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## The Indispensability of Mathematics

*Mary Leng*

### in Mathematics and Reality

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199280797
- eISBN:
- 9780191723452
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199280797.003.0003
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter discusses Hartry Field's attempt to respond to the indispensability argument by showing how to dispense with mathematics in formulating our best scientific theories. It is pointed out ... More

## More on Revision‐Theoretic Conditionals

*Hartry Field*

### in Saving Truth From Paradox

- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199230747
- eISBN:
- 9780191710933
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230747.003.0018
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter explores the ‘revisionist’ theory of the previous chapter more closely. It shows how to fit it into the semantic framework of Chapter 15, and gives an alternative modal semantics as ... More

## Kripke's Theory of Truth (Strong Kleene Version)

*Hartry Field*

### in Saving Truth From Paradox

- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199230747
- eISBN:
- 9780191710933
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230747.003.0004
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter is an exposition of the strong Kleene version of Kripke's fixed point semantics, and the theories of truth that can be obtained from it. Emphasis is put on the distinction between ... More

## Implicit Definition and the a Priori

*Bob Hale and Crispin Wright*

### in The Reason's Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780198236399
- eISBN:
- 9780191597565
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198236395.003.0006
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This paper discusses the idea, labelled as “the traditional connection” that implicit definitions aim to found a priori knowledge of logic and mathematics. In the first part, it discusses and rejects ... More

## On the Philosophical Significance of Frege's Theorem

*Crispin Wright*

### in The Reason's Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780198236399
- eISBN:
- 9780191597565
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198236395.003.0013
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Frege's theorem is the result that elementary arithmetic may be derived from the second‐ order sentence often referred to as ’Hume's Principle’ (HP). In this essay, Wright considers whether ... More

## Science without Numbers

*Hartry Field*

- Published in print:
- 2016
- Published Online:
- December 2016
- ISBN:
- 9780198777915
- eISBN:
- 9780191823381
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198777915.001.0001
- Subject:
- Philosophy, Philosophy of Science, Logic/Philosophy of Mathematics

The book argues that there is no reason to believe in the existence of mathematical entities, or the literal truth of mathematics, and in particular that physical theory does not require this. The ... More

## First Illustration of Why Mathematical Entities are Useful: Arithmetic

*Hartry Field*

### in Science without Numbers

- Published in print:
- 2016
- Published Online:
- December 2016
- ISBN:
- 9780198777915
- eISBN:
- 9780191823381
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198777915.003.0002
- Subject:
- Philosophy, Philosophy of Science, Logic/Philosophy of Mathematics

Provides an elementary illustration of the kind of application of mathematics that can be accounted for by the conservativeness of mathematics alone, without invoking the assumption that the ... More

## Second Illustration of Why Mathematical Entities are Useful: Geometry and Distance

*Hartry Field*

### in Science without Numbers

- Published in print:
- 2016
- Published Online:
- December 2016
- ISBN:
- 9780198777915
- eISBN:
- 9780191823381
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198777915.003.0003
- Subject:
- Philosophy, Philosophy of Science, Logic/Philosophy of Mathematics

Shows that the use of real numbers in geometry can be accounted for by the conservativeness of mathematics, without assuming the truth of the theory of real numbers. Focuses on Hilbert’s ... More

## Conservativeness and Deflationism

*Leon Horsten*

### in The Tarskian Turn: Deflationism and Axiomatic Truth

- Published in print:
- 2011
- Published Online:
- August 2013
- ISBN:
- 9780262015868
- eISBN:
- 9780262298643
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262015868.003.0068
- Subject:
- Philosophy, General

This chapter focuses on the relationship between deflationism and the arithmetical nonconservativeness of the compositional theory of truth. Deflationists insist that truth is somehow an ... More

## The Categoricity of Logic

*Vann McGee*

### in Foundations of Logical Consequence

- Published in print:
- 2015
- Published Online:
- June 2015
- ISBN:
- 9780198715696
- eISBN:
- 9780191783388
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198715696.003.0006
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter develops the thesis, loosely attributed to Gentzen, that the meanings of logical terms are given by the rules of inference. The author reverses the usual order of explanation, which has ... More

## Conservativeness, Cardinality, and Bad Company

*Roy T. Cook, Philip A. Ebert, and Marcus Rossberg*

### in Abstractionism: Essays in Philosophy of Mathematics

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780199645268
- eISBN:
- 9780191755330
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199645268.003.0011
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This paper argues that abstraction principles must be conservative in a number of distinct senses if they are to be acceptable, and uses this insight to present a solution to the Bad Company Problem. ... More

## Why the Utility of Mathematical Entities is Unlike the Utility of Theoretical Entities

*Hartry Field*

### in Science without Numbers

- Published in print:
- 2016
- Published Online:
- December 2016
- ISBN:
- 9780198777915
- eISBN:
- 9780191823381
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198777915.003.0001
- Subject:
- Philosophy, Philosophy of Science, Logic/Philosophy of Mathematics

Argues for the legitimacy of using mathematics to draw nominalistic conclusions (ones statable without reference to mathematical entities) from nominalistic premises, without assuming that the ... More

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