Jump to ContentJump to Main Navigation

You are looking at 1-7 of 7 items

  • Keywords: mathematical existence x
Clear All Modify Search

View:

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


The Problem of Existence in Mathematics

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:
10.1093/0198239750.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Concerns the ‘problem of existence’ in mathematics: the problem of how to understand existence assertions in mathematics. The problem can best be understood by considering how Mathematical Platonists ... More


Defending the Axioms: On the Philosophical Foundations of Set Theory

Penelope Maddy

Published in print:
2011
Published Online:
May 2011
ISBN:
9780199596188
eISBN:
9780191725395
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199596188.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

Mathematics depends on proofs, and proofs have to begin somewhere, from some fundamental assumptions. Chapter I traces the historical rise of pure mathematics and the development of set theory, ... More


Morals

Penelope Maddy

in Defending the Axioms: On the Philosophical Foundations of Set Theory

Published in print:
2011
Published Online:
May 2011
ISBN:
9780199596188
eISBN:
9780191725395
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199596188.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This concluding chapter draws a pair of morals. First, what's gone before shows that there's a form of objectivity in mathematics that doesn't depend on the existence of mathematical objects or the ... More


Arealism

Penelope Maddy

in Defending the Axioms: On the Philosophical Foundations of Set Theory

Published in print:
2011
Published Online:
May 2011
ISBN:
9780199596188
eISBN:
9780191725395
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199596188.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter returns to the juncture in Chapter II where it was assumed, temporarily, that the historical and continuing inter-relations of pure mathematics with natural science are enough to warrant ... More


The Constructibility Quantifiers

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:
10.1093/0198239750.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

Sketches the basic idea for the approach taken. A mathematical system is to be developed in which the existential theorems of traditional mathematics are to be replaced by constructibility theorems: ... More


Wittgenstein's Constructivization of Euler's Proof of the Infinity of Primes (with Mathieu Marion)

Paolo Mancosu

in The Adventure of Reason: Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940

Published in print:
2010
Published Online:
May 2011
ISBN:
9780199546534
eISBN:
9780191594939
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199546534.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Mind

This chapter relates the debate analyzed in Chapter 5 to the only instance in which Wittgenstein attempted (successfully) the constructivization of a classical proof, viz. Euler’s proof for the ... More


View: