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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


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