## The Web of Practices

*José Ferreirós*

### in Mathematical Knowledge and the Interplay of Practices

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

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691167510.003.0002
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter is a general introduction to the current trend of studies of mathematical practice, with particular emphasis on historical and philosophical work. It offers a preliminary explanation of ... More

## Agents and Frameworks

*José Ferreirós*

### in Mathematical Knowledge and the Interplay of Practices

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

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691167510.003.0003
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter introduces a “core scheme” for the analysis of mathematical practices that can be presented in a simplified way by means of a couple dubbed Framework–Agent. Mathematics in practice will ... More

## On Knowledge and Practices: A Manifesto

*José Ferreirós*

### in Mathematical Knowledge and the Interplay of Practices

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

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691167510.003.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This book proposes a novel analysis of mathematical knowledge from a practice-oriented standpoint and within the context of the philosophy of mathematics. The approach it is advocating is a ... More

## The Uniqueness of Mathematics as a Social Practice

*Jody Azzouni*

### in Tracking Reason: Proof, Consequence, and Truth

- Published in print:
- 2006
- Published Online:
- October 2011
- ISBN:
- 9780195187137
- eISBN:
- 9780199850570
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195187137.003.0010
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Before turning to mathematical practice, the chapter notes two presuppositions of any empirical study of the social inducing of consensus. First, such social inducing presupposes evidence of the ... More

## Complementarity in Mathematics

*José Ferreirós*

### in Mathematical Knowledge and the Interplay of Practices

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

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691167510.003.0004
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter presents a thesis about what it regards as a crucial complementarity of elements in mathematical practice and in the configuration of mathematical knowledge: both conceptual and ... More

## Maddy's Objections

*Mark Colyvan*

### in The Indispensability of Mathematics

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019513754X.003.0005
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Penelope Maddy's objections to the indispensability argument are considered. In two of her objections – the objection from scientific fictions and the objection from the role of mathematics in ... More

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

*Roi Wagner*

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

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691171715.001.0001
- Subject:
- Mathematics, History of Mathematics

In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and ... More

## The Philosophy of Mathematical Practice

*Paolo Mancosu (ed.)*

- Published in print:
- 2008
- Published Online:
- February 2010
- ISBN:
- 9780199296453
- eISBN:
- 9780191711961
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296453.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Contemporary philosophy of mathematics offers us an embarrassment of riches. But anyone familiar with this area will be aware of the need for new approaches that will pay closer attention to ... 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

## Mathematical Liaisons

### in The Good Life in the Scientific Revolution: Descartes, Pascal, Leibniz, and the Cultivation of Virtue

- Published in print:
- 2006
- Published Online:
- March 2013
- ISBN:
- 9780226409542
- eISBN:
- 9780226409566
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226409566.003.0004
- Subject:
- History, History of Science, Technology, and Medicine

This chapter sets some of Pascal's mathematical writings in the conversational contexts that helped refine his work. Pascal's friends—mathematicians and honnêtes homes alike—created conditions in ... More

## Truth and Knowledge in Mathematics

*Danielle Macbeth*

### in Realizing Reason: A Narrative of Truth and Knowing

- Published in print:
- 2014
- Published Online:
- May 2014
- ISBN:
- 9780198704751
- eISBN:
- 9780191774232
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198704751.003.0009
- Subject:
- Philosophy, History of Philosophy

In this chapter we see how it is that Frege’s proof shows that and how even reasoning deductively from concepts in mathematics can be ampliative, a real extension of our knowledge. Frege’s ... More

## Realizing Reason: A Narrative of Truth and Knowing

*Danielle Macbeth*

- Published in print:
- 2014
- Published Online:
- May 2014
- ISBN:
- 9780198704751
- eISBN:
- 9780191774232
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198704751.001.0001
- Subject:
- Philosophy, History of Philosophy

Realizing Reason develops three interrelated themes. First, it traces the essential moments in the historical unfolding—from the ancient Greeks, through Descartes, Kant, and developments in the ... More

## Mathematics Transformed, Again

*Danielle Macbeth*

### in Realizing Reason: A Narrative of Truth and Knowing

- Published in print:
- 2014
- Published Online:
- May 2014
- ISBN:
- 9780198704751
- eISBN:
- 9780191774232
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198704751.003.0006
- Subject:
- Philosophy, History of Philosophy

In the nineteenth century, a new form of mathematical practice emerged, led above all by Riemann in Germany but also exemplified in the work of Galois, Dedekind, Hilbert, and others. Turning their ... More

## Making a World, Mathematically

*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/9780691171715.003.0008
- Subject:
- Mathematics, History of Mathematics

This chapter looks at mathematics not only as subject to constraints but also as feeding back into the reality that shapes it. To show how mathematics changes the reality in which it evolves and ... More

## Kitcher against the Platonists

*Gideon Rosen*

### in The Philosophy of Philip Kitcher

- Published in print:
- 2016
- Published Online:
- June 2016
- ISBN:
- 9780199381357
- eISBN:
- 9780199381371
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199381357.003.0002
- Subject:
- Philosophy, General, Philosophy of Science

Gideon Rosen discusses Kitcher’s recent critique of platonism and defense of formalism. Kitcher argues that any view that attributes a subject matter to mathematics, including platonism, has no good ... More

## Poincaré and the Prehistory of Mathematical Structuralism

*Janet Folina*

### 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/9780190641221.003.0011
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, General

The view that mathematics is about abstract structure is quite deeply rooted in mathematical practice, with further philosophical views about the nature of structures emerging more recently. This ... More

## The New Entities of Abbacus and Renaissance Algebra

*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/9780691171715.003.0003
- Subject:
- Mathematics, History of Mathematics

This chapter offers a historical narrative of some elements of the new algebra that was developed in the fourteenth to sixteenth centuries in northern Italy in order to show how competing ... More

## The Functional Role of Structures in Bourbaki

*Gerhard Heinzmann and Jean Petitot*

### 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/9780190641221.003.0008
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, General

In the history of 20th-century mathematical structuralism, the figure of Bourbaki is prominent and sometimes even identified with the philosophical doctrine of structuralism. However, the Bourbaki ... More

## The Senses of Mixed Mathematics

*Richard Oosterhoff*

### in Making Mathematical Culture: University and Print in the Circle of Lefèvre d'Étaples

- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780198823520
- eISBN:
- 9780191862151
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198823520.003.0005
- Subject:
- History, History of Science, Technology, and Medicine, European Early Modern History

How did engagement with the new printed book reshape early modern disciplines? This chapter considers the rapidly changing area of Renaissance mathematics, focusing on two ‘mixed’ mathematical ... More

## A New World Order

*Danielle Macbeth*

### in Realizing Reason: A Narrative of Truth and Knowing

- Published in print:
- 2014
- Published Online:
- May 2014
- ISBN:
- 9780198704751
- eISBN:
- 9780191774232
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198704751.003.0004
- Subject:
- Philosophy, History of Philosophy

In the seventeenth century, Descartes transformed the practice of mathematics by introducing his symbolic language within which to formulate mathematical ideas, such as that of a circle or that of a ... More