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## 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

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