Aristotelian objections and post-Aristotelian responses to Plato's elemental theory, 2012
By: Mueller, Ian, Wilberding, James (Ed.), Horn, Christoph (Ed.)
Title Aristotelian objections and post-Aristotelian responses to Plato's elemental theory
Type Book Section
Language English
Date 2012
Published in Neoplatonism and the Philosophy of Nature
Pages 129-146
Categories no categories
Author(s) Mueller, Ian
Editor(s) Wilberding, James , Horn, Christoph
Translator(s)
Aristotle and Plato advanced very different theories of the traditional four elements. Whereas Plato in his Timaeus proposes a geometrical theory of these elements, Aristotle in his On the Heavens (and On Generation and Corruption) offers a qualitative analysis and offers a series of objections to Plato’s theory. These objections provided later Platonists with the opportunity to defend Plato against and possibly harmonize him with Aristotle. This paper explores Simplicius’ responses to Aristotle one by one, paying particular attention to the brand of scientific discourse that he engages in with Proclus, and to how different commitments to harmonization affect their responses to these objections. [Author’s abstract]

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In fact, precisely because these thinkers did see the sensible world as an image of the intelligible world, they devoted much time and energy to understanding its inner workings. Thus we find Neoplatonists writing on embryology, physiology, meteorology, astronomy, and much else. This volume collects essays by leading international scholars in the field that shed new light on how these thinkers sought to understand and explain nature and natural phenomena. It is thematically divided into two parts, with the first part\u2014\u2018The general metaphysics of Nature\u2019\u2014directed at the explication of central Neoplatonic metaphysical doctrines and their relation to the natural world, and the second part\u2014\u2019Platonic approaches to individual sciences\u2019\u2014showing how these same doctrines play out in individual natural sciences such as elemental physics, geography, and biology. Together these essays show that a serious examination of Neoplatonic natural philosophy has far-reaching consequences for our general understanding of the metaphysics of Platonism, as well as for our evaluation of their place in the history of science.","republication_of":null,"online_url":"","online_resources":"https:\/\/uni-koeln.sciebo.de\/s\/xHUG6gdrtjMT7K4","translation_of":null,"new_edition_of":null,"is_catalog":0,"in_bibliography":0,"is_inactive":0,"notes":null,"doi_url":null,"book":{"id":299,"pubplace":"Oxford","publisher":"Oxford University Press","series":"","volume":"","edition_no":null,"valid_from":null,"valid_until":null}}},"article":null},"sort":[2012]}

What's the Matter? Some Neo-Platonist Answers, 2010
By: Mueller, Ian, Mohr, Richard D. (Ed.), Sattler, Barbara M. (Ed.)
Title What's the Matter? Some Neo-Platonist Answers
Type Book Section
Language English
Date 2010
Published in One Book, The Whole Universe: Plato’s Timaeus Today
Pages 151-163
Categories no categories
Author(s) Mueller, Ian
Editor(s) Mohr, Richard D. , Sattler, Barbara M.
Translator(s)
In this essay I want to say a very few things about Neo-Platonist interpretations of the T im aeus relating to the receptacle and the geometric characterization of earth, water, air, and fire. The starting point of my reflections was translating Simplicius’ commentary on books 3 and 4 of Aristotle’s On th e H eavens, and much of what I say is based upon that. But I will also be invoking a passage from his commentary on Aristotle’s Physics and some material in John Philoponus and Proclus. I begin with some remarks about Simplicius’ basic conception of what we call Aristotle’s criticisms of Plato. [p. 151]

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Mathematics and Philosophy in Proclus' Commentary on Book I of Euclid's Elements, 1987
By: Mueller, Ian, Pépin, Jean (Ed.), Saffrey, Henri Dominique (Ed.)
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]

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Aristotle and Simplicius on Mathematical Infinity, 1981
By: Mueller, Ian, Theodōrakopulos, Iōannēs Nikolaou (Ed.)
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. [author's abstract]

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  • PAGE 1 OF 1
Aristotelian objections and post-Aristotelian responses to Plato's elemental theory, 2012
By: Mueller, Ian, Wilberding, James (Ed.), Horn, Christoph (Ed.)
Title Aristotelian objections and post-Aristotelian responses to Plato's elemental theory
Type Book Section
Language English
Date 2012
Published in Neoplatonism and the Philosophy of Nature
Pages 129-146
Categories no categories
Author(s) Mueller, Ian
Editor(s) Wilberding, James , Horn, Christoph
Translator(s)
Aristotle and Plato advanced very different theories of the traditional four elements. Whereas Plato in his Timaeus proposes a geometrical theory of these elements, Aristotle in his On the Heavens (and On Generation and Corruption) offers a qualitative analysis and offers a series of objections to Plato’s theory. These objections provided later Platonists with the opportunity to defend Plato against and possibly harmonize him with Aristotle. This paper explores Simplicius’ responses to Aristotle one by one, paying particular attention to the brand of scientific discourse that he engages in with Proclus, and to how different commitments to harmonization affect their responses to these objections. [Author’s abstract]

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[Author\u2019s abstract]","btype":2,"date":"2012","language":"English","online_url":"","online_resources":"https:\/\/uni-koeln.sciebo.de\/s\/QlpIOoX7gUxpkrf","doi_url":null,"categories":[],"authors":[{"id":270,"full_name":"Mueller, Ian","role":{"id":1,"role_name":"author"}},{"id":257,"full_name":"Wilberding, James","role":{"id":2,"role_name":"editor"}},{"id":256,"full_name":"Horn, Christoph","role":{"id":2,"role_name":"editor"}}],"book":null,"booksection":{"id":812,"section_of":299,"pages":"129-146","is_catalog":null,"book":{"id":299,"bilderberg_idno":null,"dare_idno":null,"catalog_idno":null,"entry_type":null,"type":4,"language":"en","title":"Neoplatonism and the Philosophy of Nature","title_transcript":"","title_translation":"","short_title":"Horn\/Wilberding2012","has_no_author":null,"volume":null,"date":"2012","edition_no":null,"free_date":"2012","abstract":"Despite Platonism\u2019s unquestioned claim to being one of the most influential movements in the history of philosophy, for a long time the conventional wisdom was that Platonists of late antiquity\u2014or Neoplatonists\u2014were so focused on other-worldly metaphysics that they simply neglected any serious study of the sensible world, which after all is \u2018merely\u2019 an image of the intelligible world, and only recently has this conventional wisdom begun to be dispelled. In fact, precisely because these thinkers did see the sensible world as an image of the intelligible world, they devoted much time and energy to understanding its inner workings. Thus we find Neoplatonists writing on embryology, physiology, meteorology, astronomy, and much else. This volume collects essays by leading international scholars in the field that shed new light on how these thinkers sought to understand and explain nature and natural phenomena. It is thematically divided into two parts, with the first part\u2014\u2018The general metaphysics of Nature\u2019\u2014directed at the explication of central Neoplatonic metaphysical doctrines and their relation to the natural world, and the second part\u2014\u2019Platonic approaches to individual sciences\u2019\u2014showing how these same doctrines play out in individual natural sciences such as elemental physics, geography, and biology. Together these essays show that a serious examination of Neoplatonic natural philosophy has far-reaching consequences for our general understanding of the metaphysics of Platonism, as well as for our evaluation of their place in the history of science.","republication_of":null,"online_url":"","online_resources":"https:\/\/uni-koeln.sciebo.de\/s\/xHUG6gdrtjMT7K4","translation_of":null,"new_edition_of":null,"is_catalog":0,"in_bibliography":0,"is_inactive":0,"notes":null,"doi_url":null,"book":{"id":299,"pubplace":"Oxford","publisher":"Oxford University Press","series":"","volume":"","edition_no":null,"valid_from":null,"valid_until":null}}},"article":null},"sort":["Aristotelian objections and post-Aristotelian responses to Plato's elemental theory"]}

Aristotle and Simplicius on Mathematical Infinity, 1981
By: Mueller, Ian, Theodōrakopulos, Iōannēs Nikolaou (Ed.)
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. [author's abstract]

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Mathematics and Philosophy in Proclus' Commentary on Book I of Euclid's Elements, 1987
By: Mueller, Ian, Pépin, Jean (Ed.), Saffrey, Henri Dominique (Ed.)
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]

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What's the Matter? Some Neo-Platonist Answers, 2010
By: Mueller, Ian, Mohr, Richard D. (Ed.), Sattler, Barbara M. (Ed.)
Title What's the Matter? Some Neo-Platonist Answers
Type Book Section
Language English
Date 2010
Published in One Book, The Whole Universe: Plato’s Timaeus Today
Pages 151-163
Categories no categories
Author(s) Mueller, Ian
Editor(s) Mohr, Richard D. , Sattler, Barbara M.
Translator(s)
In this essay I want to say a very few things about Neo-Platonist interpretations 
of the T im aeus relating to the receptacle and the geometric characterization of 
earth, water, air, and fire. The starting point of my reflections was translating 
Simplicius’ commentary on books 3 and 4 of Aristotle’s  On  th e H eavens, and 
much of what I say is based upon that. But I will also be invoking a passage from 
his commentary on Aristotle’s Physics and some material in John Philoponus and 
Proclus. I begin with some remarks about Simplicius’ basic conception of what 
we call Aristotle’s criticisms of Plato. [p. 151]

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