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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


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