Can We Identify the Theorem in Metaphysics 9, 1051a24-27 with Euclid’s Proposition 32? Geometric Deductions for the Discovery of Mathematical Knowledge
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Universidad Panamericana
2023
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| author | Francisco Miguel Ortiz Delgado |
| author_facet | Francisco Miguel Ortiz Delgado |
| contents | Can We Identify the Theorem in Metaphysics 9, 1051a24-27 with Euclid’s Proposition 32? Geometric Deductions for the Discovery of Mathematical Knowledge Francisco Miguel Ortiz Delgado Filosofía theorems Aristotle actuality potentiality ancient geometry This paper has two specific goals. The first is to demonstrate that the theorem in Metaphysics Θ 9, 1051a24-27 is not equivalent to Euclid’s Proposition 32 of book I (which contradicts some Aristotelian commentators, such as W. D. Ross, J. L. Heiberg, and T. L. Heith). Agreeing with Henry Mendell’s analysis, I argue that the two theorems are not equivalent, but I offer different reasons for such divergence: I propose a pedagogical-philosophical reason for the Aristotelian theorem being shorter than the Euclidean one (and the previous Aristotelian versions). Aristotle wants to emphasize the deductive procedure as a satisfactory method to discover scientific knowledge. The second objective, opposing some consensus about geometrical deductions/theorems in Aristotle, is to briefly propose that the theorem, exactly as we found it in Metaphysics and without any emendation to the text (therefore opposing Henry Mendell’s suggested amendments), allows the ancient philosopher to demonstrate that universal mathematical knowledge is in potence in geometrical figures. This tentatively proves that Aristotle emphasizes that geometrical deduction is sufficient to actualize mathematical knowledge. 2023 artículo científico 0188-6649 https://www.redalyc.org/articulo.oa?id=323075167002 https://www.redalyc.org/journal/3230/323075167002/ https://www.redalyc.org/journal/3230/323075167002/html/ https://www.redalyc.org/journal/3230/323075167002/323075167002.epub https://www.redalyc.org/journal/3230/323075167002/movil 10.21555/top.v660.2155 en http://www.redalyc.org/revista.oa?id=3230 Tópicos, Revista de Filosofía application/pdf Universidad Panamericana Tópicos, Revista de Filosofía (México) Num.66 |
| format | Artículo científico |
| id | redalyc_323075167002 |
| institution | Redalyc |
| language | en |
| publishDate | 2023 |
| publisher | Universidad Panamericana |
| spellingShingle | Can We Identify the Theorem in Metaphysics 9, 1051a24-27 with Euclid’s Proposition 32? Geometric Deductions for the Discovery of Mathematical Knowledge Francisco Miguel Ortiz Delgado Filosofía theorems Aristotle actuality potentiality ancient geometry Can We Identify the Theorem in Metaphysics 9, 1051a24-27 with Euclid’s Proposition 32? Geometric Deductions for the Discovery of Mathematical Knowledge Francisco Miguel Ortiz Delgado Filosofía theorems Aristotle actuality potentiality ancient geometry This paper has two specific goals. The first is to demonstrate that the theorem in Metaphysics Θ 9, 1051a24-27 is not equivalent to Euclid’s Proposition 32 of book I (which contradicts some Aristotelian commentators, such as W. D. Ross, J. L. Heiberg, and T. L. Heith). Agreeing with Henry Mendell’s analysis, I argue that the two theorems are not equivalent, but I offer different reasons for such divergence: I propose a pedagogical-philosophical reason for the Aristotelian theorem being shorter than the Euclidean one (and the previous Aristotelian versions). Aristotle wants to emphasize the deductive procedure as a satisfactory method to discover scientific knowledge. The second objective, opposing some consensus about geometrical deductions/theorems in Aristotle, is to briefly propose that the theorem, exactly as we found it in Metaphysics and without any emendation to the text (therefore opposing Henry Mendell’s suggested amendments), allows the ancient philosopher to demonstrate that universal mathematical knowledge is in potence in geometrical figures. This tentatively proves that Aristotle emphasizes that geometrical deduction is sufficient to actualize mathematical knowledge. 2023 artículo científico 0188-6649 https://www.redalyc.org/articulo.oa?id=323075167002 https://www.redalyc.org/journal/3230/323075167002/ https://www.redalyc.org/journal/3230/323075167002/html/ https://www.redalyc.org/journal/3230/323075167002/323075167002.epub https://www.redalyc.org/journal/3230/323075167002/movil 10.21555/top.v660.2155 en http://www.redalyc.org/revista.oa?id=3230 Tópicos, Revista de Filosofía application/pdf Universidad Panamericana Tópicos, Revista de Filosofía (México) Num.66 |
| title | Can We Identify the Theorem in Metaphysics 9, 1051a24-27 with Euclid’s Proposition 32? Geometric Deductions for the Discovery of Mathematical Knowledge |
| topic | Filosofía theorems Aristotle actuality potentiality ancient geometry |
| url | https://www.redalyc.org/articulo.oa?id=323075167002 https://www.redalyc.org/journal/3230/323075167002/ https://www.redalyc.org/journal/3230/323075167002/html/ https://www.redalyc.org/journal/3230/323075167002/323075167002.epub https://www.redalyc.org/journal/3230/323075167002/movil |