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Foundations without Foundationalism: A Case for Second-Order Logic

Stewart Shapiro

Published in print:
2000
Published Online:
November 2003
ISBN:
9780198250296
eISBN:
9780191598388
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198250290.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

A language is second‐order, or higher‐order, if it has bound variables that range over properties or sets of the items in the range of the ordinary, first‐order variables. This book presents a formal ... More


Constructibility and Mathematical Existence

Charles S. Chihara

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239758
eISBN:
9780191597190
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198239750.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the ... More


Mathematical Structuralism

Charles S. Chihara

in Constructibility and Mathematical Existence

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239758
eISBN:
9780191597190
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198239750.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

The first of six chapters in which rival views are critically evaluated and compared with the Constructibility view described in earlier chapters. The views considered here (forms of ‘Structuralism’) ... More


The Status of Logic

Stewart Shapiro

in New Essays on the A Priori

Published in print:
2000
Published Online:
November 2003
ISBN:
9780199241279
eISBN:
9780191597107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199241279.003.0014
Subject:
Philosophy, Metaphysics/Epistemology

It seems that if a thinker in an argument arrives at an empirical conclusion, then some of the belief‐formation or reasoning principles she employs must be a priori if the reasoning is to be ... More


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