## Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap

*Michael Potter*

- Published in print:
- 2002
- Published Online:
- May 2007
- ISBN:
- 9780199252619
- eISBN:
- 9780191712647
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199252619.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This book is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. It reassesses the brilliant ... More

## Thiele: Pioneer in Statistics

*Steffen L. Lauritzen*

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198509721
- eISBN:
- 9780191709197
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509721.001.0001
- Subject:
- Mathematics, Probability / Statistics

Thorvald Nicolai Thiele was a brilliant Danish researcher of the 19th century. He was a professor of Astronomy at the University of Copenhagen and the founder of Hafnia, the first Danish private ... More

## Matter Matters: Metaphysics and Methodology in the Early Modern Period

*Kurt Smith*

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199583652
- eISBN:
- 9780191723155
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199583652.001.0001
- Subject:
- Philosophy, History of Philosophy, Metaphysics/Epistemology

Why is there a material world? Why is it fundamentally mathematical? This book explores a seventeenth‐century answer to these questions as it emerged from the works of Descartes and Leibniz. What we ... 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

## Science in the Looking Glass: What Do Scientists Really Know?

*E. Brian Davies*

- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199219186
- eISBN:
- 9780191711695
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199219186.001.0001
- Subject:
- Physics, History of Physics

How do scientific conjectures become laws? Why does proof mean different things in different sciences? Do numbers exist, or were they invented? Why do some laws turn out to be wrong? This book ... More

## The grid

*Louis A. Girifalco*

### in The Universal Force: Gravity - Creator of Worlds

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199228966
- eISBN:
- 9780191711183
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199228966.003.0004
- Subject:
- Physics, History of Physics

Descartes believed he was meant to create the ultimate natural philosophy. He relied primarily on reason and philosophic principles, so most of the physics he developed was wrong. But he was a great ... More

## The Rational Disciplines: Logic and Mathematics 1

*David M. Armstrong*

### in Sketch for a Systematic Metaphysics

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199590612
- eISBN:
- 9780191723391
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199590612.003.0012
- Subject:
- Philosophy, Philosophy of Mind, Metaphysics/Epistemology

Logical and mathematical truths differ from the empirical sciences in being necessary; they can be discovered a priori and in general can be proved (contra Quine). How is this possible? This problem ... More

## Science & Reason

*Henry E. Kyburg*

- Published in print:
- 1991
- Published Online:
- October 2011
- ISBN:
- 9780195062533
- eISBN:
- 9780199853038
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195062533.001.0001
- Subject:
- Philosophy, Philosophy of Science

This book presents views on a wide range of philosophical problems associated with the study and practice of science and mathematics. The main structure of the book consists of a presentation of ... 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

## 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

## 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

## Mathematical Knowledge and the Interplay of Practices

*José Ferreirós*

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691167510
- eISBN:
- 9781400874002
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691167510.001.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction ... More

## Set Theory and its Philosophy: A Critical Introduction

*Michael Potter*

- Published in print:
- 2004
- Published Online:
- September 2011
- ISBN:
- 9780199269730
- eISBN:
- 9780191699443
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269730.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

This book presents a philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. The book offers an ... More

## Definition

*Richard Robinson*

- Published in print:
- 1963
- Published Online:
- October 2011
- ISBN:
- 9780198241607
- eISBN:
- 9780191680397
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198241607.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

Definition has been practised and discussed for nearly two and a half millenniums. It has been more widely adopted, and less often reviled, than any other part of the original theory of logic drawn ... More

## The Existence of Space and Time

*Ian Hinckfuss*

- Published in print:
- 1975
- Published Online:
- October 2011
- ISBN:
- 9780198245193
- eISBN:
- 9780191680854
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198245193.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology

This book is intended as an introduction to the philosophical problems of space and time, suitable for any reader who has an interest in the nature of the universe and who has a secondary-school ... More

## Cartesian Method and the Problem of Reduction

*Emily R. Grosholz*

- Published in print:
- 1991
- Published Online:
- October 2011
- ISBN:
- 9780198242505
- eISBN:
- 9780191680502
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198242505.001.0001
- Subject:
- Philosophy, History of Philosophy, Logic/Philosophy of Mathematics

Cartesian method, construed as a way of organizing domains of knowledge according to the ‘order of reason’, was a powerful reductive tool. Descartes produced important ... More

## College Trustee

*Paul C. Gutjahr*

### in Charles Hodge: Guardian of American Orthodoxy

- Published in print:
- 2011
- Published Online:
- May 2011
- ISBN:
- 9780199740420
- eISBN:
- 9780199894703
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199740420.003.0041
- Subject:
- Religion, Church History

Chapter forty-one deals with the years immediately following the death of so many of Hodge’s friends and family. He underwent intense bouts of grief and his physical health was not strong. He was ... 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

## 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

## Foundations without Foundationalism: A Case for Second-Order Logic

*Stewart Shapiro*

- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198250296
- eISBN:
- 9780191598388
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250290.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

A language is second‐order, or higher‐order, if it has bound variables that range over properties or sets of the items in the range of the ordinary, first‐order variables. This book presents a formal ... More