| Title | Mathematics and Philosophy in Proclus' Commentary on Book I of Euclid's Elements |
| Type | Book Section |
| Language | English |
| Date | 1987 |
| Published in | Proclus, lecteur et interprète des anciens. Actes du colloque international du CNRS, Paris (2-4 octobre 1985) |
| Pages | 305-318 |
| Categories | no categories |
| Author(s) | Mueller, Ian |
| Editor(s) | Pépin, Jean , Saffrey, Henri Dominique |
| Translator(s) |
| In the prologue to his commentary on book I of Euclid’s Elements Proclus refers to two areas of disagreement among the Platonists concerning mathematics. In the first passage in which he does this (29.14ff.) he indicates that some philoi from his own hearth encourage students to disdain mathematics, enlisting on their side Plato himself because of some of Socrates’ remarks in the Republic, notably the rhetorical question of 533 c 3-5 [...]. The second passage comes at the end of Proclus’ famous description of the character of geometry [...]. In this paper I wish to pursue these disagreements in the hopes of throwing light on distinctive features of Proclus’ philosophy of mathematics. [Introduction, p. 305] |
| Online Resources | https://uni-koeln.sciebo.de/s/pxjytHOeGkGM4YU |
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| Title | Aristotle and Simplicius on Mathematical Infinity |
| Type | Book Section |
| Language | English |
| Date | 1981 |
| Published in | Proceedings of the World Congress on Aristotle, Thessaloniki August 7-14 1978 |
| Pages | 179-182 |
| Categories | no categories |
| Author(s) | Mueller, Ian |
| Editor(s) | Theodōrakopulos, Iōannēs Nikolaou |
| Translator(s) |
| Aristotle was the first not only to distinguish between potential and actual infinity but also to insist that potential infinity alone is enough for mathematics thus initiating an issue still central to the philosophy of mathematics. Modern scholarship, however, has attacked Aristotle's thesis because, according to the received doctrine, it does not square with Euclidean geometry and it also seems to contravene Aristotle's belief in the finitude of the physical universe. This monograph, the first thorough study of the issue, puts Aristotle's views on infinity in the proper perspective. Through a close study of the relevant Aristotelian passages it shows that the Stagirite's theory of infinity forms a well argued philosophical position which does not bear on his belief in a finite cosmos and does not undermine the Euclidean nature of geometry. The monograph draws a much more positive picture of Aristotle's views and reaffirms his disputed stature as a serious philosopher of mathematics. This innovative and stimulating contribution will be essential reading to a wide range of scholars, including classicists, philosophers of science and mathematics as well as historians of ideas. [offical abstract] |
| Online Resources | https://uni-koeln.sciebo.de/s/DzSu75ClPoubkKm |
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| Title | Aristotle and Simplicius on Mathematical Infinity |
| Type | Book Section |
| Language | English |
| Date | 1981 |
| Published in | Proceedings of the World Congress on Aristotle, Thessaloniki August 7-14 1978 |
| Pages | 179-182 |
| Categories | no categories |
| Author(s) | Mueller, Ian |
| Editor(s) | Theodōrakopulos, Iōannēs Nikolaou |
| Translator(s) |
Aristotle was the first not only to distinguish between potential and actual infinity but also to insist that potential infinity alone is enough for mathematics thus initiating an issue still central to the philosophy of mathematics. Modern scholarship, however, has attacked Aristotle's thesis because, according to the received doctrine, it does not square with Euclidean geometry and it also seems to contravene Aristotle's belief in the finitude of the physical universe. This monograph, the first thorough study of the issue, puts Aristotle's views on infinity in the proper perspective. Through a close study of the relevant Aristotelian passages it shows that the Stagirite's theory of infinity forms a well argued philosophical position which does not bear on his belief in a finite cosmos and does not undermine the Euclidean nature of geometry. The monograph draws a much more positive picture of Aristotle's views and reaffirms his disputed stature as a serious philosopher of mathematics. This innovative and stimulating contribution will be essential reading to a wide range of scholars, including classicists, philosophers of science and mathematics as well as historians of ideas. [offical abstract] |
| Online Resources | https://uni-koeln.sciebo.de/s/DzSu75ClPoubkKm |
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| Title | Mathematics and Philosophy in Proclus' Commentary on Book I of Euclid's Elements |
| Type | Book Section |
| Language | English |
| Date | 1987 |
| Published in | Proclus, lecteur et interprète des anciens. Actes du colloque international du CNRS, Paris (2-4 octobre 1985) |
| Pages | 305-318 |
| Categories | no categories |
| Author(s) | Mueller, Ian |
| Editor(s) | Pépin, Jean , Saffrey, Henri Dominique |
| Translator(s) |
In the prologue to his commentary on book I of Euclid’s Elements Proclus refers to two areas of disagreement among the Platonists concerning mathematics. In the first passage in which he does this (29.14ff.) he indicates that some philoi from his own hearth encourage students to disdain mathematics, enlisting on their side Plato himself because of some of Socrates’ remarks in the Republic, notably the rhetorical question of 533 c 3-5 [...]. The second passage comes at the end of Proclus’ famous description of the character of geometry [...]. In this paper I wish to pursue these disagreements in the hopes of throwing light on distinctive features of Proclus’ philosophy of mathematics. [Introduction, p. 305] |
| Online Resources | https://uni-koeln.sciebo.de/s/pxjytHOeGkGM4YU |
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