Encyclopedia.com. [32] All three modes of apprehension partake of truth; but in what manner scientific perception (epistemonike aisthesis) did so, we unfortunately do not learn. Complete Dictionary of Scientific Biography. [63] His moral earnestness is also expressed in the warning that the ears of children should be guarded against the poison of immoral speeches. Xenocratic definition is - of or relating to the philosopher Xenocrates or to his doctrines in which he combined Pythagorean conceptions with Platonism. Among these are theories about the Earth and moon, including the reason for an eclipse and accurate descriptions of the lunar surface. [65] According to Plutarch, Xenocrates result was 1,002,000,000,000 (a "myriad-and-twenty times a myriad-myriad"). None of Xenocrates’ writings has survived. Wanting in quickness of apprehension and natural grace[15] he compensated by persevering and thorough-going industry,[16] pure benevolence,[17] purity of morals,[18] unselfishness,[19] and a moral earnestness, which compelled esteem and trust even from the Athenians of his own age.[20]. When Athens was stormed by Sulla’s troops in March 86 b.c., the Academy, located in front of the western gate, was destroyed together with its priceless library.1. [25], Xenocrates made a more definite division between the three departments of philosophy, than Speusippus,[30] but at the same time abandoned Plato's heuristic method of conducting through doubts (aporiai), and adopted instead a mode of bringing forward his doctrines in which they were developed dogmatically.[31]. Then, copy and paste the text into your bibliography or works cited list. Dictionaries thesauruses pictures and press releases, Complete Dictionary of Scientific Biography. Plato apparently insisted that the contents of philosophical doctrines be communicated only to those who would strictly observe definite precautions, and consequently he often veiled his meaning through the use of metaphors and myths. He was the first philosopher to live in Athens and the first to propose several important theories about the cosmos. If, like other Platonists, he designated the material principle as undefined duality, the world-soul was probably described by him as the first defined duality, the conditioning or defining principle of every separate definitude in the sphere of the material and changeable, but not extending beyond it. According to tradition, Hippocrates was a merchant whose goods had been captured by pirates. Therefore, that information is unavailable for most Encyclopedia.com content. Diogenes Laertius gives the titles of two mathematics books by Xenocrates, namely On numbers and The theory of numbers. He was not only a mathematician but also a scholar, polymath, poet who wrote on grammar, philosophy and contemporary history. [11], Xenocrates resented the Macedonian influence then dominant at Athens. 410–339 bce) and Xenocrates (396–314 bce). He sent for Xenocrates, who was not in Athens at this time, and designated him his successor. (Berlin, 1899); and Heinze, Xenocrates, frag, 61 In Themistius’ reference to the fifth book of περί Φύσεωѕ it is possible to glean an indication that Xenocrates may have introduced the definition of soul as number. He appears to have called it in the highest sense the individual soul, in a derivative sense a self-moving number, that is, the first number endowed with motion. ), or Gaius Sallustius Crispus, was a Roman statesman and historian. [56], Still he maintained that virtue alone is valuable in itself, and that the value of every thing else is conditional. Xenocrates zĭnŏk´rətēz , 396–314 BC, Greek philosopher, b. Chalcedon, successor of Speusippus as head of the Academy. Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. [4], Moving to Athens in early youth, he became the pupil of Aeschines Socraticus,[5] but subsequently joined himself to Plato,[6] whom he accompanied to Sicily in 361. Philosophy. He credits Xenophanes withcomposing verses “in epic meter, as well as elegiacs and iambicsattacking Hesiod an… He tried to supplement the Platonic doctrine at various points, and at the same time to give it a more direct applicability to life. 4. 31–59; H. Dörrie, “Xenokrates,” in Pauly–Wissowa, Real Encyclopadie der classischen Altertumswissenschaft, 2nd ser., IX 1512-1528; R. Heinze, Xenocrates. Though not an original thinker, he was an exception…, (fl. We know nothing further about the mode in which Xenocrates carried out his dialectic, as it is probable that what was peculiar to Aristotelian logic did not remain unnoticed in it, for it can hardly be doubted that the division of the existent into the absolutely existent, and the relatively existent,[33] attributed to Xenocrates, was opposed to the Aristotelian table of categories. On this point, see H. F. Cherniss, Aristotle’s Criticism of Plato and the Academy, I (Baltimore, 1944; repr. He wrote on physical subjects: some parts of his Analytica posteriora show an unusual grasp of the mathematical method. Reports of Xenocrates’ teaching have survived only in the works of Aristotle and in Cicero and other Roman authors. Complete Dictionary of Scientific Biography. Xenocrates, seeking to render Plato’s theories teachable without recourse to such means, established a system of doctrinal propositions. [59] In this sense he on the one hand denoted (perfect) happiness as the possession of personal virtue, and the capabilities adapted to it, and therefore reckoned among its constituent elements, besides moral actions conditions and facilities, those movements and relations also without which external good things cannot be attained,[60] and on the other hand did not allow that wisdom, understood as the science of first causes or intelligible essence, or as theoretical understanding, is by itself the true wisdom which should be striven after by people,[61] and therefore seems to have regarded this human wisdom as at the same time exerted in investigating, defining, and applying. at the lastest) and about ten years laster accompanied Plato to Syracuse, the latter’s second or third voyage to that city. "Xenocrates of Chalcedon His father was named Agathon (Ancient Greek: Ἀγάθωνος) or Agathanor (Ancient Greek: Ἀγαθάνορος). As a sublunary daemonical power (as Hera, Poseidon, Demeter), it dwells in the elements, and these daemonical natures, midway between gods and men, are related to them as the isosceles triangle is to the equilateral and the scalene. [55] According, therefore, as what belongs to the intermediate region is adapted to bring about or to hinder the good, Xenocrates appears to have designated it as good or evil, probably with the proviso, that by misuse what is good might become evil, and vice versa, that by virtue, what is evil might become good. In particular, in his comprehensive outline, Xenocrates provided for a gradation of all the elements that make up ontology, physics, ethics, and epistemology. Darstellung der Lehre und Sammlung der Fragmente (Leipzig, 1892; repr., Hildesheim, 1965); S. Mekler, ed., Academicorum philosophorum index Herculanensis (Berlin, 1902), esp. In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. He seems to have described them as first, original lines, and in a similar sense to have spoken of original plain figures and bodies,[50] convinced that the principia of the existent should be sought not in the material, not in the divisible which attains to the condition of a phenomenon, but merely in the ideal definitude of form. [14] In 314/3, he died from hitting his head, after tripping over a bronze pot in his house.[14]. Removing to Athens in early youth, he became the pupil of the Socratic Aeschines, but presently joined himself to Plato , whom he attended to Sicily in 361. The list of his writings, which is entirely preserved in Diogenes Laertius (IV, 11–14), contains about seventy titles. 38–39; Diogenes Laertius, De vitis philosophorum, IV, ch. He went to Athens to prosecute them but met with little success in recovering his property. As a mathematician Xenocrates moved in a very different realm than what we usually associate with mathematics. Along with these traits, Xenocrates is reported to have displayed singular diligence. Aristaeus the Elder was a Greek mathematician who worked on conic sections.. Aristaeus the Elder was probably older than, but still a contemporary of, Euclid. Xenocrates (c. 396–314 B.C.E. ) He entered the Academy (in 378 b.c. Isocrates Xenocrates wrote on philosophy and mathematics. Xenocrates (zĬnŏk´rətēz), 396–314 BC, Greek philosopher, b. Chalcedon, successor of Speusippus as head of the Academy. The best contribution of Archimedes in mathematics is known as the invention of compound pulleys, antiquity, and screw pump. [12] Being unable to pay the tax levied upon resident aliens, he is said to have been saved only by the courage of the orator Lycurgus,[13] or even to have been bought by Demetrius Phalereus, and then emancipated. But it immediately became apparent that others, especially Aristotle, understood Plato in a wholly different way with respect to certain key questions. [8] In 339/8 BC, Xenocrates succeeded Speusippus in the presidency of the school,[9] defeating his competitors Menedemus of Pyrrha and Heraclides Ponticus by a few votes. A Roman citizen, Ptolemy was ethnically an Egyptian, though Hellenized; like many Hellenized Egyptians at the time, he may have possibly identified as Greek, though he would have been viewed as an Egyptian by the Roman rulers. According to a number of less substantiated anecdotes about Xenocrates, he is depicted as good–natured, gentle, and considerate–but it is also quite clear that he lacked the charis (“graciousness”) of his teacher Plato. He had the unique talent … Butthere are a few sources other than Aristotle. [62] How decidedly he insisted not only on the recognition of the unconditional nature of moral excellence, but on morality of thought, is shown by his declaration, that it comes to the same thing whether one casts longing eyes, or sets one's feet upon the property of others. Even here Xenocrates's preference for symbolic modes of sensualising or denoting appears: he connected the above three stages of knowledge with the three Fates: Atropos, Clotho, and Lachesis. + Before giving details of Plato 's life we will take a few moments to discuss how definite the details are which we give below. The first of the Greek atomists, Leucippus was probably the founder of the school of Abdera, whose most…, Sallust (86-ca. 388) commentary on Aristotle’s De anima; see Commentaria in Aristotelem Graeca, V, pt. The opposing candidates, Heraclitus Ponticus and Menedemus of Pyrrha, thereupon left the Academy. Xenocrates was a student of Plato and, as head of the Academy from 339 b.c. [41], How Xenocrates tried to establish and connect scientifically these assumptions, which appear to be taken chiefly from his books on the nature of the gods,[42] we do not learn, and can only discover the one fundamental idea at the basis of them, that all grades of existence are penetrated by divine power, and that this grows less and less energetic in proportion as it descends to the perishable and individual. Xenocrates adhered closely to the Platonist doctrine, and he is accounted the typical representative of the Old Academy. [29] Besides philosophical treatises, he wrote poetry (epē) and paraenesis. Besides Polemon, the statesman Phocion, Chaeron (tyrant of Pellene), the academic Crantor, the Stoic Zeno and Epicurus are said to have frequented his lectures. The story of Xenocrates may be incorrect: "In Greece, one of the very few references to combinatorics is a statement by Plutarch about the number of compound statements from 10 simple propositions; Plutarch quotes Chrysippus, Hipparchus, and Xenocrates on the subject, so all apparently had some interest in the subject. Xenocrates’ real legacy lies in the conception he sketched of a hierarchy of all existing things that culminates in a single, highest point, the One. Xenocrates is known to have written a book On Numbers, and a Theory of Numbers, besides books on geometry. [64], Xenocrates is known to have written a book On Numbers, and a Theory of Numbers, besides books on geometry. (b. Chalcedon [now Kadiköy], Birthynia [now Turkey], 396/395 b.c. [4], With a comprehensive work on Dialectic (τῆς περὶ τὸ διαλέγεσθαι πραγματείας βιϐλία ιδ΄) there were also separate treatises On Knowledge, On Knowledgibility (περὶ ἐπιστήμης α΄, περὶ ἐπιστημοσύνης α΄), On Divisions (διαιρέσεις η΄), On Genera and Species (περὶ γενῶν καὶ εἰδῶν α΄), On Ideas (περὶ ἰδεῶν), On the Opposite (περὶ τοῦ ἐναντίου), and others, to which probably the work On Mediate Thought (τῶν περὶ τὴν διάνοιαν η΄)[21] also belonged. When Alexander the Great sent him 30 talents of gold, he sent it back, saying that a king, not a philosopher, needs money. His approach to numbers was metaphysical rather than computational. 317[?]–ca. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates. . He distinguished from the good and the bad something which is neither good nor bad. The only quotation that seems to bear the stamp of authenticity is in Themistius’ (A.D. P. 399, n. 325. 35 B.C. [29] Plutarch writes that Xenocrates once attempted to find the total number of syllables that could be made from the letters of the alphabet. ." One of them is Proclus, who says, commenting on theParmenides(Cousin 1864, 888.11–19, 36–38; fr.30H, 94IP): ‘The founder’ is Plato. Two works by Xenocrates on Physics are mentioned (περὶ φύσεως ϛ΄ - φυσικῆς ἀκροάσεως ϛ΄),[22] as are also books On the Gods (περὶ Θεῶν β΄),[23] On the Existent (περὶ τοῦ ὄντος),[24] On the One (περὶ τοῦ ἑνός), On the Indefinite (περὶ τοῦ ἀορίστου),[25] On the Soul (περὶ ψυχῆς),[26] On the Emotions (περὶ τῶν παθῶν α΄)[24] On Memory (περὶ μνήμης), etc. 2–also in English, R. D. Hicks, trans., Lives of Eminent Philoso phers, I (Cambridge, Mass–London, 1966), 380–393; and U. von Wilamowitz–Moellendorff, Platon, sein Leben und seine Werke, 4th ed., I (Berlin, 1948), 579–581. . The biographical anecdotes state that he never left the Academy (where all his work was done) more than once a year. [2] By the most probable calculation[3] he was born 396/5 BC, and died 314/3 BC at the age of 82. ), Encyclopedia.com. Plutarch unfortunately, does not give us any further details, and contented himself with describing the well-known assumption of Xenocrates, that the soul is a self-moving number. On this point he was at odds with the political views of his predecessor Speusippus, who had supported Athens’ pro–Macedonian policies. He is said to have made more explicit the division of philosophy into the three parts of Physics, Dialectic and Ethics. עילם, ' eylam; Elamite halhatamti; Akk. Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA). Xenocrates (/zəˈnɒkrəˌtiːz/; Greek: Ξενοκράτης; c. 396/5 – 314/3 BC[1]) of Chalcedon was a Greek philosopher, mathematician, and leader (scholarch) of the Platonic Academy from 339/8 to 314/3 BC. © 2019 Encyclopedia.com | All rights reserved. Xenocrates, who had accompanied Plato on one of his visits to Sicily, became head of the Academy in 339 B.C. He may very well, in accordance with this, have regarded the point as a merely subjectively admissible presupposition, and a passage of Aristotle respecting this assumption[51] should perhaps be referred to him. [47] He approximated to the Pythagoreans in this, that (as is clear from his explanation of the soul) he regarded number as the conditioning principle of consciousness, and consequently of knowledge also; he thought it necessary, however, to supply what was wanting in the Pythagorean assumption by the more accurate definition, borrowed from Plato, that it is only insofar as number reconciles the opposition between the same and the different, and has raised itself to self-motion, that it is soul. Xenocrates probably found himself confronted with a difficult situation. Rejecting the annalistic method of writing history, he co…, Elam His teachings followed those of Plato, which he attempted to define more closely, often with mathematical elements.He was also an avid student of the council of the thirty-three. Úno 11. greek mathematics contributions. After Plato’s death, Xenocrates and Aristotle were invited to Assos, where they remained until the overthrow of Hermias of Atarneus, in 342 b.c. Hence too he was for proving the incorporeality of the soul by the fact that it is not nourished as the body is.[45]. Nevertheless, an election was held, which Xenocrates won by only a few votes. His teachings followed those of Plato, which he attempted to define more closely, often with mathematical elements. [clarification needed] He distinguished three forms of being: the sensible, the intelligible, and a third compounded of the two, to which correspond respectively, sense, intellect and opinion. His works on philosophy, politics and mathematics were very influential and laid the foundations for Euclid's systematic approach to mathematics. Plato’s successor, his nephew Speusippus, headed the Academy until his death in 340/339 b.c. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list. Retrieved February 24, 2021 from Encyclopedia.com: https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/xenocrates-chalcedon. In 322 b.c. was the fourth of the famous 10 Attic Greek orators. 27 'Xenocrates' Metaphysics: Fr. Th… Laertius adds that when Xenophanes was“banished from his native city” he “joined thecolony planted at Elea” (in Italy), and also lived at Zancle andCatana (two Greek communities in Sicily). Since Xenocrates was not a citizen of Athens, Antipatrus did not recognize his status as a legitimate ambassador. He considered unity and duality to be gods which rule the universe, and the soul a self-moving number. Xenocrates is known to have written a book on numbers, theory of numbers and geometry. Platonic philosophy did not originate solely with the Dialogues of Plato. Later Arabi… Few details of Ptolemy's life are known. [24] His four books on Royalty he had addressed to Alexander (στοιχεῖα πρὸς Ἀλέξανδρον περὶ βασιλείας δ΄). Rather, he belongs to the long line of those who have attempted to overcome a type of dualism within the philosophical tradition. The settlement was reached "at the price of a constitutional change: thousands of poor Athenians were disenfranchised," and Xenocrates said "that he did not want to become a citizen within a constitution he had struggled to prevent".