The Euclidean Programme:
The Euclidean Programme embodies a traditional sort of epistemological foundationalism, according to which knowledge - especially mathematical knowledge - is obtained by deduction from self-evident axioms or first principles. Epistemologists have examined foundationalism extensively, but neglected i...
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2024
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| Schriftenreihe: | Cambridge elements. Elements in the philosophy of mathematics
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| Links: | https://doi.org/10.1017/9781009221955 |
| Zusammenfassung: | The Euclidean Programme embodies a traditional sort of epistemological foundationalism, according to which knowledge - especially mathematical knowledge - is obtained by deduction from self-evident axioms or first principles. Epistemologists have examined foundationalism extensively, but neglected its historically dominant Euclidean form. By contrast, this book offers a detailed examination of Euclidean foundationalism, which, following Lakatos, the authors call the Euclidean Programme. The book rationally reconstructs the programme's key principles, showing it to be an epistemological interpretation of the axiomatic method. It then compares the reconstructed programme with select historical sources: Euclid's Elements, Aristotle's Posterior Analytics, Descartes's Discourse on Method, Pascal's On the Geometric Mind and a twentieth-century account of axiomatisation. The second half of the book philosophically assesses the programme, exploring whether various areas of contemporary mathematics conform to it. The book concludes by outlining a replacement for the Euclidean Programme. |
| Umfang: | 1 Online-Ressource (73 Seiten) |
| ISBN: | 9781009221955 |
| ISSN: | 2399-2883 |
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| 520 | |a The Euclidean Programme embodies a traditional sort of epistemological foundationalism, according to which knowledge - especially mathematical knowledge - is obtained by deduction from self-evident axioms or first principles. Epistemologists have examined foundationalism extensively, but neglected its historically dominant Euclidean form. By contrast, this book offers a detailed examination of Euclidean foundationalism, which, following Lakatos, the authors call the Euclidean Programme. The book rationally reconstructs the programme's key principles, showing it to be an epistemological interpretation of the axiomatic method. It then compares the reconstructed programme with select historical sources: Euclid's Elements, Aristotle's Posterior Analytics, Descartes's Discourse on Method, Pascal's On the Geometric Mind and a twentieth-century account of axiomatisation. The second half of the book philosophically assesses the programme, exploring whether various areas of contemporary mathematics conform to it. The book concludes by outlining a replacement for the Euclidean Programme. | ||
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| isbn | 9781009221955 |
| issn | 2399-2883 |
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| series2 | Cambridge elements. Elements in the philosophy of mathematics |
| spelling | Paseau, A. C. The Euclidean Programme A.C. Paseau, Wesley Wrigley Cambridge Cambridge University Press 2024 1 Online-Ressource (73 Seiten) txt c cr Cambridge elements. Elements in the philosophy of mathematics 2399-2883 The Euclidean Programme embodies a traditional sort of epistemological foundationalism, according to which knowledge - especially mathematical knowledge - is obtained by deduction from self-evident axioms or first principles. Epistemologists have examined foundationalism extensively, but neglected its historically dominant Euclidean form. By contrast, this book offers a detailed examination of Euclidean foundationalism, which, following Lakatos, the authors call the Euclidean Programme. The book rationally reconstructs the programme's key principles, showing it to be an epistemological interpretation of the axiomatic method. It then compares the reconstructed programme with select historical sources: Euclid's Elements, Aristotle's Posterior Analytics, Descartes's Discourse on Method, Pascal's On the Geometric Mind and a twentieth-century account of axiomatisation. The second half of the book philosophically assesses the programme, exploring whether various areas of contemporary mathematics conform to it. The book concludes by outlining a replacement for the Euclidean Programme. Wrigley, Wesley Erscheint auch als Druck-Ausgabe 9781009221986 Erscheint auch als Druck-Ausgabe 9781009494403 |
| spellingShingle | Paseau, A. C. The Euclidean Programme |
| title | The Euclidean Programme |
| title_auth | The Euclidean Programme |
| title_exact_search | The Euclidean Programme |
| title_full | The Euclidean Programme A.C. Paseau, Wesley Wrigley |
| title_fullStr | The Euclidean Programme A.C. Paseau, Wesley Wrigley |
| title_full_unstemmed | The Euclidean Programme A.C. Paseau, Wesley Wrigley |
| title_short | The Euclidean Programme |
| title_sort | euclidean programme |
| work_keys_str_mv | AT paseauac theeuclideanprogramme AT wrigleywesley theeuclideanprogramme AT paseauac euclideanprogramme AT wrigleywesley euclideanprogramme |