## 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

## 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

## 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

## 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 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

## 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

## 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