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## 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

## 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 Game Theory Phenomenon

*Paul Erickson*

### in The World the Game theorists Made

- Published in print:
- 2015
- Published Online:
- May 2016
- ISBN:
- 9780226097039
- eISBN:
- 9780226097206
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226097206.003.0001
- Subject:
- History, History of Science, Technology, and Medicine

Writing about game theory’s past presents several historiographical challenges. At least prior to its prominent appearances in economics since the 1980s, game theory does not correlate neatly with ... More

## The Development of Analysis: A Case Study

*Philip Kitcher*

### in The Nature of Mathematical Knowledge

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195035410.003.0011
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Concludes with a more sustained look at a single part of the history of mathematics, the development of analysis from the seventeenth century to the work of Dedekind, Cantor and Frege. The discussion ... More

## Toward a Defensible Empiricism

*Philip Kitcher*

### in The Nature of Mathematical Knowledge

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195035410.003.0006
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The next stage is to set up the main question for the rest of the book: How is empirical mathematical knowledge possible? The outline of an answer is given: relatively simple experiences provide ... More

## Eight centuries of mathematical traditions

*John Fauvel*

### in Oxford Figures: Eight Centuries of the Mathematical Sciences

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780199681976
- eISBN:
- 9780191761737
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199681976.003.0001
- Subject:
- Mathematics, History of Mathematics

In this introductory chapter we survey various traditions in the 800-year-old story of mathematics at Oxford University. These traditions include the medieval heritage, studies of logic, mathematical ... More

## Introduction and Overview

*Erich H. Reck and Georg Schiemer*

### in The Prehistory of Mathematical Structuralism

- Published in print:
- 2020
- Published Online:
- June 2020
- ISBN:
- 9780190641221
- eISBN:
- 9780190641245
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190641221.003.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, General

The core idea of mathematical structuralism is that mathematical theories, always or at least in many central cases, are meant to characterize abstract structures (as opposed to more concrete, ... More

## Geometry on my Mind

*David D. Nolte*

### in Galileo Unbound: A Path Across Life, the Universe and Everything

- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198805847
- eISBN:
- 9780191843808
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805847.003.0005
- Subject:
- Physics, History of Physics

This chapter reviews the history of modern geometry with a focus on the topics that provided the foundation for the new visualization of physics. It begins with Carl Gauss and Bernhard Riemann, who ... More

## Measuring Music

*Roger Mathew Grant*

### in Beating Time and Measuring Music in the Early Modern Era

- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780199367283
- eISBN:
- 9780199367306
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199367283.003.0005
- Subject:
- Music, Theory, Analysis, Composition

Through the long eighteenth century, the relationship between motion and time was rewritten. Time, in this new view, was no longer a conceptual descendant of motion but was, in its new form, ... More

## Nascent Newtonian, 1690–1716

*Anna Marie Roos*

### in Martin Folkes (1690-1754): Newtonian, Antiquary, Connoisseur

- Published in print:
- 2021
- Published Online:
- April 2021
- ISBN:
- 9780198830061
- eISBN:
- 9780191868528
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198830061.003.0002
- Subject:
- Mathematics, History of Mathematics

This chapter assesses Folkes’s early life and letters as a nascent Newtonian. We demonstrate to what extent Folkes’s education with French Huguenot scholars Abraham de Moivre and Jacques Louis ... More

## The Relevance of Romanticism: Essays on German Romantic Philosophy

*Dalia Nassar (ed.)*

- Published in print:
- 2014
- Published Online:
- April 2014
- ISBN:
- 9780199976201
- eISBN:
- 9780199395507
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199976201.001.0001
- Subject:
- Philosophy, History of Philosophy

In the last two decades, philosophers have become increasingly aware of the fact that, in spite of significant differences between the contemporary and romantic contexts, romanticism continues to ... More

## Oxford Figures: Eight Centuries of the Mathematical Sciences

*John Fauvel, Raymond Flood, and Robin Wilson (eds)*

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780199681976
- eISBN:
- 9780191761737
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199681976.001.0001
- Subject:
- Mathematics, History of Mathematics

For eight centuries mathematics has been researched and studied at Oxford, and the subject and its teaching have undergone profound changes during that time. This is the story of the intellectual and ... More

## Combinatorics: Ancient and Modern

*Robin Wilson and John J. Watkins (eds)*

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to ... More

## Aristotle’s Actual Infinities

*Jacob Rosen*

### in Oxford Studies in Ancient Philosophy, Volume 59

- Published in print:
- 2021
- Published Online:
- October 2021
- ISBN:
- 9780198859000
- eISBN:
- 9780191891625
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198859000.003.0004
- Subject:
- Philosophy, Ancient Philosophy

In histories of thought about the infinite, Aristotle is constantly said to have rejected any form of actual infinite, and to have allowed quantities to be at most potentially infinite. Aristotle ... More

## Quick(er) Calculations: How to add, subtract, multiply, square, and square root more swiftly

*Trevor Davis Lipscombe*

- Published in print:
- 2021
- Published Online:
- May 2021
- ISBN:
- 9780198852650
- eISBN:
- 9780191887222
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198852650.001.0001
- Subject:
- Mathematics, Educational Mathematics

Quick(er) Calculations describes tips, tricks, and techniques to enable the reader to add, subtract, multiply, divide, find square roots, and form squares more rapidly than before. There are over 600 ... More

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