A Hellenistic Legacy: the Foundation for an ‘Unorthodox’ World View Within the Byzantine Tradition
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Chrysippus's Dog As a Case Study in Non-Linguistic Cognition
Chrysippus’s Dog as a Case Study in Non-Linguistic Cognition Michael Rescorla Abstract: I critique an ancient argument for the possibility of non-linguistic deductive inference. The argument, attributed to Chrysippus, describes a dog whose behavior supposedly reflects disjunctive syllogistic reasoning. Drawing on contemporary robotics, I urge that we can equally well explain the dog’s behavior by citing probabilistic reasoning over cognitive maps. I then critique various experimentally-based arguments from scientific psychology that echo Chrysippus’s anecdotal presentation. §1. Language and thought Do non-linguistic creatures think? Debate over this question tends to calcify into two extreme doctrines. The first, espoused by Descartes, regards language as necessary for cognition. Modern proponents include Brandom (1994, pp. 145-157), Davidson (1984, pp. 155-170), McDowell (1996), and Sellars (1963, pp. 177-189). Cartesians may grant that ascribing cognitive activity to non-linguistic creatures is instrumentally useful, but they regard such ascriptions as strictly speaking false. The second extreme doctrine, espoused by Gassendi, Hume, and Locke, maintains that linguistic and non-linguistic cognition are fundamentally the same. Modern proponents include Fodor (2003), Peacocke (1997), Stalnaker (1984), and many others. Proponents may grant that non- linguistic creatures entertain a narrower range of thoughts than us, but they deny any principled difference in kind.1 2 An intermediate position holds that non-linguistic creatures display cognitive activity of a fundamentally different kind than human thought. Hobbes and Leibniz favored this intermediate position. Modern advocates include Bermudez (2003), Carruthers (2002, 2004), Dummett (1993, pp. 147-149), Malcolm (1972), and Putnam (1992, pp. 28-30). -
Mathematical Discourse in Philosophical Authors: Examples from Theon of Smyrna and Cleomedes on Mathematical Astronomy
Mathematical discourse in philosophical authors: Examples from Theon of Smyrna and Cleomedes on mathematical astronomy Nathan Sidoli Introduction Ancient philosophers and other intellectuals often mention the work of mathematicians, al- though the latter rarely return the favor.1 The most obvious reason for this stems from the im- personal nature of mathematical discourse, which tends to eschew any discussion of personal, or lived, experience. There seems to be more at stake than this, however, because when math- ematicians do mention names they almost always belong to the small group of people who are known to us as mathematicians, or who are known to us through their mathematical works.2 In order to be accepted as a member of the group of mathematicians, one must not only have mastered various technical concepts and methods, but must also have learned how to express oneself in a stylized form of Greek prose that has often struck the uninitiated as peculiar.3 Be- cause of the specialized nature of this type of intellectual activity, in order to gain real mastery it was probably necessary to have studied it from youth, or to have had the time to apply oneself uninterruptedly.4 Hence, the private nature of ancient education meant that there were many educated individuals who had not mastered, or perhaps even been much exposed to, aspects of ancient mathematical thought and practice that we would regard as rather elementary (Cribiore 2001; Sidoli 2015). Starting from at least the late Hellenistic period, and especially during the Imperial and Late- Ancient periods, some authors sought to address this situation in a variety of different ways— such as discussing technical topics in more elementary modes, rewriting mathematical argu- ments so as to be intelligible to a broader audience, or incorporating mathematical material di- rectly into philosophical curricula. -
Implementing Eratosthenes' Discovery in the Classroom: Educational
Implementing Eratosthenes’ Discovery in the Classroom: Educational Difficulties Needing Attention Nicolas Decamp, C. de Hosson To cite this version: Nicolas Decamp, C. de Hosson. Implementing Eratosthenes’ Discovery in the Classroom: Educational Difficulties Needing Attention. Science and Education, Springer Verlag, 2012, 21 (6), pp.911-920. 10.1007/s11191-010-9286-3. hal-01663445 HAL Id: hal-01663445 https://hal.archives-ouvertes.fr/hal-01663445 Submitted on 18 Dec 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Sci & Educ DOI 10.1007/s11191-010-9286-3 Implementing Eratosthenes’ Discovery in the Classroom: Educational Difficulties Needing Attention Nicolas De´camp • Ce´cile de Hosson Ó Springer Science+Business Media B.V. 2010 Abstract This paper presents a critical analysis of the accepted educational use of the method performed by Eratosthenes to measure the circumference of Earth which is often considered as a relevant means of dealing with issues related to the nature of science and its history. This method relies on a number of assumptions among which the parallelism of sun rays. The assumption of sun rays parallelism (if it is accurate) does not appear spontaneous for students who consider sun rays to be divergent. -
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. -
Passionate Platonism: Plutarch on the Positive Role of Non-Rational Affects in the Good Life
Passionate Platonism: Plutarch on the Positive Role of Non-Rational Affects in the Good Life by David Ryan Morphew A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Classical Studies) in The University of Michigan 2018 Doctoral Committee: Professor Victor Caston, Chair Professor Sara Ahbel-Rappe Professor Richard Janko Professor Arlene Saxonhouse David Ryan Morphew [email protected] ORCID iD: 0000-0003-4773-4952 ©David Ryan Morphew 2018 DEDICATION To my wife, Renae, whom I met as I began this project, and who has supported me throughout its development. ii ACKNOWLEDGMENTS First and foremost, I am grateful to my advisors and dissertation committee for their encouragement, support, challenges, and constructive feedback. I am chiefly indebted to Victor Caston for his comments on successive versions of chapters, for his great insight and foresight in guiding me in the following project, and for steering me to work on Plutarch’s Moralia in the first place. No less am I thankful for what he has taught me about being a scholar, mentor, and teacher, by his advice and especially by his example. There is not space here to express in any adequate way my gratitude also to Sara Ahbel-Rappe and Richard Janko. They have been constant sources of inspiration. I continue to be in awe of their ability to provide constructive criticism and to give incisive critiques coupled with encouragement and suggestions. I am also indebted to Arlene Saxonhouse for helping me to see the scope and import of the following thesis not only as of interest to the history of philosophy but also in teaching our students to reflect on the kind of life that we want to live. -
The Seven Sages.Pdf
Document belonging to the Greek Mythology Link, a web site created by Carlos Parada, author of Genealogical Guide to Greek Mythology Characters • Places • Topics • Images • Bibliography • PDF Editions About • Copyright © 1997 Carlos Parada and Maicar Förlag. The Seven Sages of Greece Search the GML advanced Sections in this Page Introduction: The Labyrinth of Wisdom The Seven Sages of Greece Thales Solon Chilon Pittacus Bias "… wisdom is a form of goodness, and is not scientific knowledge but Cleobulus another kind of cognition." (Aristotle, Eudemian Ethics 1246b, 35). Periander Anacharsis Myson Epimenides Pherecydes Table: Lists of the Seven Sages Notes and Sources of Quotations Introduction: The Labyrinth of Wisdom For a god wisdom is perhaps a divine meal to be swallowed at one gulp without need of mastication, and that would be the end of the story. The deities are known for their simplicity. The matter of human wisdom, however, could fill all archives on earth without ever exhausting itself. Humanity is notorious for its complexity. And men proudly say "Good things are difficult." But is wisdom a labyrinth, or "thinking makes it so"? And when did the saga of human wisdom begin and with whom? The Poet When humans contemplated Dawn for the first time, wisdom was the treasure of the poet alone. Of all men he was the wisest, for the gods had chosen his soul as receptacle of their confidences. Thus filled with inspiration divine, the poet knew better than any other man the secrets of the world. And since Apollo found more pleasure in leading the Muses than in warming his tripod, neither the inspiration of the Pythia nor that of seers could match the poet's wisdom. -
1 Florian Marion the Ἐξαίφνης in the Platonic Tradition: from Kinematics to Dynamics (Draft) Studies on Platonic 'The
F. Marion – The ἐξαίφνης in the Platonic Tradition: from Kinematics to Dynamics Florian Marion The ἐξαίφνης in the Platonic Tradition: from Kinematics to Dynamics (Draft) Studies on Platonic ‘Theoria motus abstracti’ are often focused on dynamics rather than kinematics, in particular on psychic self-motion. This state of affairs is, of course, far from being a bland academic accident: according to Plato, dynamics is the higher science while kinematics is lower on the ‘scientific’ spectrum1. Furthermore, when scholars investigate Platonic abstract kinematics, in front of them there is a very limited set of texts2. Among them, one of the most interesting undoubtedly remains a passage of Parmenides in which Plato challenges the puzzle of the ‘instant of change’, namely the famous text about the ‘sudden’ (τὸ ἐξαίφνης). Plato’s ἐξαίφνης actually is a terminus technicus and a terminus mysticus at once3, in such a way that from Antiquity until today this Platonic concept has been interpreted in very different fashions, either in a physical fashion or in a mystical one. Nevertheless, it has not been analysed how those two directions have been already followed by the Platonic Tradition. So, the aim of this paper is to provide some acquaintance with the exegetical history of ἐξαίφνης inside the Platonic Tradition, from Plato to Marsilio Ficino, by way of Middle Platonism and Greek Neoplatonism. After exposing Plato’s argument of Parm, 156c-157b and its various interpretations (1), I shall investigate the ways by which Middle Platonists (especially Taurus) and Early Neoplatonists as Plotinus and Iamblichus have understood Plato’s use of ἐξαίφνης (2), and finally how this notion had been transferred from kinematics to dynamics in Later Neoplatonism (3). -
The Fragments of Zeno and Cleanthes, but Having an Important
,1(70 THE FRAGMENTS OF ZENO AND CLEANTHES. ftonton: C. J. CLAY AND SONS, CAMBRIDGE UNIVERSITY PRESS WAREHOUSE, AVE MARIA LANE. ambriDse: DEIGHTON, BELL, AND CO. ltip>ifl: F. A. BROCKHAUS. #tto Hork: MACMILLAX AND CO. THE FRAGMENTS OF ZENO AND CLEANTHES WITH INTRODUCTION AND EXPLANATORY NOTES. AX ESSAY WHICH OBTAINED THE HARE PRIZE IX THE YEAR 1889. BY A. C. PEARSON, M.A. LATE SCHOLAR OF CHRIST S COLLEGE, CAMBRIDGE. LONDON: C. J. CLAY AND SONS, CAMBRIDGE UNIVERSITY PRESS WAREHOUSE. 1891 [All Rights reserved.] Cambridge : PBIXTKIi BY C. J. CLAY, M.A. AND SONS, AT THK UNIVERSITY PRKSS. PREFACE. S dissertation is published in accordance with thr conditions attached to the Hare Prize, and appears nearly in its original form. For many reasons, however, I should have desired to subject the work to a more under the searching revision than has been practicable circumstances. Indeed, error is especially difficult t<> avoid in dealing with a large body of scattered authorities, a the majority of which can only be consulted in public- library. to be for The obligations, which require acknowledged of Zeno and the present collection of the fragments former are Cleanthes, are both special and general. The Philo- soon disposed of. In the Neue Jahrbticher fur Wellmann an lofjie for 1878, p. 435 foil., published article on Zeno of Citium, which was the first serious of Zeno from that attempt to discriminate the teaching of Wellmann were of the Stoa in general. The omissions of the supplied and the first complete collection fragments of Cleanthes was made by Wachsmuth in two Gottingen I programs published in 187-i LS75 (Commentationes s et II de Zenone Citiensi et Cleaitt/ie Assio). -
A Reading of Porphyry's on Abstinence From
UNIVERSITY OF CALIFORNIA Los Angeles Justice Purity Piety: A Reading of Porphyry’s On Abstinence from Ensouled Beings A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Classics by Alexander Press 2020 © Copyright by Alexander Press 2020 ABSTRACT OF THE DISSERTATION Justice Purity Piety: A Reading of Porphyry’s On Abstinence from Ensouled Beings by Alexander Press Doctor of Philosophy in Classics University of California, Los Angeles, 2020 Professor David Blank, Chair Abstract: Presenting a range of arguments against meat-eating, many strikingly familiar, Porphyry’s On Abstinence from Ensouled Beings (Greek Περὶ ἀποχῆς ἐµψύχων, Latin De abstinentia ab esu animalium) offers a sweeping view of the ancient debate concerning animals and their treatment. At the same time, because of its advocacy of an asceticism informed by its author’s Neoplatonism, Abstinence is often taken to be concerned primarily with the health of the human soul. By approaching Abstinence as a work of moral suasion and a work of literature, whose intra- and intertextual resonances yield something more than a collection of propositions or an invitation to Quellenforschung, I aim to push beyond interpretations that bracket the arguments regarding animals as merely dialectical; cast the text’s other-directed principle of justice as wholly ii subordinated to a self-directed principle of purity; or accept as decisive Porphyry’s exclusion of craftsmen, athletes, soldiers, sailors, and orators from his call to vegetarianism. -
Pavle Stojanović on the STATUS of NATURAL DIVINATION in STOICISM1 ABSTRACT: Cicero's De Divinatione Portrays the Stoics As U
THEORIA 1 https://doi.org/10.2298/THEO2001005S (2020) : 63 : str. 5-16 Originalni naučni rad Original Scientific Paper Pavle Stojanović ON THE STATUS OF NATURAL DIVINATION IN STOICISM1 ABSTRACT: Cicero’s De divinatione portrays the Stoics as unanimous in advocating both natural and technical divination. I argue that, contrary to this, the earlier leaders of the school like Chrysippus had reasons to consider natural divination to be sig nificantly epistemically inferior to its technical counterpart. The much more favorable treatment of natural divination in De divinatione is likely the result of changes intro duced later, probably by Posidonius. KEY WORDS: Stoicism, divination, knowledge, Cicero, Chrysippus, Posidonius. Barring few notable exceptions—Xenophanes of Colophon, the Epicureans, the Academics under Arcesilaus and Carneades, and the Pyrrhonists—ancient philoso- phers generally thought that divination is a legitimate method of predicting future events based on divinely supplied signs. Starting with Plato (Phaed. 244a8-d5), it was not uncommon to distinguish between two kinds of divination. According to him, the former involves predicting future events while the diviner is in altered mental states such as dreaming, melancholy, mania, frenzy, etc. The latter is employed by the „clear- headed“ (ἔμφρονες), who derive predictions from prolonged and repeated observation of signs such as bird movements, animal entrails, astronomical and meteorological phenomena, etc., and their connections with subsequent events. Among the philoso- -
The Two Earths of Eratosthenes Author(S): Christián Carlos Carman and James Evans Source: Isis, Vol
University of Puget Sound Sound Ideas All Faculty Scholarship Faculty Scholarship 3-2015 The woT Earths of Eratosthenes James Evans University of Puget Sound, [email protected] Christián Carlos Carman Buenos Aires, Argentina Follow this and additional works at: http://soundideas.pugetsound.edu/faculty_pubs Citation Christián C. Carman and James Evans, “The wT o Earths of Eratosthenes,” Isis 106 (2015), 1-16. This Article is brought to you for free and open access by the Faculty Scholarship at Sound Ideas. It has been accepted for inclusion in All Faculty Scholarship by an authorized administrator of Sound Ideas. For more information, please contact [email protected]. The Two Earths of Eratosthenes Author(s): Christián Carlos Carman and James Evans Source: Isis, Vol. 106, No. 1 (March 2015), pp. 1-16 Published by: The University of Chicago Press on behalf of The History of Science Society Stable URL: http://www.jstor.org/stable/10.1086/681034 . Accessed: 08/12/2015 15:41 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press and The History of Science Society are collaborating with JSTOR to digitize, preserve and extend access to Isis. -
Index Rerum Et Nominum Antiquorum
INDEX RERUM ET NOMINUM ANTIQUORUM For nomina antiqua see also index locorum potiorum. The numbers again refer to the location in the footnotes (abbreviated n, e.g. 47n156 means p. 47 note 156), in the complementary notes (abbreviated en, e.g. 129cn225 means p. 129 complementary note 225), and in the text (just the page number). The cross-references in the notes may also be of some help. Aelius Donatus see Donatus Archimedes 6n13, 13, 24, 24n81, Aelius Theon 56n185, 122cn5 37n127, 40, 41,41nl37, 43, 44,45- Aetius 47n156, 129cn225 8,45n148,48n158,48n159,53, atnov tlj~ £mypacplj~ see 53n177, 62n206,92, 103, 103n349, isagogical questions (title) 103n353, 113, 115, 115n382, 116, Albinus 12, 71, 72n250 117 Alcinous 99, 99n337, 107n364, Archytas of Tarentum 119n397 111, 112, 114, 120n400 Aristaeus mathematicus 10, Alexander of Aphrodisias 11n31, 21, 64 23n79, 107n364, 108n365, 111-2, Aristarchus of Samos 14 111-2n374, 112n375, 114, 126cn89 Aristotle 4nl0, 12, 13n39, 33n118, Alexander of Lycopolis on 34, 43,46,47, 47nl56, 48, 52, Demiurge 108, 108n365 56n185, 66n226, 67n227, 67n228, Alexander Polyhistor 1 02n343 68n229, 82n290,83n295,86-7,95, 0./..oyov see line(s) 103n353, 109, 111, 112n375, 114, Ammonius Hermiae 13, 20, 115-6, 118, 119, 123cn11, 124- 21n68,43,43n143,45,48,56,88, 5cn67, 131cn357 88n313,92, 129cn260, 130cn308 Aristoxeneans 73n255 avayvrocrt~, avaytvcOOKElV, see arithmetic 9n25, 19, 22, 24n80, reading (study) 29, 57, 61nl96, 79, 82-91, 83n295, an-Nayrizi see Anaritius 118, 120n403 an-Nadim see at N arithmology 19, 90 ava/..oy{a