The view of Xenocrates is based on the same ideas.
He was a fellow-pupil of Polemo in the school of Xenocrates at Athens, and was the first commentator on Plato.
The appointment of Plato's nephew, Speusippus, to succeed his uncle in the Academy induced Aristotle and Xenocrates to leave Athens together and repair to the court of Hermias.
Indeed, according to Ammonius, Plato too had talked as he walked in the Academy; and all his followers were called Peripatetics, until, while the pupils of Xenocrates took the name " Academics," those of Aristotle retained the general name.
But Heracleides and Hestiacus, Speusippus and Xenocrates were also present and wrote similar reports.
What is more, both Speusippus and Xenocrates founded their own philosophies on this very Pythagoreanism of Plato.
Xenocrates as president from 339 onwards taught that the one and many are principles, only without distinguishing mathematical from formal numbers.
Moreover, the successors of Plato in the Academy, Speusippus and Xenocrates, showed the same belief in the essentiality of virtue.
Xenocrates took the tolerant view that it is the possession of appropriate virtue and noble actions, requiring as conditions bodily and external goods.
It is probable that when, after Plato's death and the accession of Speusippus in 347, Aristotle with Xenocrates left Athens to visit his former pupil Hermias, the three discussed this moderate system of Ethics in which the two philosophers nearly agreed.
In the History of Art the original Greek authorities are Duris of Samos (born c. 340 B.C.), Xenocrates of Sicyon (fl.
61, Lysippum Sicyonium Duris negat ullius fuisse discipulum, &c.); the notices of the successive developments of art, and the list of workers in bronze and painters, to Xenocrates; and a large amount of miscellaneous information to Antigonus.
The main merit of his account of ancient art, the only classical work of its kind, is that it is a compilation ultimately founded on the lost textbooks of Xenocrates and on the biographies of Duris and Antigonus.
Neither Theophrastus at the Lyceum, nor Xenocrates and Polemo at the Academy, nor Stilpo, who was drawing crowds to hear him at Megara, could be said to have inherited much of the great reformer's intellectual vigour, to say nothing of his moral earnestness.
Xenocrates indeed, identifying ideal and mathematical numbers, sought to ' That Plato did not neglect, but rather encouraged, classificatory science is shown, not only by a well-known fragment of the comic poet Epicrates, which describes a party of Academics engaged in investigating, under the eye of Plato, the affinities of the common pumpkin, but also by the Timaeus, which, while it carefully discriminates science from ontology, plainly recognizes the importance of the study of natural kinds.
XENOCRATES, of Chalcedon, Greek philosopher, scholarch or rector of the Academy from 339 to 314 B.C., was born in 396.
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.
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.
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).
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.
It is found in the theories of Speusippus, Xenocrates, and also to some extent in those of the Peripatetics.
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.
Valuing philosophy chiefly for its influence upon conduct, Xenocrates bestowed especial attention upon ethics.
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.