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Rh (347 ), in company with Aristotle he paid a visit to Hermias at Atarneus. In 339, Aristotle being then in Macedonia, Xenocrates succeeded Speusippus in the presidency of the school, defeating his competitors Menedemus and Heracleides by a few votes. On three occasions he was member of an Athenian legation, once to Philip, twice to Antipater. Soon after the death of Demosthenes in 322, resenting the Macedonian influence then dominant at Athens, Xenocrates declined the citizenship offered to him at the instance of Phocion, and, being unable to pay the tax levied upon resident aliens, was, it is said, sold, or on the point of being sold, into slavery. He died in 314, and was succeeded as scholarch by Polemon, whom he had reclaimed from a life of profligacy. Besides Polemon, the statesman Phocion, Chaeron, tyrant of Pellene, the Academic Crantor, the Stoic Zeno and Epicurus are alleged to have frequented his lectures.

Xenocrates's earnestness and strength of character won for him universal respect, and stories were remembered in proof of his purity, integrity and benevolence. Wanting in quickness of apprehension and in native grace, he made up for these deficiencies by a conscientious love of truth and an untiring industry. Less original than Speusippus, he adhered more closely to the letter of Platonic doctrine, and is accounted the typical representative of the Old Academy. In his writings, which were numerous, he seems to have covered nearly the whole of the Academic programme; but metaphysics and ethics were the subjects which principally engaged his thoughts. He is said to have invented, or at least to have emphasized, the tripartition of philosophy under the heads of physic, dialectic and ethic.

In his ontology Xenocrates built upon Plato's foundations: that is to say, with Plato he postulated ideas or numbers to be the causes of nature's organic products, and derived these ideas or numbers from unity (which is active) and plurality (which is passive). But he put upon this fundamental dogma a new interpretation. According to Plato, existence is mind pluralized: mind as a unity, i.e. universal mind, apprehends its own plurality as eternal, immutable, intelligible ideas; and mind as a plurality, i.e. particular mind, perceives its own plurality as transitory, mutable, sensible things. The idea, inasmuch as it is a law of universal mind, which in particular minds produces aggregates of sensations called things, is a “determinant”, and as such is styled “quantity” and perhaps “number” ; but the ideal numbers are distinct from arithmetical numbers. Xenocrates, however, failing, as it would seem, to grasp the idealism which was the metaphysical foundation of Plato's theory of natural kinds, took for his principles arithmetical unity and plurality, and accordingly identified ideal numbers with arithmetical numbers. In thus reverting to the crudities of certain Pythagoreans, he laid himself open to the criticisms of Aristotle, who, in his Metaphysics, recognizing amongst contemporary Platonists three principal groups—(1) those who, like Plato, distinguished mathematical and ideal numbers; (2) those who, like Xenocrates, identified them; and (3) those who, like Speusippus, postulated mathematical numbers only—has much to say against the Xenocratean interpretation of the theory, and in particular points out that, if the ideas are numbers made up of arithmetical units, they not only cease to be principles, but also become subject to arithmetical operations. Xenocrates's theory of inorganic nature was substantially identical with the theory of the elements which is propounded in the Timaeus, 53 C seq. Nevertheless, holding that every dimension has a principle of its own, he rejected the derivation of the elemental solids—pyramid, octahedron, icosahedron and cube—from triangular surfaces, and in so far approximated to atomism. Moreover, to the tetrad of simple elements—viz. fire, air, water, earth—he added the, ether.

His cosmology, which is drawn almost entirely from the Timaeus, and, as he intimated, is not to be regarded as a cosmogony, should be studied in connexion with his psychology. Soul is a self-moving number, derived from the two fundamental principles, unity and plurality, whence it obtains its powers of rest and motion. It is incorporeal, and may exist apart from body. The irrational soul, as well as the rational soul, is immortal. The universe, the heavenly bodies, man, animals, and presumably plants, are each of them endowed with a soul, which is more or less perfect according to the position which it occupies in the descending scale of creation. With this Platonic philosopheme Xenocrates combines the current theology, identifying the universe and the heavenly bodies with the greater gods, and reserving a place between them and mortals for the lesser divinities.

If the extant authorities are to be trusted, Xenocrates recognized three grades of cognition, each appropriated to a region of its own—viz. knowledge, opinion and sensation, having for their respective objects supra-celestials or ideas, celestials or stars, and infra-celestials or things. Even here the mythological tendency displays itself—, and   being severally committed to Atropos, Lachesis and Clotho. Of Xenocrates's

logic we know only that with Plato he distinguished and , rejecting the Aristotelian list of ten categories as a superfluity.

Valuing philosophy chiefly for its influence upon conduct, Xenocrates bestowed especial attention upon ethics. The catalogue of his works shows that he had written largely upon this subject; but the indications of doctrine which have survived are scanty, and may be summed up in a few sentences. Things are goods, ills or neutrals. Goods are of three sorts—mental, bodily, external; but of all goods virtue is incomparably the greatest. Happiness consists in the possession of virtue, and consequently is independent of personal and extraneous advantages. The virtuous man is pure, not in act only, but also in heart. To the attainment of virtue the best help is philosophy; for the philosopher does of his own accord what others do under the compulsion of law. Speculative wisdom and practical wisdom are to be distinguished. Meagre as these statements are, they suffice to show that in ethics, as elsewhere, Xenocrates worked upon Platonic lines.

Xenocrates was not in any sense a great thinker. His metaphysic was a travesty rather than a reproduction of that of his master. His ethic had little which was distinctive. But his austere life and commanding personality made him an effective teacher, and his influence, kept alive by his pupils Polemon and Crates, ceased only when Arcesilaus, the founder of the so-called Second Academy, gave a new direction to the studies of the school.

See D. Van de Wynpersse, De Xenocrate Chalcedonio (Leiden, 1822); C. A. Brandis, ''Gesch. d. griechisch-römischen Philosophie'' (Berlin, 1853), ii. 2, 1; E. Zeller, Philosophie d. Griechen (Leipzig, 1875), ii. 1; F. W. A. Mullach, Fragmenta Philosophorum Graecorum (Paris, 1881), iii. (Author:Henry Jackson (1839-1921))  XENOPHANES of Colophon, the reputed founder of the Eleatic school of philosophy, is supposed to have been born in the third or fourth decade of the 6th century An exile from his Ionian home, he resided for a time in Sicily, at Zancle and at Catana, and afterwards established himself in southern Italy, at Elea, a Phocaean colony founded in the sixty-first Olympiad (536-533). In one of the extant fragments he speaks of himself as having begun his wanderings sixty-seven years before, when he was twenty-five years of age, so that he was not less than ninety-two when he died. His teaching found expression in poems, which, he recited rhapsodically in the course of his travels. In the more considerable of the elegiac fragments which have survived, he ridicules the doctrine of the migration of souls (xviii.), asserts the claims of wisdom against the prevalent athleticism, which seemed to him to conduce neither to the good government of states nor to their material prosperity (xix.), reprobates the introduction of Lydian luxury into Colophon (xx.), and recommends the reasonable enjoyment of social pleasures (xxi.). Of the epic fragments, the more important are those in which he attacks the “anthropomorphic and anthropopathic polytheism” of his contemporaries. According to Aristotle, “the first of Eleatic unitarians was not careful to say whether the unity which he postulated was finite or infinite, but, contemplating the whole firmament, declared that the One is God.” Whether Xenophanes was a monotheist, whose assertion of the unity of God suggested to Parmenides the doctrine of the unity of Being, or a pantheist, whose assertion of the unity of God was also a declaration of the unity of Being, so that he anticipated Parmenides— in other words, whether Xenophanes's teaching was purely theological or had also a philosophical significance—is a question about which authorities have differed and will probably continue to differ. The silence of the extant fragments, which have not one word about the unity of Being, favours the one view; the voice of antiquity, which proclaims Xenophanes the founder of Eleaticism, has been thought to favour the other.

Of Xenophanes's utterances about (1) God, (2) the world, (3) knowledge, the following survive: (1) “There is one God, greatest among gods and men, neither in shape nor in thought like unto mortals. . . . He is all sight, all mind, all ear (i.e. not a composite organism). . . . Without an effort ruleth he all things by thought. He abideth ever in the same place motionless, and it befitteth him not to wander hither and thither. . . . Yet men imagine gods to be born, and to have raiment and voice and body, like themselves. Even so the gods of the Ethiopians are swarthy and flat-nosed, the gods of the Thracians are fair-haired and blue-eyed. . . . Even so Homer and Hesiod attributed to the gods all that is a shame and a reproach among men—theft, adultery, deceit and other lawless acts. . . . Even so oxen, lions and horses, if they had hands wherewith to grave images, would fashion gods