## Philosophy of Mathematics: Structure and Ontology

*Stewart Shapiro*

- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780195139303
- eISBN:
- 9780199833658
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195139305.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The philosophy of mathematics articulated and defended in this book goes by the name of “structuralism”, and its slogan is that mathematics is the science of structure. The subject matter of ... More

## Mathematics and Its Philosophy

*Stewart Shapiro*

### in Philosophy of Mathematics: Structure and Ontology

- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780195139303
- eISBN:
- 9780199833658
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195139305.003.0002
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter deals with the relationship between the practice of mathematics and the philosophy of mathematics. The philosopher of mathematics is, or should be, concerned with mathematics as it is ... More

## Das Überraschende: Wittgenstein on the Surprising in Mathematics

*Juliet Floyd*

### in Wittgenstein and the Philosophy of Mind

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199737666
- eISBN:
- 9780199933372
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199737666.003.0010
- Subject:
- Philosophy, Philosophy of Mind, General

This chapter explores the epistemic role that surprise and other psychological reactions play in mathematics. The chapter pursues the issue for its own sake, but also for its usefulness in ... More

## Realism in Mathematics

*Penelope Maddy*

- Published in print:
- 1992
- Published Online:
- November 2003
- ISBN:
- 9780198240358
- eISBN:
- 9780191597978
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019824035X.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Many mathematicians understand their work as an effort to describe the denizens and features of an abstract mathematical world or worlds. Most philosophers of mathematics consider views of this sort ... More

## The Nature of Mathematical Knowledge

*Philip Kitcher*

- Published in print:
- 1985
- Published Online:
- November 2003
- ISBN:
- 9780195035414
- eISBN:
- 9780199833368
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195035410.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The Nature of Mathematical Knowledge develops and defends an empiricist approach to mathematical knowledge. After offering an account of a priori knowledge, it argues that none of the ... More

## The Metaphysical Unity of Natural Philosophy

*Stephen Gaukroger*

### in The Collapse of Mechanism and the Rise of Sensibility: Science and the Shaping of Modernity, 1680-1760

- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199594931
- eISBN:
- 9780191595745
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199594931.003.0004
- Subject:
- Philosophy, Philosophy of Science, General

The chapter explores the collapse of mechanism and the competition between Newton's and Leibniz's non‐mechanistic models of physical explanation; the relation between Leibniz's metaphysics and his ... More

## Mathematics as a Science of Patterns

*Michael D. Resnik*

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250142.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Mathematics is regarded as our most developed science, and yet philosophical troubles surface as soon as we inquire about its subject matter partly because mathematics itself says nothing about the ... More

## Mathematics without Numbers: Towards a Modal-Structural Interpretation

*Geoffrey Hellman*

- Published in print:
- 1993
- Published Online:
- November 2003
- ISBN:
- 9780198240341
- eISBN:
- 9780191597664
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198240341.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to ... More

## Finding a problem

*Michael Potter*

### in Wittgenstein's Notes on Logic

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199215836
- eISBN:
- 9780191721243
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215836.003.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This chapter addresses the question of what led Wittgenstein to study philosophy with Russell in Cambridge. Since the narrative of Wittgenstein's life before 1911 is well summarized in available ... More

## The Indispensability of Mathematics

*Mark Colyvan*

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019513754X.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Looks at the Quine–Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical ... 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

## Second Philosophy: A Naturalistic Method

*Penelope Maddy*

- Published in print:
- 2007
- Published Online:
- January 2009
- ISBN:
- 9780199273669
- eISBN:
- 9780191706264
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199273669.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. This book describes and practices a particularly austere form of ... More

## Number

*George Bealer*

### in Quality and Concept

- Published in print:
- 1982
- Published Online:
- October 2011
- ISBN:
- 9780198244288
- eISBN:
- 9780191680762
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198244288.003.0007
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Mind

Since the theory of properties, relations, and propositions (PRPs) is a full-fledged part of natural logic, it can support a well justified logicist philosophy of mathematics. This chapter argues ... More

## Leibniz's Constructivism and Infinitely Folded Matter

*Samuel Levey*

### in New Essays on the Rationalists

- Published in print:
- 2003
- Published Online:
- November 2003
- ISBN:
- 9780195165418
- eISBN:
- 9780199868285
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195165411.003.0006
- Subject:
- Philosophy, History of Philosophy

“Leibniz's Constructivism and Infinitely Folded Matter” This essay examines Leibniz's account of the structure of matter and its relation to his views of the infinite. Leibniz interprets the actually ... More

## A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics

*John P. Burgess and Gideon Rosen*

- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198250128
- eISBN:
- 9780191597138
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250126.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Numbers and other mathematical objects are exceptional in having no locations in space and time and no causes or effects in the physical world. This makes it difficult to account for the possibility ... More

## Future Philosophy

*Paul Thagard*

### in Natural Philosophy: From Social Brains to Knowledge, Reality, Morality, and Beauty

- Published in print:
- 2019
- Published Online:
- March 2019
- ISBN:
- 9780190678739
- eISBN:
- 9780190686451
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190678739.003.0010
- Subject:
- Psychology, Cognitive Models and Architectures

Philosophy hangs together by coherence relations tied to scientific evidence. Multilevel materialism in the philosophy of mind fits well bidirectionally with reliable coherentism in epistemology. ... More

## Truth and the Absence of Fact

*Hartry Field*

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199242894
- eISBN:
- 9780191597381
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199242895.001.0001
- Subject:
- Philosophy, General

This is a collection of papers, written over many years, with substantial postscripts tying them together and giving an updated perspective on them. The first five are on the notions of truth and ... More

## Frege and Other Philosophers

*Michael Dummett*

- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198236283
- eISBN:
- 9780191597343
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019823628X.001.0001
- Subject:
- Philosophy, History of Philosophy

This book deals with Frege's philosophy by comparing and contrasting his views with those of other philosophers, mostly contemporary with him.

## Naturalism in Mathematics

*Penelope Maddy*

- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198250753
- eISBN:
- 9780191597961
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250754.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

It is well known that certain natural statements of set theory, like Cantor's continuum hypothesis (CH), cannot be proved or disproved on the basis of the standard axioms (Zermelo–Fraenkel with ... More

## A Constraints-Based Philosophy of Mathematical Practice

*Roi Wagner*

### in Making and Breaking Mathematical Sense: Histories and Philosophies of Mathematical Practice

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780691171715
- eISBN:
- 9781400883783
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691171715.003.0004
- Subject:
- Mathematics, History of Mathematics

This chapter describes a constraints-based philosophy of mathematical practice and shows that mathematics can be so many different things, even if we look at a particular branch of mathematics in a ... More