Xenocrates resented the Macedonian influence then dominant at Athens. Soon after the death of Demosthenes (c. 322), Xenocrates declined the citizenship offered to him at the instance of Phocion, and, being unable to pay the tax levied upon resident aliens, he was saved only by the courage of the orator Lycurgus, or even to have been bought by Demetrius Phalereus, and then emancipated. In 314, he died from hitting his head, after tripping over a bronze pot in his house.
Xenocrates 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.
Wanting in quickness of apprehension and natural grace he compensated by persevering and thorough-going industry, pure benevolence, purity of morals, unselfishness, and a moral earnestness, which compelled esteem and trust even from the Athenians of his own age.
Xenocrates adhered closely to the Platonist doctrine, and he 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 program; but metaphysics and ethics were the subjects which principally engaged his thoughts. He is said to have made more explicit the division of philosophy into the three parts of Physics, Dialectic and Ethics.
Xenocrates recognized three grades of cognition, each appropriated to a region of its own: knowledge, sensation, and opinion. He referred knowledge (episteme) to that essence which is the object of pure thought, and is not included in the phenomenal world; sensation (aisthesis) to that which passes into the world of phenomena; opinion (doxa) to that essence which is at once the object of sensuous perception, and, mathematically, of pure reason - the essence of heaven or the stars; so that he conceived of doxa in a higher sense, and endeavoured, more definitely than Plato, to exhibit mathematics as mediating between knowledge and sensuous perception All three modes of apprehension partake of truth; but in what manner scientific perception (epistemonike aisthesis) did so, we unfortunately do not learn. 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. 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, attributed to Xenocrates, was opposed to the Aristotelian table of categories.
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. He appears to hare 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. To this world-soul Zeus, or the world-spirit, has entrusted - in what degree and in what extent, we do not learn - dominion over that which is liable to motion and change. The divine power of the world-soul is then again represented, in the different spheres of the universe, as infusing soul into the planets, Sun, and Moon, - in a purer form, in the shape of Olympic gods. 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. The divine world-soul which reigns over the whole domain of sublunary changes he appears to have designated as the last Zeus, the last divine activity.
It is not till we get to the sphere of the separate daemonical powers of nature that the opposition between good and evil begins, and the daemonical power is appeased by means of a stubbornness which it finds there congenial to it; the good daemonical power makes happy those in whom it takes up its abode, the bad ruins them; for eudaimonia is the indwelling of a good daemon, the opposite the indwelling of a bad one.
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, 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. Hence he also appears to have maintained that as far as consciousness extends, so far also extends an intuition of that all-ruling divine power, of which he represented even irrational animals as partaking. But neither the thick nor the thin, to the different combinations of which he appears to have tried to refer the various grades of material existence, were regarded by him as in themselves partaking of soul; doubtless because he referred them immediately to the divine activity, and was far from attempting to reconcile the duality of the principia, or to resolve them into an original unity. Hence too he was for proving the incorporeality of the soul by the fact that it is not nourished as the body is.
It is probable, that, after the example of Plato, he designated the divine principium as alone indivisible, and remaining like itself; the material, as the divisible, partaking of multiformity, and different, and that from the union of the two, or from the limitation of the unlimited by the absolute unity, he deduced number, and for that reason called the soul of the universe, like that of individual beings, a self moving number, which, by virtue of its twofold root in the same and the different, shares equally in permanence and motion, and attains to consciousness by means of the reconciliation of this opposition.
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.
In the derivation of things according to the series of the numbers he seems to have gone further than any of his predecessors. 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. We find a similar attempt at the supplementation of the Platonic doctrine in Xenocrates's assumption of indivisible lines. In them he thought he had discovered what, according to Plato, God alone knows, and he among men who is loved by him, namely, the elements or principia of the Platonic triangles. He seems to have described them as first, original lines, and in a similar sense to have spoken of original plain figures and bodies, 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. 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 should perhaps be referred to him.
While, however, Xenocrates (and with him Speusippus and the other philosophers of the older Academy) would not accept that these intermediate things, such as health, beauty, fame, good fortune, etc. were valuable in themselves, he did not accept that they were absolutely worthless or indifferent. 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.
Still he maintained that virtue alone is valuable in itself, and that the value of every thing else is conditional. According to this, happiness should coincide with the consciousness of virtue, though its reference to the relations of human life requires the additional condition, that it is only in the enjoyment of the good things and circumstances originally designed for it by nature that it attains to completion; to these good things, however, sensuous gratification does not belong. 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, 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, and therefore seems to have regarded this human wisdom as at the same time exerted in investigating, defining, and applying. 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. His moral earnestness is also expressed in the warning that the ears of children should be guarded against the poison of immoral speeches.