‐theoretic realism of the mathematician, survey the basic forms of realism in philosophy, and attempt to disentangle the issues of realism from debates over the ... More


Numbers

Penelope Maddy

in Realism in Mathematics

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240358
eISBN:
9780191597978
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019824035X.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics

Begins with a review of Benacerraf's metaphysical challenge to mathematical realism based on sets: how, for example, can number theory be the study of particular sets when other sets with the same ... More


The Argument from Collections

Christopher Menzel

in Two Dozen (or so) Arguments for God: The Plantinga Project

Published in print:
2018
Published Online:
September 2018
ISBN:
9780190842215
eISBN:
9780190874445
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190842215.003.0003
Subject:
Religion, Theology

Very broadly, an argument from collections is an argument that purports to show that our beliefs about sets imply—in some sense—the existence of God. Plantinga (2007) first sketched such an argument ... More


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