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. Upon his master's death, 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 Heraclides Ponticus 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 (fl 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 said 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

those who, like Plato, distinguished mathematical and ideal numbers;
those who, like Xenocrates, identified them; and
those who, like Speusippus, postulated mathematical numbers only

Aristotle 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 the classical elements (fire, air, water, and 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 connection 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: knowledge, opinion, and sensation. Their objects, respectively, are supra-celestials or ideas, celestials or stars, and infra-celestials or things. Of Xenocrates's logic we know only that he sided with Plato, 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.

On numbers and The theory of numbers.

http://plato.stanford.edu/entries/xenocrates/

References

D. Van de Wynpersse, De Xenocrate Chalcedonio (Leiden, 1822)
CA Brandis, Geschichte die griechisch-romischen Philosophie (Berlin, 1853), ii. 2, I
Eduard Zeller, Philosophie die Griechen (Leipzig, 1875), ii. I
FWA Mullach, Fragmenta Philosophorum Graecorum (Paris, 1881), iii.
R. Heinze, Xenocrates (1892)

This entry was originally from the 1911 Encyclopedia Britannica.

Ancient Greeks