## 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