PROCLUS on HESIOD's WORKS and DAYS Patrizia Marzillo
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Proclus on the Elements and the Celestial Bodies
PROCLUS ON THE ELEMENTS AND THE CELESTIAL BODIES PHYSICAL TH UGHT IN LATE NEOPLAT NISM Lucas Siorvanes A Thesis submitted for the Degree of Doctor of Philosophy to the Dept. of History and Philosophy of Science, Science Faculty, University College London. Deuember 1986 - 2 - ABSTRACT Until recently, the period of Late Antiquity had been largely regarded as a sterile age of irrationality and of decline in science. This pioneering work, supported by first-hand study of primary sources, argues that this opinion is profoundly mistaken. It focuses in particular on Proclus, the head of the Platonic School at Athens in the 5th c. AD, and the chief spokesman for the ideas of the dominant school of thought of that time, Neoplatonism. Part I, divided into two Sections, is an introductory guide to Proclus' philosophical and cosmological system, its general principles and its graded ordering of the states of existence. Part II concentrates on his physical theories on the Elements and the celestial bodies, in Sections A and B respectively, with chapters (or sub-sections) on topics including the structure, properties and motion of the Elements; light; space and matter; the composition and motion of the celestial bodies; and the order of planets. The picture that emerges from the study is that much of the Aristotelian physics, so prevalent in Classical Antiquity, was rejected. The concepts which were developed instead included the geometrization of matter, the four-Element composition of the universe, that of self-generated, free motion in space for the heavenly bodies, and that of immanent force or power. -
Plato As "Architectof Science"
Plato as "Architectof Science" LEONID ZHMUD ABSTRACT The figureof the cordialhost of the Academy,who invitedthe mostgifted math- ematiciansand cultivatedpure research, whose keen intellectwas able if not to solve the particularproblem then at least to show the methodfor its solution: this figureis quite familiarto studentsof Greekscience. But was the Academy as such a centerof scientificresearch, and did Plato really set for mathemati- cians and astronomersthe problemsthey shouldstudy and methodsthey should use? Oursources tell aboutPlato's friendship or at leastacquaintance with many brilliantmathematicians of his day (Theodorus,Archytas, Theaetetus), but they were neverhis pupils,rather vice versa- he learnedmuch from them and actively used this knowledgein developinghis philosophy.There is no reliableevidence that Eudoxus,Menaechmus, Dinostratus, Theudius, and others, whom many scholarsunite into the groupof so-called"Academic mathematicians," ever were his pupilsor close associates.Our analysis of therelevant passages (Eratosthenes' Platonicus, Sosigenes ap. Simplicius, Proclus' Catalogue of geometers, and Philodemus'History of the Academy,etc.) shows thatthe very tendencyof por- trayingPlato as the architectof sciencegoes back to the earlyAcademy and is bornout of interpretationsof his dialogues. I Plato's relationship to the exact sciences used to be one of the traditional problems in the history of ancient Greek science and philosophy.' From the nineteenth century on it was examined in various aspects, the most significant of which were the historical, philosophical and methodological. In the last century and at the beginning of this century attention was paid peredominantly, although not exclusively, to the first of these aspects, especially to the questions how great Plato's contribution to specific math- ematical research really was, and how reliable our sources are in ascrib- ing to him particular scientific discoveries. -
Chapter Two Democritus and the Different Limits to Divisibility
CHAPTER TWO DEMOCRITUS AND THE DIFFERENT LIMITS TO DIVISIBILITY § 0. Introduction In the previous chapter I tried to give an extensive analysis of the reasoning in and behind the first arguments in the history of philosophy in which problems of continuity and infinite divisibility emerged. The impact of these arguments must have been enormous. Designed to show that rationally speaking one was better off with an Eleatic universe without plurality and without motion, Zeno’s paradoxes were a challenge to everyone who wanted to salvage at least those two basic features of the world of common sense. On the other hand, sceptics, for whatever reason weary of common sense, could employ Zeno-style arguments to keep up the pressure. The most notable representative of the latter group is Gorgias, who in his book On not-being or On nature referred to ‘Zeno’s argument’, presumably in a demonstration that what is without body and does not have parts, is not. It is possible that this followed an earlier argument of his that whatever is one, must be without body.1 We recognize here what Aristotle calls Zeno’s principle, that what does not have bulk or size, is not. Also in the following we meet familiar Zenonian themes: Further, if it moves and shifts [as] one, what is, is divided, not being continuous, and there [it is] not something. Hence, if it moves everywhere, it is divided everywhere. But if that is the case, then everywhere it is not. For it is there deprived of being, he says, where it is divided, instead of ‘void’ using ‘being divided’.2 Gorgias is talking here about the situation that there is motion within what is. -
Proclus and Artemis: on the Relevance of Neoplatonism to the Modern Study of Ancient Religion
Kernos Revue internationale et pluridisciplinaire de religion grecque antique 13 | 2000 Varia Proclus and Artemis: On the Relevance of Neoplatonism to the Modern Study of Ancient Religion Spyridon Rangos Electronic version URL: http://journals.openedition.org/kernos/1293 DOI: 10.4000/kernos.1293 ISSN: 2034-7871 Publisher Centre international d'étude de la religion grecque antique Printed version Date of publication: 1 January 2000 ISSN: 0776-3824 Electronic reference Spyridon Rangos, « Proclus and Artemis: On the Relevance of Neoplatonism to the Modern Study of Ancient Religion », Kernos [Online], 13 | 2000, Online since 21 April 2011, connection on 01 May 2019. URL : http://journals.openedition.org/kernos/1293 ; DOI : 10.4000/kernos.1293 Kernos Kernos, 13 (2000), p. 47-84. Proclus and Artemis: On the Relevance of Neoplatonism to the Modern Study of Andent Religion* Imagine the situation in which contemporary philosophers would find themselves if Wittgenstein introduced, in his Philosophical Investigations, the religious figure of Jesus as Logos and Son of God in order to illuminate the puzzlement ofthe private-language paradox, or if in the second division of Being and Time Heidegger mentioned the archangel Michael to support the argument of 'being toward death'. Similar is the perplexity that a modern reader is bound to encounter when, after a highly sophisticated analysis of demanding metaphysical questions about the relationship of the one and the many, finitude and infinity, mind and body, Proclus, l in ail seriousness and without the slightest touch of irony, assigns to some traditional gods of Greek polytheism a definitive place in the structure of being. -
Neoplatonic Asclepius: Science and Religion at the Crossroads of Aristotelian Biology, Hippocratic Medicine and Platonic Theurgy
Studia Antiqua et Archaeologica 23(2): 333–349 Neoplatonic Asclepius: Science and religion at the crossroads of Aristotelian biology, Hippocratic medicine and Platonic theurgy Eugene AFONASIN1 Abstract. In the first part of the paper, I will briefly discuss certain peculiarities of the medical profession in antiquity. In his Philosophical History (fr. 80–84 Athanassiadi) Damascius narrates about a philosopher, named Asclepiodotus, whose interests ranged from Platonic philosophy to Aristotelian natural sciences. Asclepiodotus’ instructor in medical matters, a son of a doctor from the island of Rhodos, Iacobus, is pictured by Damascius as an exemplary figure (fr. 84), who, unlike many of his contemporaries, always tested the opinions of others and gained a reputation of an extremely successful physician, although the methods of treatment, ascribed to him by Damascius, are highly reminiscent of those presented as the Pythagorean by Iamblichus (On the Pythagorean way of life 244). In this respect both Iacobus and Asclepiodotus are conformed to the best standards of medical ethics, and pass the test set by Galen in his “On examination by which the best physicians are recognized”, except perhaps by the fact that they preferred to base their activities on such authorities as Aristotle and the Methodist Soranus rather than on a list of the “dogmatists” proposed by Galen. In the second part of the paper, dedicated to the cult of Asclepius in Late Antiquity, I will look at various kinds of evidence taken from the Neoplatonic philosophers. Having discussed first the principal philosophical interpretations of Asclepius found in Apuleius, Aelianus, Macrobius, Julian, Porphyry, Iamblichus, Proclus, Damascius, etc., we turn to Proclus’ attitude to Athena and Asclepius as reflected in Marinus’ Vita Procli and finally discuss the cult of Eshmun as found in Damascius. -
Philosophy in Ancient Greek Biography. Turnhout: Brepols, 2016
Revista Classica, v. 30, n. 2, p. 137-142, 2017 137 BONAZZI, Mauro; SCHORN, Stefan. Bios Philosophos: Philosophy in Ancient Greek Biography. Turnhout: Brepols, 2016. 313p. ISBN 978-2-503-56546-0 Gustavo Laet Gomes* * Mestre em Filosofia Bernardo C. D. A. Vasconcelos** pela Universidade Federal de Minas Gerais. guslaet@ gmail.com Bios Philosophos. Philosophy in Ancient Greek Biography (Brepols, 2016), organized by Mauro Bonazzi and Stefan Schorn, delivers a ** Mestre em Filosofia pela both deep and wide tour through the philosophical aspects of Greek Universidade Federal biographical production. On one hand, it does not concentrate only in de Minas Gerais. the later periods of Greek philosophy, when biographical production bernardovasconcelos abounded, but goes all the way back to the fourth century BCE, when @gmail.com biographical texts were fragmentary and mingled with other styles. On the other, it tries to unveil the philosophical motives in the works of authors who tend to be disregarded as historians, biographers, hagiographers or even as mere fans of the most prominent figures of their own schools. In our review, we will attempt to give a brief account of the ten articles that make up this volume, which, in turn, will hopefully provide an overview of the different connections between the biographies and biographers and their philosophical motives. Thomas Bénatouïl’s Pythagore chez Dicéarque: anectodes biographiques et critique de la philosophie contemplative (p. 11-36) proposes an inversion of the traditional interpretation regarding the testimony of Dicaearchus of Messana about the life of Pythagoras. Since antiquity, Dicaearchus’ reports tend to be seen as positive, because they present a Pythagoras devoid of mysticism and apparently more interested in practical matters. -
A Acerbi, F., 45 Adam, C., 166–169, 171, 175, 176, 178–181, 183–185
Index A 80, 81, 84, 86, 87, 93, 97, 98, 107, 112, Acerbi, F., 45 137, 198, 201, 212, 233, 235, 236 Adam, C., 166–169, 171, 175, 176, 178–181, Arius Didymus, 35 183–185, 187, 188, 200, 201 Arnauld, 217, 227, 233, 239–242, 245 Adams, R.M., 234, 245, 306 Arnzen, R., 55 Adorno, T.W., 147 Arriaga, R.de, 6 Adrastos, 77–81, 89, 96 Arthur, R, 254 Aetius, 35 Athenaeus, 39 Agapius, 56 Atherton, M., 170, 174 Aglietta, M., 151 Aujac, G., 145 Aichelin, J., 232 Autolycus, 15, 20, 21, 23, 24 Aiken, J.A., 148 Ayers, M., 229 Aime, M., 145 Aksamija, N., 152 Alberti, L.B., 9, 148, 150 B Alembert, J.d', 70 Bacon, R., 165, 166 Alexander of Aphrodisias, 16, 35, 43, 54, 56, Banu Musa, 53 58, 61, 77, 78, 81 Barnes, J., 38, 212, 235 Algra, K., 34, 35, 38 Barozzi, F., 115, 119, 120 Al-Haytham, 164–167 Barrow, I., 6, 220 Alhazen, see Ibn Al-Haytham Basileides of Tyre, 37 Al-Khwārizmī, 92 Baudrillard, J., 144 Al-Kindī, 161, 162, 164, 165 Bayle, P., 237 Al-Nayrizi, 55–57, 59 Beauchamp, T.L., 274 Al-Sijzī, 110 Bechtle, G., 105 Allison, H.E., 283 Belting, H., 145, 148 Andronicus of Rhodes, 102 Benatouïl, T., 114 Apollodorus, 41, 42 Benjamin, W., 144, 145, 148 Apollonios of Perge (Apollonius), 15, 19–21, Bentley, R., 223–226 23–27, 37, 38, 52, 53, 63, 81, 106, 123 Berggren, J.L., 94 Apostle Thomas, 147 Berkeley, G., 11, 160, 161, 166, 170, 186 Aratus, 24 Bernadete, J., 212, 213 Arbini, R., 170 Bernanos, G., 137 Archedemus, 41 Bernoulli, J., 233 Archimedes, 15, 19–21, 23, 24, 27, 29, 38, 39, Bessel, F.W., 72 44, 45, 47, 68, 106, 123 Bioesmat-Martagon, L., 72 Ariew, R., 110, 212, 214 Blumenberg, H., 143 Aristaeus, 27 Boer, E., 93 Ariston, 39 Bolyai, J., 11 Aristotle, 3, 5, 6, 15, 16, 18, 19, 24–34, 36, Bonola, R., 70 40–45, 47–50, 55, 58, 60, 61, 68, 75, Borelli, G.A., 6 © Springer International Publishing Switzerland 2015 311 V. -
Assessing Porphyry's Reaction to Plotinus's Doctrine of The
HeyJ LII (2011), pp. 1–10 DOI: 10.1111/j.1468-2265.2011.00686.x PORPHYRY THE APOSTATE: ASSESSING PORPHYRY’S REACTION TO PLOTINUS’S DOCTRINE OF THE ONE SEAMUS O’NEILL Memorial University of Newfoundland St. John’s, Canada In an article in the first volume of Harris’s Studies in Neoplatonism, Patrick Atherton described what he saw as a radical difference between the trinitarian and Neoplatonic first principles. The distinction he draws is seminal: because the first principle, or , produces all things, all that follows from it is determined by its nature. Whereas the unity of what Atherton describes as the ‘Neoplatonic One’ transcends all relation and difference, The trinitarian , by contrast, appears as an attempt to reconcile the requirement of unity with that of difference within the principle itself: is now recognised as a moment within the unity, as belonging to the principle as unity. Such a position requires a very different interpretation of the relation between the principle and its derivatives than that found in Neoplatonism.1 Recent scholarship on Porphyry, however, suggests that the important distinction Atherton adverts to is not resolvable into distinctly Neoplatonic and trinitarian camps. What Atherton describes as ‘Neoplatonism’ is more diverse, as scholars debate the subtle differences between the doctrines of Plotinus, Porphyry, Iamblichus, Augustine, and Proclus, among others. For example, John Dillon and Steven Strange have recently argued that Porphyry’s doctrine of the first principle is in fact – as Atherton describes the two positions – ‘trinitarian’ rather than ‘Neoplatonic’. Atherton’s characterization of the Neoplatonic describes more narrowly the Plotinian One, for Plotinus is the only Neoplatonist who maintains the absolute transcendence of the first principle beyond all relation and difference. -
Naming the Principles in Democritus: an Epistemological Problem
apeiron 2017; 50(4): 435–448 Enrico Piergiacomi* Naming the Principles in Democritus: An Epistemological Problem DOI 10.1515/apeiron-2016-0058 Abstract: It is well known that Democritus posited two principles of reality, i. e. atoms and void, and that he gave them many names. Synonyms of atom include the terms “body”, “form” and “thing” or δέν, while void was also called “space”, “infinite” and “no-thing” or μηδέν. What usually escapes the attention of scholars is the problematic outcome that this apparently plain mode of expression raises at the epistemological level. Indeed, according to Proclus (In Plat. Crat. 16 = fr. 68 B 26 DK), Democritus believed that names are not established by nature, but by convention, which may imply that they do not express the true nature of the object named. Proclus gives four proofs on his behalf, among which we find the ἰσορροπία argument. Names do not have a natural link with the objects they refer to and, therefore, do not express their inner essence, since thesamethingwillreceivedifferent designations and meanings, none of which fully expresses its real φύσις. Now, I will argue that, if we apply this idea to the principles, it follows that Democritus may have acknowledged that they are not fully comprehensible to human beings. The fact that both the atom and the void are assigned different names/meanings shows that their nature escapes human under- standing.Atthesametime,Iwillalso briefly suggest that the “ἰσορροπία argument” does not lead to skepticism. Instead, it leads to a rational dog- matism, which recognizes that atoms and void exist, are known and can be expressed through language, although no mind can fully comprehend their essence. -
MATH 520 Fall 2007 Historical Background
MATH 520 – Foundations of Geometry Historical Background The word geometry is derived from the Greek words meaning “earth measure” implying that geometry involves measuring earthly things. Ancient geometry in part has its beginnings in the practical need necessary for the agriculture of the Babylonians (modern region is southern Iraq from around Baghdad to the Persian Gulf) and Egyptians, civilizations “known for their engineering prowess in marsh drainage, irrigation, flood control, and the erection of great edifices and structures” (Eves, 1969). There is evidence from clay tablets that the Babylonians (~ 1900 BC) were familiar with Pythagorean Triples long before Pythagoras lived. 1 The Egyptians used the formula ++= dbcaA ))(( to calculate the area of an arbitrary quadrilateral with 4 successive sides a, b, c, and d. This formula proves correct for rectangles but not for quadrilaterals in general. Not until the 6th century B.C. did mathematicians begin to question whether such empirical results were always true. The contemporary study of geometry bears little resemblance to its historical beginnings in that it does not necessarily require that we measure anything or even restrict ourselves to the earth. People/Characters Thales of Miletus (ca. 640 – 546 B.C.) Greek Most often credited with initiating the formal study of demonstrative geometry as a discipline – The Father of Demonstrative Geometry; A Wise Man of Antiquity Well traveled throughout Babylonia, Egypt, and the Middle East. Thales knew the work and culture of the regions. He began to generalize and demonstrate geometric propositions by using logical reasoning to argue in favor of propositions rather than simply going with the “it works so use it” method. -
Thomas Taylor's Dissent from Some 18Th
Leo Catana, Thomas Taylor’s dissent from some 18th-century views on Platonic philosophy' The ethical and theological context Catana, Leo Published in: International Journal of the Platonic Tradition DOI: 10.1163/18725473-12341262 Publication date: 2013 Document version Publisher's PDF, also known as Version of record Citation for published version (APA): Catana, L. (2013). Leo Catana, Thomas Taylor’s dissent from some 18th-century views on Platonic philosophy': The ethical and theological context. International Journal of the Platonic Tradition, 7(2), 180-220. https://doi.org/10.1163/18725473-12341262 Download date: 26. Sep. 2021 The International Journal of the Platonic Tradition The International Journal of the Platonic Tradition 7 (2013) 180-220 brill.com/jpt Thomas Taylor’s Dissent from Some 18th-Century Views on Platonic Philosophy: The Ethical and Theological Context Leo Catana University of Copenhagen [email protected] Abstract Thomas Taylor’s interpretation of Plato’s works in 1804 was condemned as guilty by association immediately after its publication. Taylor’s 1804 and 1809 reviewer thus made a hasty generalisation in which the qualities of Neoplatonism, assumed to be negative, were transferred to Taylor’s own interpretation, which made use of Neoplatonist thinkers. For this reason, Taylor has typically been marginalised as an interpreter of Plato. This article does not deny the association between Taylor and Neoplatonism. Instead, it examines the historical and historiographical reasons for the reviewer’s assumption that Neoplatonic readings of Plato are erroneous by definition. In particular, it argues that the reviewer relied on, and tacitly accepted, ethical and theological premises going back to the historiography of philosophy developed by Jacob Brucker in his Historia critica philosophiae (1742-44). -
SCHOLIA, COMMENTARIES, and LEXICA on SPECIFIC LITERARY WORKS 2 Scholia, Commentaries, and Lexica on Specific Literary Works
18 SCHOLIA, COMMENTARIES, AND LEXICA ON SPECIFIC LITERARY WORKS 2 Scholia, Commentaries, and Lexica on Specific Literary Works 2.1 ARCHAIC AND CLASSICAL POETRY This category includes the most famous and most often cited scholia. By far the most important are the Homer scholia, but those on Pindar and the Attic drama- tists are also significant. 2.1.1 Homer Ancient scholarship on Homer was extensive and of high quality, for the best scholars of antiquity devoted much of their time and energy to the Homeric poems. Work on Homer that could be described as scholarship goes back at least to the classical period and probably to the sixth century bc, and editing the text of Homer was one of the main tasks of the first Alexandrian scholars. Zenodotus, Aristophanes of Byzantium, and Aristarchus probably all produced editions of the Iliad and Odyssey, and Aristarchus wrote extensive commentaries, while Zenodotus and Aristophanes compiled glossaries of primarily Homeric words. In addition, the early and persistent use of Homer as a school text meant that there was a tradi- tion of school exegesis that reached back as far as the classical period. Though none of the very early work on Homer survives in its original form, a surprising amount is preserved in various later compilations, so we often know, for example, the read- ings of several different Alexandrian scholars for a particular passage, and even some of the arguments behind these readings (although the arguments preserved in later sources cannot always be assumed to be those of the editor himself). Two principal sources for the ancient scholarship on Homer survive: the scholia and Eustathius’ commentaries, both of which are gigantic works filling many vol- umes in modern editions.