*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 ...
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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 available accounts of a priori mathematical knowledge is viable. It then constructs an approach to the content of mathematical statements, viewing mathematics as grounded in our manipulations of physical reality. From these crude beginnings, mathematics unfolds through the successive modifications of mathematical practice, spurred by the presence of unsolved problems. This process of unfolding is considered in general, and illustrated by considering the historical development of analysis from the seventeenth century to the end of the nineteenth.Less

*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 available accounts of a priori mathematical knowledge is viable. It then constructs an approach to the content of mathematical statements, viewing mathematics as grounded in our manipulations of physical reality. From these crude beginnings, mathematics unfolds through the successive modifications of mathematical practice, spurred by the presence of unsolved problems. This process of unfolding is considered in general, and illustrated by considering the historical development of analysis from the seventeenth century to the end of the nineteenth.

*Philip Kitcher*

- 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 ...
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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 is linked to the general account of Chapters 7–9.Less

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 is linked to the general account of Chapters 7–9.

*Philip Kitcher*

- 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 ...
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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 knowledge of elementary mathematics; the historical process extends the basic mathematical knowledge in extraordinary ways.Less

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 knowledge of elementary mathematics; the historical process extends the basic mathematical knowledge in extraordinary ways.

*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 ...
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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 “persist,” and the questions that the romantics raised remain relevant today. The Relevance of Romanticism: Essays on Early German Romantic Philosophy is the first collection of essays that directly considers the reasons why philosophers have recently become deeply interested in romantic thought. Through historical and systematic reconstructions, the volume offers greater understanding of romanticism as a philosophical movement and deeper insight into the role that romantic thought plays—or can play—in contemporary philosophical debates. Sixteen essays by both established and emerging scholars discussing key romantic themes and concerns highlight the diversity within both romantic thought and its contemporary reception. Part 1 consists of the first published encounter between Manfred Frank and Frederick Beiser, in which the two major scholars discuss their differing interpretations of philosophical romanticism. Part 2 draws significant connections between romantic conceptions of history, sociability, hermeneutics, and education and explores the ways in which these views can illuminate questions in contemporary social-political philosophy and theories of interpretation. Part 3 consists in some of the most innovative takes on romantic aesthetics, which seek to bring romantic thought into dialogue, with, for instance, contemporary analytic aesthetics and theories of cognition. Part 4 offers a rare rigorous engagement with romantic conceptions of science, and demonstrates ways in which the romantic view of nature, experimentation, and mathematics need not be relegated to historical curiosities.Less

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 “persist,” and the questions that the romantics raised remain relevant today. *The Relevance of Romanticism: Essays on Early German Romantic Philosophy* is the first collection of essays that directly considers the reasons why philosophers have recently become deeply interested in romantic thought. Through historical and systematic reconstructions, the volume offers greater understanding of romanticism as a philosophical movement and deeper insight into the role that romantic thought plays—or can play—in contemporary philosophical debates. Sixteen essays by both established and emerging scholars discussing key romantic themes and concerns highlight the diversity within *both* romantic thought *and* its contemporary reception. Part 1 consists of the first published encounter between Manfred Frank and Frederick Beiser, in which the two major scholars discuss their differing interpretations of philosophical romanticism. Part 2 draws significant connections between romantic conceptions of history, sociability, hermeneutics, and education and explores the ways in which these views can illuminate questions in contemporary social-political philosophy and theories of interpretation. Part 3 consists in some of the most innovative takes on romantic aesthetics, which seek to bring romantic thought into dialogue, with, for instance, contemporary analytic aesthetics and theories of cognition. Part 4 offers a rare rigorous engagement with romantic conceptions of science, and demonstrates ways in which the romantic view of nature, experimentation, and mathematics need not be relegated to historical curiosities.