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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


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


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


Mathematical Reality

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:
10.1093/0195035410.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

We can gain empirical knowledge of elementary arithmetic and elementary geometry because the primitive core of these subjects consists of truths about manipulations of reality. Full arithmetic and ... More


A Priori Knowledge Revisited

Philip Kitcher

in New Essays on the A Priori

Published in print:
2000
Published Online:
November 2003
ISBN:
9780199241279
eISBN:
9780191597107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199241279.003.0004
Subject:
Philosophy, Metaphysics/Epistemology

Philip Kitcher defends his rejection of the thesis that mathematical knowledge is possible if such knowledge is a priori against a number of objections. His main line of argument is to suggest a ... More


Objectivity in Mathematical Knowledge

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/9780691167510.003.0009
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter proposes an idea for reconciling the hypothetical conception of mathematics with the traditional idea of the objectivity of mathematical knowledge. The basic notion is that, because new ... More


Numbers

Lance J. Rips

in Lines of Thought: Central Concepts in Cognitive Psychology

Published in print:
2011
Published Online:
January 2011
ISBN:
9780195183054
eISBN:
9780199865109
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195183054.003.0003
Subject:
Psychology, Cognitive Psychology

This chapter canvasses proposed connections between minds and numbers that might make knowledge of mathematics possible. The goal is to determine whether any promising leads are available in ... More


Positing Mathematical Objects

Michael D. Resnik

in Mathematics as a Science of Patterns

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198250142
eISBN:
9780191598296
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198250142.003.0009
Subject:
Philosophy, Logic/Philosophy of Mathematics

If, as I grant, mathematical objects are abstract entities existing outside of space and time, and if the idea of supernaturally grasping abstract entities is scientifically unacceptable, then we ... More


Mathematical Intuition

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:
10.1093/0195035410.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

If we are to obtain a priori mathematical knowledge by following proofs, then we have to be able to have a priori knowledge of the axioms. This chapter (along with Chapter 4) examines the major ... 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


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


Mathematical Knowledge and Reliable Authority

C. A. J. Coady

in Testimony: A Philosophical Study

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198235514
eISBN:
9780191597220
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198235518.003.0014
Subject:
Philosophy, Metaphysics/Epistemology

There is a common view that mathematical truths can be known only a priori, by intuition or grasping a proof, but the possibility of transmitting mathematical knowledge by testimony cuts against this ... 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


Patterns of Mathematical Change

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:
10.1093/0195035410.003.0010
Subject:
Philosophy, Logic/Philosophy of Mathematics

Describes some types of inference and principles of theory choice that are involved in the growth of mathematics.


Mathematical Change and Scientific Change

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:
10.1093/0195035410.003.0008
Subject:
Philosophy, Logic/Philosophy of Mathematics

Chapters 7–9 offer a general account of the growth of mathematics. Introduce the notion of a mathematical practice, a multidimensional entity consisting of a language, accepted statements, accepted ... More


A Priori and A Posteriori Knowledge

Colin McGinn

in Knowledge and Reality: Selected Essays

Published in print:
2002
Published Online:
November 2003
ISBN:
9780199251582
eISBN:
9780191598012
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199251584.003.0003
Subject:
Philosophy, Metaphysics/Epistemology

McGinn defends a causal criterion for distinguishing a priori from a posteriori knowledge. In the case of a posteriori knowledge, the subject matter of a knower's ground for believing a proposition ... More


Doubts About Realism

Michael D. Resnik

in Mathematics as a Science of Patterns

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198250142
eISBN:
9780191598296
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198250142.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

One of the strongest motivations for being an anti‐realist with regard to mathematics is the difficulty in formulating a plausible realist epistemology, given that there seems to be a lack of ties ... More


A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics

John P. Burgess and Gideon Rosen

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198250128
eISBN:
9780191597138
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198250126.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Numbers and other mathematical objects are exceptional in having no locations in space and time and no causes or effects in the physical world. This makes it difficult to account for the possibility ... More


Deflationism and Mathematical Truth

Charles S. Chihara

in Constructibility and Mathematical Existence

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239758
eISBN:
9780191597190
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198239750.003.0012
Subject:
Philosophy, Logic/Philosophy of Mathematics

Takes up Field's version of Logicism—a position that he calls ‘deflationism’. Unlike traditional Logicists, Field does not analyse mathematical propositions into purely logical ones, but he does ... More


Mathematical Concepts and Definitions

Jamie Tappenden

in The Philosophy of Mathematical Practice

Published in print:
2008
Published Online:
February 2010
ISBN:
9780199296453
eISBN:
9780191711961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296453.003.0010
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter lays some preliminary groundwork for answering the question: What kind of success have we attained when we introduce a ‘good’ mathematical concept or definition? What sort of ... More


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