Plato was not a mathematical Platonist
This text shows that Plato keeps a clear distinction between mathematical and metaphysical realism and the knife he uses to slice the difference is method. The philosopher's dialectical method requires that we tether the truth of hypotheses to existing metaphysical objects. The mathematician�...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press
2023.
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| Edición: | First edition |
| Colección: | Cambridge elements. Elements in the philosophy of mathematics.
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009769420206719 |
| Sumario: | This text shows that Plato keeps a clear distinction between mathematical and metaphysical realism and the knife he uses to slice the difference is method. The philosopher's dialectical method requires that we tether the truth of hypotheses to existing metaphysical objects. The mathematician's hypothetical method, by contrast, takes hypotheses as if they were first principles, so no metaphysical account of their truth is needed. Thus, we come to Plato's methodological as - if realism: in mathematics, we treat our hypotheses as if they were first principles, and, consequently, our objects as if they existed, and we do this for the purpose of solving problems. Taking the road suggested by Plato's 'Republic', this book shows that methodological commitments to mathematical objects are made in light of mathematical practice; foundational considerations; and, mathematical applicability. |
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| Notas: | Also issued in print: 2023. "An online version of this work is published at doi.org/10.1017/9781009313797 under a Creative Commons Open Access license CC-BY-NC-ND 4.0 which permits re-use, distribution and reproduction in any medium for non-commercial purposes providing appropriate credit to the original work is given"--Title page verso. |
| Descripción Física: | 1 online resource (48 pages) : digital, PDF file(s) |
| Público: | Specialized. |
| Bibliografía: | Includes bibliographical references. |
| ISBN: | 9781009313773 9781009313803 9781009313797 |
| Acceso: | Open Access. |
