Modern incarnations of the Aristotelian concepts of Continuum and Topos
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866912088362844160 |
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| author | Protin, Clarence |
| author_facet | Protin, Clarence |
| contents | The aim of this paper is i) to argue for the feasibility and fruitfulness of a balance between the phenomenological method seeking intuitive evidence and the axiomatic-deductive method and ii) that there should be a mutual understanding between philosophy and mathematics and a cultivation of a historical self-awareness with regards to their common source in Greek philosophy. To this end we show how Aristotle's theory of \emph{sunekhês, apeiron} and \emph{topos} and related notions can be given a rigorous interpretation in terms of modern topology and geometry as well as category theory. This is facilitated by the fact that in Aristotle himself we already find a balance between intuition and formal logic. We also show how these powerful Aristotelian intuitions and concepts are found incarnated in diverse domains of modern mathematics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_05889 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Modern incarnations of the Aristotelian concepts of Continuum and Topos Protin, Clarence History and Overview Category Theory 03-02 18-02 The aim of this paper is i) to argue for the feasibility and fruitfulness of a balance between the phenomenological method seeking intuitive evidence and the axiomatic-deductive method and ii) that there should be a mutual understanding between philosophy and mathematics and a cultivation of a historical self-awareness with regards to their common source in Greek philosophy. To this end we show how Aristotle's theory of \emph{sunekhês, apeiron} and \emph{topos} and related notions can be given a rigorous interpretation in terms of modern topology and geometry as well as category theory. This is facilitated by the fact that in Aristotle himself we already find a balance between intuition and formal logic. We also show how these powerful Aristotelian intuitions and concepts are found incarnated in diverse domains of modern mathematics. |
| title | Modern incarnations of the Aristotelian concepts of Continuum and Topos |
| topic | History and Overview Category Theory 03-02 18-02 |
| url | https://arxiv.org/abs/2105.05889 |