Porphyry

Porphyry of Tyre (/ˈpɔːrfɪri/; Greek: Πορφύριος, Porphýrios; Arabic: فرفوريوس‎, Furfūriyūs; c. 234 – c. 305 AD) was a Phoenician[1] Neoplatonic philosopher born in Tyre, Roman Syria[2] during Roman rule.[a] He edited and published The Enneads, the only collection of the work of Plotinus, his teacher. His commentary on Euclid's Elements was used as a source by Pappus of Alexandria.[3]

He wrote original works on a wide variety of topics, ranging from music to Homer to vegetarianism.[b] His Isagoge, or Introduction, an introduction to logic and philosophy,[c] was the standard textbook on logic throughout the Middle Ages in its Latin and Arabic translations.[4] Through works such as Philosophy from Oracles and Against the Christians (which was banned by Constantine the Great),[5] he was involved in a controversy with early Christians.[6]

Biography

The Suda (a 10th century Byzantine encyclopedia based on many sources now lost) reports that Porphyry was born in Phoenician city of Tyre.[7] His parents named him Malchus ("king" in the Semitic languages)[d] but his teacher in Athens, Cassius Longinus, gave him the name Porphyrius ("clad in purple"), possibly a reference to his Phoenician heritage, or a punning allusion to his name and the color of royal robes. Under Longinus he studied grammar and rhetoric.

In 262 he went to Rome, attracted by the reputation of Plotinus, and for six years devoted himself to the practice of Neoplatonism, during which time he severely modified his diet. At one point he became suicidal.[8] On the advice of Plotinus he went to live in Sicily for five years to recover his mental health. On returning to Rome, he lectured on philosophy and completed an edition of the writings of Plotinus (who had died in the meantime) together with a biography of his teacher. Iamblichus is mentioned in ancient Neoplatonic writings as his pupil, but this most likely means only that he was the dominant figure in the next generation of philosophers. The two men differed publicly on the issue of theurgy.

In his later years, he married Marcella, a widow with seven children and an enthusiastic student of philosophy. Little more is known of his life, and the date of his death is uncertain.
Introduction (Isagoge)
Imaginary debate between Averroes (1126–1198 AD) and Porphyry (234–c. 305 AD). Monfredo de Monte Imperiali Liber de herbis, 14th century.[9]

Porphyry is best known for his contributions to philosophy. Apart from writing the Aids to the Study of the Intelligibles (Ἀφορμαὶ πρὸς τὰ νοητά; Sententiae Ad Intelligibilia Ducentes), a basic summary of Neoplatonism, he is especially appreciated for his Introduction to Categories (Introductio in Praedicamenta or Isagoge et in Aristotelis Categorias commentarium), a very short work often considered to be a commentary on Aristotle's Categories, hence the title.[e] According to Barnes 2003, however, the correct title is simply Introduction (Εἰσαγωγή Isagoge), and the book is an introduction not to the Categories in particular, but to logic in general, comprising as it does the theories of predication, definition, and proof. The Introduction describes how qualities attributed to things may be classified, famously breaking down the philosophical concept of substance into the five components genus, species, difference, property, accident.

As Porphyry's most influential contribution to philosophy, the Introduction to Categories incorporated Aristotle's logic into Neoplatonism, in particular the doctrine of the categories of being interpreted in terms of entities (in later philosophy, "universal"). Boethius' Isagoge, a Latin translation of Porphyry's "Introduction", became a standard medieval textbook in European schools and universities, which set the stage for medieval philosophical-theological developments of logic and the problem of universals. In medieval textbooks, the all-important Arbor porphyriana ("Porphyrian Tree") illustrates his logical classification of substance. To this day, taxonomy benefits from concepts in Porphyry's Tree, in classifying living organisms (see cladistics).

The Introduction was translated into Arabic by Abd-Allāh Ibn al-Muqaffaʿ from a Syriac version. With the Arabicized name Isāghūjī (إيساغوجي) it long remained the standard introductory logic text in the Muslim world and influenced the study of theology, philosophy, grammar, and jurisprudence. Besides the adaptations and epitomes of this work, many independent works on logic by Muslim philosophers have been entitled Isāghūjī. Porphyry's discussion of accident sparked a long-running debate on the application of accident and essence.[10]
Philosophy from Oracles (De Philosophia ex Oraculis Haurienda)

Porphyry is also known as an opponent of Christianity and defender of Paganism; his precise contribution to the philosophical approach to traditional religion may be discovered in the fragments of Philosophy from Oracles (Περὶ τῆς ἐκ λογίων φιλοσοφίας; De Philosophia ex Oraculis Haurienda), which was originally three books in length. There is debate as to whether it was written in his youth (as Eunapius reports[8]) or closer in time to the persecutions of Christians under Diocletian and Galerius.[f]

Whether or not Porphyry was the pagan philosopher opponent in Lactantius' Divine Institutes, written at the time of the persecutions, has long been discussed. The fragments of the Philosophy from Oracles are only quoted by Christians, especially Eusebius, Theodoret, Augustine, and John Philoponus. The fragments contain oracles identifying proper sacrificial procedure, the nature of astrological fate, and other topics relevant for Greek and Roman religion in the third century. Whether this work contradicts his treatise defending vegetarianism, which also warned the philosopher to avoid animal sacrifice, is disputed among scholars.[12]
Against the Christians (Adversus Christianos)
Main article: Against the Christians
See also: Celsus
Porphyry, a detail of the Tree of Jesse, 1535, Sucevița Monastery.

During his retirement in Sicily, Porphyry wrote Against the Christians (Κατὰ Χριστιανῶν; Adversus Christianos) which consisted of fifteen books. Some thirty Christian apologists, such as Methodius, Eusebius, Apollinaris, Augustine, Jerome, etc., responded to his challenge. In fact, everything known about Porphyry's arguments is found in these refutations, largely because Theodosius II ordered every copy burned in A.D. 435 and again in 448.[13][14][15][16]

Porphyry became one of the most able pagan adversaries of Christianity of his day. His aim was not to disprove the substance of Christianity's teachings but rather the records within which the teachings are communicated.[17]

Augustine and the 5th-century ecclesiastical historian Socrates of Constantinople, assert that Porphyry was once a Christian.[18]
Other subjects

Porphyry was opposed to the theurgy of his disciple Iamblichus. Much of Iamblichus' mysteries is dedicated to the defense of mystic theurgic divine possession against the critiques of Porphyry. French philosopher Pierre Hadot maintains that for Porphyry, spiritual exercises are an essential part of spiritual development.[19]

Porphyry was, like Pythagoras, an advocate of vegetarianism on spiritual and ethical grounds. These two philosophers are perhaps the most famous vegetarians of classical antiquity. He wrote the On Abstinence from Animal Food (Περὶ ἀποχῆς ἐμψύχων; De Abstinentia ab Esu Animalium), advocating against the consumption of animals, and he is cited with approval in vegetarian literature up to the present day.

Porphyry also wrote widely on astrology, religion, philosophy, and musical theory. He produced a History of Philosophy (Philosophos historia) with vitae of philosophers that included a life of his teacher, Plotinus. His life of Plato from book iv exists only in quotes by Cyril of Alexandria. [g] His book Vita Pythagorae on the life of Pythagoras is not to be confused with the book of the same name by Iamblichus. His commentary on Ptolemy's Harmonics[20] (Eis ta Harmonika Ptolemaiou hypomnēma) is an important source for the history of ancient harmonic theory.

Porphyry also wrote about Homer. Apart from several lost texts known only from quotes by other authors, two texts survive at least in large parts: the Homerian Questions (Homēriká zētḗmata, largely a philological comment on the Iliad and Odyssey) and About the cave of the Nymphs in the Odyssey (Peri tou en Odysseia tōn nymphōn antrou).
Extant works

Life of Plotinus. Editions: Luc Brisson, La Vie de Plotin. Histoire de l'antiquité classique 6 & 16, Paris: Librairie Philosophique J. Vrin: 1986–1992, 2 vols; A. H. Armstrong, Plotinus, Loeb Classical Library, Cambridge, Massachusetts: Harvard University Press, 1968, pp. 2-84. Translation: Neoplatonic Saints: The Lives of Plotinus and Proclus. Translated Texts for Historians 35 (Liverpool: Liverpool University Press, 2000).
Life of Pythagoras. Edition: E. des Places, Vie de Pythagore, Lettre à Marcella, Paris: Les Belles Lettre, 1982.
Introduction to Aristotle's Categories (Isagoge). Translations: E. Warren, Isagoge, Mediaeval Sources in Translation 16, Toronto: Pontifical Institute of Mediaeval Studies, 1975; J. Barnes, Porphyry's Introduction. Translation of the 'Isagoge' with a Commentary, Oxford, 2003; Steven K. Strange, Porphyry. On Aristotle's Categories, Ithaca, New York, 1992; Octavius Freire Owen, The Organon or Logical Treatises of Aristotle with the Introduction of Porphyry. Bohn's Classical Library 11–12, London: G. Bell, 1908–1910, 2 vols; Paul Vincent Spade, Five Texts on the Mediaeval Problem of Universals: Porphyry, Boethius, Abelard, Duns Scotus, Ockham,Indianapolis: Hackett, 1994.
Introduction to the Tetrabiblos of Ptolemy. Editions: Stefan Weinstock, in: Franz Cumont (ed.), Catalogus Codicum astrologorum Graecorum, (Brussels, 1940): V.4, 187-228; Kommentar zur Harmonielehre des Ptolemaios Ingemar Düring. ed. (Göteborg: Elanders, 1932). Translation: James Herschel Holden, Porphyry the Philosopher, Introduction to the Tetrabiblos and Serapio of Alexandria, Astrological Definitions, Tempe, Az.: A.F.A., Inc., 2009.
Against the Christians (Contra Christianos). Editions: A. Ramos Jurado, J. Ritoré Ponce, A. Carmona Vázquez, I. Rodríguez Moreno, J. Ortolá Salas, J. M. Zamora Calvo (eds), Contra los Cristianos: Recopilación de Fragmentos, Traducción, Introducción y Notas – (Cádiz: Servicio de Publicaciones de la Universidad de Cádiz 2006); Adolf von Harnack, Porphyrius, "Gegen die Christen," 15 Bücher: Zeugnisse, Fragmente und Referate. Abhandlungen der königlich preussischen Akademie der Wissenschaften: Jahrgang 1916: philosoph.-hist. Klasse: Nr. 1 (Berlin: 1916). Translations: R. M. Berchman, Porphyry Against the Christians, Ancient Mediterranean and Medieval Texts and Contexts 1, Leiden: Brill, 2005; R. Joseph Hoffmann, Porphyry’s Against the Christians: The Literary Remains, Amherst: Prometheus Books, 1994.
Commentary on Plato's Timaeus. Edition: A. R. Sodano, Porphyrii in Platonis Timaeum commentarium fragmenta, Napoli: 1964.
Homeric Questions. Edition: The Homeric Questions: a Bilingual Edition – Lang Classical Studies 2, R. R. Schlunk, trans. (Frankfurt-am-Main: Lang, 1993).
On the caves of the nymphs (De antro nympharum). Edition: The Cave of the Nymphs in the Odyssey. A revised text with translation by Seminar Classics 609, State University of New York at Buffalo, Arethusa Monograph 1 (Buffalo: Dept. of Classics, State University of New York at Buffalo, 1969). Translation: Robert Lamberton, On the Cave of the Nymphs, Barrytown, N. Y.: Station Hill Press, 1983.
On the abstinence of eating animals (De abstinentia ab esu animalium). Edition: Jean Bouffartigue, M. Patillon, and Alain-Philippe Segonds, edd., 3 vols., Budé (Paris, 1979–1995). Translation: Gilliam Clark, On Abstinence from Killing Animals, Ithaca: Cornell University Press, 2000.
On philosophy from oracles (De Philosophia ex oraculis haurienda). Edition: G. Wolf, Berlin: 1956.
Aids to the Study of the Intelligibles (Sententiae ad Intelligibilia Ducentes). Edition: E. Lamberz, Leipzig: Teubner, 1975. Translation: K. Guthrie, Launching-Points to the Realm of Mind, Grand Rapids, Michigan, 1988.
Letter to Marcella. Edition: Kathleen O’Brien Wicker, Porphyry, the Philosopher, to Marcella: Text and Translation with Introduction and Notes , Text and Translations 28; Graeco-Roman Religion Series 10 (Atlanata: Scholars Press, 1987); Pros Markellan Griechischer Text, herausgegeben, übersetzt, eingeleitet und erklärt von W. Pötscher (Leiden: E. J. Brill, 1969). Translation: Alice Zimmern, Porphyry's Letter to His Wife Marcella Concerning the Life of Philosophy and the Ascent to the Gods, Grand Rapids, Michigan, 1989.
Letter to Anebo (Epistula ad Anebonem). Edition: A. R. Sodano, Naples: L'arte Tipografia: 1958.

Lost works

Ad Gedalium, a lost commentary on Aristotle's Categories in seven books.[21] The testimonia are published in Andrew Smith (ed.), Porphyrius, Porphyrii Philosophi fragmenta. Fragmenta Arabica David Wasserstein interpretante, Berlin: Walter de Gruyter, 1993.

Works of uncertain attribution

Ad Gaurum (of uncertain attribution).[22] Edition: K. Kalbfleisch. Abhandlungen der Preussischen Akadamie der Wissenschaft. phil.-hist. kl. (1895): 33-62. Translation: J. Wilberding, To Gaurus On How Embryos are Ensouled, and On What is in our Power. Ancient Commentators on Aristotle Series, R. Sorabji (ed.), Bristol: Classical Press, 2011.
#6 and #9 in Corpus dei Papiri Filosofici Greci e Latini III: Commentari – (Florence: Leo S. Olschki, 1995) may or may not be by Porphyry.

Editions and translations of multiple works

Fragments: Andrew Smith, Stvtgardiae et Lipsiae: B. G. Tevbneri, 1993.
Opuscula selecta Augusts Nauck, ed. (Lipsiae: B. G. Tevbneri, 1886) (online at archive.org).
Select Works of Porphyry. Translated by T. Taylor (Guildford, 1994). Contains Abstinence from Eating Animal Food, the Sententiae and the Cave of the Nymphs.
Translations of several fragments are contained in Appendix 1 of Religion and Identity in Porphyry of Tyre by Aaron Johnson (Cambridge, 2013).

See also

Basilides of Tyre
Macarius Magnes – his work Apocriticus contains a series of excerpts from Porphyry's Against the Christians

References
Footnotes

For Porphyry's dates, place of birth and philosophical school, see Barker 2003, pp. 1226–1227. Sarton 1936, pp. 429–430 identifies Transjordania as Porphyry's place of birth.
For a comprehensive list see Beutler (1894–1980); Guthrie 1988, p. 91 provides another list
Barnes 2003, p. xv clarifies that the Isagoge "[was] not an Introduction to the Categories, rather "[since it was] an introduction to the study of logic, [it] was... an introduction to philosophy--and hence accidentally an introduction to the Categories."
For connotations of West Semitic M-L-K, see Moloch and Malik; compare theophoric names like Abimelech.
Barnes 2003, p. xiv outlines the history of the opinion that Porphyry meant for his Isagoge to be an introductory work to the Categories.
The Christian apologist Eusebius states that "some Greek" might say "How can these people be thought worthy of forbearance? They have not only turned away from those who from earliest time have been thought of as divine among all Greeks and barbarians... but by emperors, law-givers and philosophers— all of a given mind... And to what sort of penalties might they not be subjected who... are fugitives from the things of their Fathers?" This material, once thought to be part of Against the Christians, but reassigned by Wilken 1979 to Philosophy from Oracles, is quoted in Digeser 1998, p. 129. However, it may not have been by Porphyry at all.[11]

Notopoulos 1940, pp. 284–293 attempted a reconstruction from Apuleius' use of it.

Citations

Aaron P. Johnson, Religion and Identity in Porphyry of Tyre: The Limits of Hellenism in Late Antiquity (Greek Culture in the Roman World) Cambridge University Press, May 20, 2013, p. 236 "...at the very least, we can affirm that all external evidence points to his being a Tyrian from Phoencia." https://books.google.com/
Schott, Jeremy M. (2013-04-23). Christianity, Empire, and the Making of Religion in Late Antiquity. University of Pennsylvania Press. ISBN 978-0-8122-0346-2.
O'Connor, John J.; Robertson, Edmund F., "Porphyry Malchus", MacTutor History of Mathematics archive, University of St Andrews.
Barnes 2003, p. ix.
Clarke 1989, p. 9.
Digeser 1998.
Suda, Porphyry
Eunapius (1921). "Lives of the Philosophers and Sophists". tertullian.org. pp. 343–565. Retrieved 6 September 2019.
Sadaune 2014, p. 112.
Rahman 1986, pp. 271-273.
Johnson 2010, p. 53-58.
Johnson 2013, p. 135.
Digeser 1998, p. 130: "Constantine and other emperors banned and burned Porphyry's work".
Socrates Scholasticus 1885, pp. Book I, Ch 9, pp. 30-31, Letter of Constantine proscribing the works of Porphyry and Arius.
Stevenson 1987: Gelasius, Historia Ecclesiastica, II.36
Froom 1950, p. 326.
Froom 1950, p. 327.
Socrates Scholasticus 1885b, pp. Book III, Ch 23.
Hadot 1995, p. 100.
"Τοξόλυρος - Εἰς τὰ ἁρμονικὰ Πτολεμαίου ὑπόμνημα - φιλοσοφικό Ακαδημίας" [In Ptolemy's Harmonized Memoirs – Philosophical Academy] (in Greek). Archived from the original on 2011-07-21.
Simplicius, In Aristotelis Categorias commentarium, 2.5-9v

Barnes 2011, p. 109, n. 22.

Sources

Barker, A. (2003). "Porphyry". In Hornblower, S.; Spawforth, A. (eds.). Oxford Classical Dictionary (revised 3rd ed.). pp. 1226–1227.
Barnes, Jonathan (2003). Porphyry: Introduction. Oxford: Clarendon. ISBN 9780199246144.
Barnes, Jonathan (2011). Method and Metaphysics: Essays in Ancient Philosophy. Volume I. Oxford: OUP. ISBN 978-0-19-957751-4.
Beutler, R. (1894–1980). "Porphyrios (21)" in A. Pauly, G. Wissowa, W. Kroll, K. Witte, K. Mittelhaus and K. Ziegler, eds., Paulys Realencyclopädie der classischen Altertumswissenschaft, vol. 22.1.
Clarke, Gillian (1989). Iamblichus : On the Pythagorean Life. Liverpool University Press. ISBN 978-0-85323-326-8.
Digeser, Elizabeth DePalma (1998). "Lactantius, Porphyry, and the Debate over Religious Toleration". Journal of Roman Studies. 88: 129–146. doi:10.2307/300808. ISSN 0075-4358. JSTOR 300808.
Froom, LeRoy (1950). The Prophetic Faith of our Fathers (PDF). Volume 1. Washington, DC: Review and Herald.
Guthrie, Kenneth Sylvan (1988). "The Works of Porphyry". Porphyry's Launching-points to the realm of mind: an introduction to the neoplatonic philosophy of Plotinus. Phanes Press. ISBN 978-0-933999-59-6. also available at tertullian.org
Hadot, P. (1995). Philosophy as a Way of Life. Oxford: Blackwell.
Johnson, Aaron (2010). "Rethinking the Authenticity of Porphyry, c.Christ. fr. 1". Studia Patristica. 46: 53–58.
Johnson, Aaron P. (2013). Religion and Identity in Porphyry of Tyre: The Limits of Hellenism in Late Antiquity. Cambridge University Press. ISBN 978-1-107-01273-8.
Notopoulos, James A. (1940). "Porphyry's Life of Plato". Classical Philology. 35 (3): 284–293. doi:10.1086/362396. ISSN 0009-837X. S2CID 161160877.
Rahman, F. (1986). "ʿARAŻ". Encyclopaedia Iranica. Vol. II, Fasc. 3. pp. 271–273.
Sarton, G. (1936). "The Unity and Diversity of the Mediterranean World". Osiris. 2: 406–463. doi:10.1086/368462. S2CID 143379839.
Sadaune, Samuel (2014). Inventions et decouvertes au Moyen-Age [Inventions and Discoveries of the Middle Ages] (in French). Ouest-France. ISBN 9782737362415.
Socrates Scholasticus (1885). Historia Ecclesiastica . Book I, Ch 9, pp. 30-31 – via Wikisource.
Socrates Scholasticus (1885b). Historia Ecclesiastica . Book III, Ch 23 – via Wikisource.
Stevenson, James (1987). A New Eusebius: Documents Illustrating the History of the Church to AD 337. SPCK. ISBN 978-0-281-04268-5.
Wilken, R. (1979). "Pagan Criticism of Christianity: Greek Religion and Christian Faith". In Schoedel and, W.; Wilken, R. (eds.). Early Christian Literature and the Classical Intellectual Tradition. pp. 117–134.

Further reading

Bidez, J. (1913). Vie de Porphyre. Ghent.
Clark, Gillian, "Porphyry of Tyre on the New Barbarians," in R. Miles (ed), Constructing Identities in Late Antiquity (London: Routledge, 1999), 112–132; = in Eadem, Body and Gender, Soul and Reason in Late Antiquity (Farnham; Burlington, VT, Ashgate, 2011) (Variorum collected studies series, CS978), art. XIV.
Clark, Gillian, "Philosophic Lives and the philosophic life: Porphyry and Iamblichus," in T. Hägg and P. Rousseau (eds), Greek Biography and Panegyric in Late Antiquity (Berkeley and Los Angeles, University of California Press, 2000), 29–51; = in Eadem, Body and Gender, Soul and Reason in Late Antiquity (Farnham; Burlington, VT, Ashgate, 2011) (Variorum collected studies series, CS978), art. XV.
Clark, Gillian, "Fattening the soul: Christian asceticism and Porphyry On Abstinence," Studia Patristica, 35, 2001, 41-51; = in Eadem, Body and Gender, Soul and Reason in Late Antiquity (Farnham; Burlington, VT, Ashgate, 2011) (Variorum collected studies series, CS978), art. XVI.
Emilsson, E., "Porphyry". Retrieved April 19, 2009.
Iamblichus: De mysteriis. Translated with an Introduction and Notes by Emma C. Clarke, John M. Dillon and Jackson P. Hershbell (Society of Biblical Literature; 2003) ISBN 1-58983-058-X.
Girgenti, G. (1987) Porfirio negli ultimi cinquant'anni: bibliografia sistematica e ragionata della letteratura primaria e secondaria riguardante il pensiero porfiriano e i suoi influssi storici Milan.
Smith, Andrew (1987) Porphyrian Studies since 1913, in W. Haase, ed., Aufstieg und Niedergang der Römischen Welt II.36.2, pp. 717–773.
Smith, Andrew (1974) Porphyry's Place in the Neoplatonic Tradition. A Study in post-Plotinian Neoplatonism, The Hague, Nijhoff.
Zuiddam, B. A. "Old Critics and Modern Theology," Dutch Reformed Theological Journal (South Africa), xxxvi, 1995, No. 2.

External links
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Media related to Porphyry (philosopher) at Wikimedia Commons
Wikisource logo Works written by or about Porphyry at Wikisource
Wikisource-logo.svg Greek Wikisource has original text related to this article: Πορφύριος
Quotations related to Porphyry (philosopher) at Wikiquote
Porphyry Malchus (mathematician) – entry in MacTutor History of Maths Archives.
Emilsson, Eyjólfur. "Porphyry". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy..
Περὶ τοῦ ἐν Ὀδυσσείᾳ τῶν Νυμφῶν Ἄντρου (The Cave of the Nymphs in the Odyssey), original Greek text.
Εἰσαγωγὴ εἰς τὴν Ἀποτελεσματικὴν τοῦ Πτολεμαίου (Introduction to Ptolemy's Tetrabiblos), original Greek text.
Porphyry, On Abstinence from Animal Food, Book I, translated by Thomas Taylor.
Porphyry, On Abstinence from Animal Food, Book II, translated by Thomas Taylor.
Porphyry, On Abstinence from Animal Food, Book III, translated by Thomas Taylor.
Porphyry, On Abstinence from Animal Food, Book IV, translated by Thomas Taylor.
Porphyry, On the Cave of Nymphs, translated by Thomas Taylor.
Porphyry, Auxiliaries to the Perception of Intelligible Natures, translated by Thomas Taylor.
Porphyry, Isagoge, translated by Octavius Freire Owen.
The Isagoge, or Introduction of Porphyry, translated by Thomas Taylor with an extensive preface by the translator.
Porphyry, On the Life of Plotinus
Porphyry, Comments on the Book of Daniel.
Additional texts, edited by Roger Pearse
Works by Porphyry at LibriVox (public domain audiobooks)

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Platonists
Academic
Old

Plato Aristotle Eudoxus Philip of Opus Aristonymus Coriscus and Erastus of Scepsis Demetrius of Amphipolis Euaeon of Lampsacus Heraclides and Python of Aenus Hestiaeus of Perinthus Lastheneia of Mantinea Timolaus of Cyzicus Speusippus Axiothea of Phlius Heraclides Ponticus Menedemus of Pyrrha Xenocrates Crantor Polemon Crates of Athens

Skeptic
Middle

Arcesilaus Diocles of Cnidus Lacydes Telecles and Evander Hegesinus

New

Carneades Hagnon of Tarsus Metrodorus of Stratonicea Clitomachus Charmadas Aeschines of Neapolis Philo of Larissa Cicero Dio of Alexandria

Middle Platonist

Antiochus Philo of Alexandria Plutarch Justin Martyr Gaius Albinus Alcinous Apuleius Atticus Maximus of Tyre Numenius of Apamea Longinus Clement of Alexandria Origen the Pagan Calcidius

Neoplatonist
Ancient

Ammonius Saccas Plotinus
Disciples Origen Amelius Porphyry Iamblichus Sopater Eustathius of Cappadocia Sosipatra Aedesius Dexippus Chrysanthius Theodorus of Asine Julian Sallustius Maximus of Ephesus Eusebius of Myndus Priscus of Epirus Antoninus Gregory of Nyssa Hypatia Gaius Marius Victorinus Augustine Macrobius

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Plutarch of Athens Asclepigenia Hierocles Syrianus Hermias Aedesia Proclus Ammonius Hermiae Asclepiodotus Hegias Zenodotus Marinus Agapius Isidore Damascius Simplicius Priscian

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Boethius John Philoponus Olympiodorus Pseudo-Dionysius the Areopagite John Scotus Eriugena

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Al-Farabi

Anselm Peter Abelard

Chartres

Bernard Gilbert Thierry

Henry of Ghent Bonaventure Theodoric of Freiberg Meister Eckhart Berthold of Moosburg Paul of Venice

Modern
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Florentine Academy

Plethon Marsilio Ficino Cristoforo Landino Giovanni Pico della Mirandola

Cambridge

Ralph Cudworth Henry More Anne Conway

Petrus Ramus Giordano Bruno Blaise Pascal Emanuel Swedenborg

German idealist

Gottfried Wilhelm Leibniz Christian Wolff Moses Mendelssohn Immanuel Kant Johann Gottlieb Fichte Friedrich Wilhelm Joseph Schelling Arthur Schopenhauer G. W. F. Hegel Hermann Lotze Otto Weininger

Thomas Taylor Ralph Waldo Emerson Josiah Royce Søren Kierkegaard Henri Bergson Aleksei Losev

Contemporary
Analytic
Gottlob Frege G. E. Moore Kurt Gödel Alonzo Church Roderick Chisholm Michael Dummett W. V. O. Quine David Kaplan Saul Kripke Alvin Plantinga Peter van Inwagen Nicholas Wolterstorff Crispin Wright Edward N. Zalta
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Edmund Husserl Roman Ingarden Leo Strauss

Miscellaneous

Philip K. Dick Joseph Ratzinger Bernard Bolzano

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Ancient Greek and Hellenistic mathematics (Euclidean geometry)
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(timeline)
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Concepts/definitions
Circles of Apollonius
Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine of proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center
Results
In Elements
Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon
Apollonius
Apollonius's theorem
Other
Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus
Centers
Cyrene Library of Alexandria Platonic Academy
Other
Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction

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