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## Set Theory and The Philosophy of Mathematics

*Graham Priest*

### in In Contradiction

- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0011
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter discusses certain aspects of naive set theory, that is, set theory in which the abstraction scheme holds for all formulas of the language of set theory, and some of its implications for ... More

## Naturalism and Mathematical Practice

*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/9780199280797.003.0004
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

‘Naturalism’, as we have used the term, is the commitment to look to science to discover what we ought to believe. If one reads ‘science’ broadly, to include pure mathematics, then this commitment ... More

## Anti-Realism in Mathematics

*Charles S. Chihara*

### in The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic

- Published in print:
- 2001
- Published Online:
- October 2011
- ISBN:
- 9780199246557
- eISBN:
- 9780191697609
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199246557.003.0010
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter discusses the implications of the modal theory developed in this book in terms of mathematics. It focuses on Mathematical Realism, because its own position regarding the ontology of ... More

## What Is Mathematical Realism?

*Michael D. Resnik*

### in Mathematics as a Science of Patterns

- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198250142
- eISBN:
- 9780191598296
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250142.003.0002
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Talk of truth plays a major role in formulating realism, to the point that realist theories are often criticized by attacking the correspondence theory of truth that they are presumed to defend. In ... More

## Mathematics and Its Applications

*Mark Colyvan*

### in The Indispensability of Mathematics

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780195137545
- eISBN:
- 9780199833139
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019513754X.003.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Indispensability arguments are introduced and their connection to scientific realism is discussed. The Quine–Putnam indispensability argument for mathematical realism is then outlined. In particular, ... More

## The Case for Mathematical Realism

*Michael D. Resnik*

### in Mathematics as a Science of Patterns

- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198250142
- eISBN:
- 9780191598296
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250142.003.0003
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The application of mathematics to science and the enormous success that derives from it is, perhaps, the strongest evidence in favour of mathematical realism. Quine and Putnam have taken the ... More

## Doubts About Realism

*Michael D. Resnik*

### in Mathematics as a Science of Patterns

- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198250142
- eISBN:
- 9780191598296
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250142.003.0005
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

One of the strongest motivations for being an anti‐realist with regard to mathematics is the difficulty in formulating a plausible realist epistemology, given that there seems to be a lack of ties ... More

## Modal Realism

*Charles S. Chihara*

### in The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic

- Published in print:
- 2001
- Published Online:
- October 2011
- ISBN:
- 9780199246557
- eISBN:
- 9780191697609
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199246557.003.0004
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

The models studied in modal logic are set theoretical structures. So one can regard the model theory of modal logic as a branch of set theory. The philosophical question arises: what is the ... More

## Conclusion

*Mark Colyvan*

### in The Indispensability of Mathematics

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780195137545
- eISBN:
- 9780199833139
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019513754X.003.0007
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The varieties of mathematical realism that are consistent with the indispensability argument are outlined. It is shown that the argument is silent on many issues such as whether numbers are sets, and ... More

## Recent Attempts at Blunting the Indispensability Thesis

*Michael D. Resnik*

### in Mathematics as a Science of Patterns

- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198250142
- eISBN:
- 9780191598296
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250142.003.0004
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The indispensability thesis maintains both that using mathematical terms and assertions is an indispensable part of scientific practice and that this practice commits science to mathematical objects ... More

## Positing Mathematical Objects

*Michael D. Resnik*

### in Mathematics as a Science of Patterns

- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198250142
- eISBN:
- 9780191598296
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250142.003.0009
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

If, as I grant, mathematical objects are abstract entities existing outside of space and time, and if the idea of supernaturally grasping abstract entities is scientifically unacceptable, then we ... More

## The Elusive Distinction Between Mathematics and Natural Science

*Michael D. Resnik*

### in Mathematics as a Science of Patterns

- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198250142
- eISBN:
- 9780191598296
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250142.003.0006
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

It is commonly believed that the epistemology of mathematics must be different from the epistemology of science because their objects are different in kind, i.e. metaphysically different. In this ... More

## Holism: Evidence in Science and Mathematics

*Michael D. Resnik*

### in Mathematics as a Science of Patterns

- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198250142
- eISBN:
- 9780191598296
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250142.003.0007
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

I present a theory of justification for mathematical beliefs that is both non‐foundationalist, in that it claims that some mathematics must be justified indirectly in terms of its consequences, and ... More

## Justification and Explanation in Mathematics and Morality

*Justin Clarke-Doane*

### in Oxford Studies in Metaethics, Volume 10

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780198738695
- eISBN:
- 9780191802515
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198738695.003.0004
- Subject:
- Philosophy, Moral Philosophy

In his influential book, The Nature of Morality, Gilbert Harman writes: “In explaining the observations that support a physical theory, scientists typically appeal to mathematical principles. On the ... More

## Sums in verse or a mathematical aesthetic?

*Duncan F. Kennedy*

### in Forgotten Stars: Rediscovering Manilius' Astronomica

- Published in print:
- 2011
- Published Online:
- May 2011
- ISBN:
- 9780199586462
- eISBN:
- 9780191724961
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199586462.003.0010
- Subject:
- Classical Studies, Literary Studies: Classical, Early, and Medieval

This chapter sets out to offer a more sympathetic characterization of the role of mathematics in the Astronomica than A. E. Housman’s famous but dismissive quip about Manilius’ ‘eminent aptitude for ... More

## Random Numbers and God’s Nature

*James Bradley*

### in Abraham's Dice: Chance and Providence in the Monotheistic Traditions

- Published in print:
- 2016
- Published Online:
- May 2016
- ISBN:
- 9780190277154
- eISBN:
- 9780190277185
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780190277154.003.0004
- Subject:
- Religion, Theology

“Randomness,” despite being a common term, does not unfortunately have a common definition. Disciplines have strongly varying intuitions about its meaning. Researchers in a branch of theoretical ... More

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