(Ξενοκράτης), the philosopher, was a native of Chalcedon (Cic. Ac. 1.4 ; Athen. 12.530d.; Stob. Ecl. Phys. 1.3 ; Suid. s.v. comp. Strabo xii. p.566b. He is called a Carchedonian only through a clerical error in Clem. Alex. Cohort. p. 33, and Strom. 5.430, &c). According to the most probable calculation (D. L. 4.14; comp. Censorin. 100.15 ; Wynpersee, p. 6, &c) he was born Ol. 96. 1 (B. C. 396), and died Ol. 116. 3 (B. C. 314) at the age of 82. He is stated to have attached himself first to Aeschines the Socratic (Athen. 11.507c), and afterwards, while still a youth, to Plato. (D. L. 4.6.) His close connection with Plato is indicated (to pass over insignificant or untrustworthy stories in Diog. Laert. &c, see Wynpersee, p. 13, &c) by the account that he accompanied him to Syracuse. (D. L. 4.6, &c) After the death of Plato he betook himself, with Aristotle, to Hermias, tyrant of Atarneus and Assus (Strab. xii. p.610), and, after his return to Athens, was repeatedly sent on embassies to Philip of Macedonia, and at a later time to Antipater (Ol. 114. 3), during the Lamian war. (D. L. 4.8, 9, ib. Interp.) The want of quick apprehension and natural grace (D. L. 4.6; Plut. Conj. Praec. p. 141) he compensated by persevering and thorough-going industry (D. L. 4.6, 11 ; comp. Plut. de recta Rat. aud. p. 47e), pure benevolence (D. L. 4.10; Aelian, Ael. VH 13.3), purity of morals (D. L. 4.7; Plut. Comp. Cimon. c. Lucullo, 100.1; Cic. de Off. 1.30; Valer. Max. 2.10), unselfishness (D. L. 4.8, &c ; Cic. Tusc. 5.32; see Menag. on Diog. Laert.), and a moral earnestness, which compelled esteem and trust even from the Athenians of his own age (D. L. 4.7; Cic. Att. 1.15; Plut. de Adulat. et Amic. discr. p. 71e). Yet even he experienced the fickleness of popular favour, and being too poor to pay the protection-money (μετοίκιον), is said to have been saved only by the courage of the orator Lycurgus (Plut. Flam. 100.12, X. Orat. Vitae, 7; but compare Phocion, 100.29), or even to have been bought by Demetrius Phalereus, and then emancipated. (D. L. 4.14.) He became president of the Academy even before the death of Speusippus, who was bowed down by sickness, and occupied that post for twenty-five years. (Id. 4.14, comp. 3.)

If we consider that Aristotle and Theophrastus wrote upon the doctrines of Xenocrates (Diog. (Laert. 5.25, 47), that men like Panaetius and Cicero entertained a high regard for him (Cic. de Fin. 4.28, Acad. 1.4), we must not dream of being able, even in any degree, to estimate completely and accurately his mind or the philosophical direction which it took. How he strove to make himself master of the knowledge of his age, and to establish his own fundamental doctrines or those of Plato, by applying them to particular cases, we see by the titles of his treatises, bare as they have come down to us. With a more comprehensive work on Dialectic (τῆς περὶ τὸ διαλέγεσθαι πραγματείας Βιβλία ιδ́ there were connected separate treatises on science, on scientificness (περὶ ἐπιστήμης ά, περὶ ἐπιστημοσύνης ά), on divisions (διαιρέσεις ή), on genera and species (περὶ γενῶν καὶ εἰδῶν ά), on ideas (περὶ ἰδεῶν), on the opposite (περὶ τοῦ ἐναντίου), and others, to which probably the work on mediate thought (τῶν περὶ τὴν διάνοιαν ή, Diog. Laeft. 4.13, 12; comp. Cic. Ac. 4.46) also belonged. Two works by Xenocrates on Physics are mentioned (περὶ φύσεως σ́ -φυσικῆς ἀκροάσεως σ́. ib. 11, 13), as are also books upon the gods (περὶ Θεῶν β́, ib. 13; comp. Cic. de Nat. Deor. 1.13), on the existent (περὶ τοῦ ὄντος, ib. 12), on the One (περὶ τοῦ ἑνός, ib.), on the indefinite (περὶ τοῦ ἀορίστου, ib. 11), on the soul (περὶ ψυχῆς, ib. 13), on the affections (περὶ τῶν παθῶν ά, ib. 12), on memory (περὶ μνήμης, ib.), &c In like manner, with the more general ethical treatises on happiness (περὶ εὐδαιμονίας β́, ib. 12), and on virtue (περὶ ἀρετῆς β́, ib.) there were connected separate books on individual virtues, on the voluntary, &c (ibid.) His four books on royalty he had addressed to Alexander (στοιχεῖα πρὸς Ἀλέξανδρον περὶ βασιλείας δ́; comp. Plut. ad v. Colot. p. 1126. d.). Besides these he had written treatises on the State (περὶ πολιτείας ά, D. L. 4.12; πολιτικός ά, ib. 13), on the power of law (περὶ δυνάμεως νόηου ά, ib. 12), &c, as well as upon geometry, arithmetic, and astrology (ib. 13, 14).

Xenocrates appears to have made a still more definite division between the three departments of philosophy, for the purpose of the scientific treatment of them, than Speusippas (Sext. Emp. ad v. Math. 7.16), but at the same time to have abandoned Plato's heuristic (εὑριστική) method of conducting through doubts (ἀπορίαι), and to have adopted in its stead a mode of bringing forward his doctrines in which they were developed dogmatically (Sext. Emp. Hypotyp. 1.2; comp. Cic. Ac. 1.4; D. L. 4.11, 16). Xenocrates also seized more sharply and distinctly the separation and connection. of the different modes of cognition and comprehension, than did Specusippus. He referred science (ἐπιστήμη) to that essence which is the object of pure thought, and is not included in the phenomenal world; sensuous perception (αἴσθησις) to that which passes into the world of phenomena; conception (δόξα) 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 δόξα in a higher sense, and endeavoured, more decidedly than Plato, to exhibit mathematics as mediating between knowledge and sensuous perception (Sext. Emp. ad v. Math. 7.147, &c. ; comp. Boeth. in Aristot. Interp. p. 297). All three modes of apprehension partake of truth; but in what manner scientific perception (ἐπιστημονικὴ ἄσθησις) 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 Parcae, Atropos, Lachesis, and Clotho. It is the more to be regretted that we know nothing further about the mode in which Xenocrates carried out his dialectic, as it is probable that what was peculiar to the 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 (τὸ καθ̓ αὑτὸ καὶ τὸ πρός τι, Simpl. in Arist. Catey. iii. f. 6, b ; Schol. in Arist. p. 47), attributed to Xenocrates, was opposed to the Aristotelian table of categories.

We know from Plutarch (de Animae procreat. e Tim. p. 1012d., 1013, e.) that Xenocrates, if he did not explain the Platonic construction of the world-soul as Crantor after him did, yet conceived of it in a peculiar manner, so that one branch of interpretation of the connected itself with him; and further (Arist. de Caelo, 1.10. p. 279b., 32, Metaph. 14.4; Schol. in Arist. p. 488b. &c, 827, b.) we learn that he stood at the head of those who, regarding the universe as un-originated and imperishable, looked upon the chronic succession in the Platonic theory as a form in which to denote the relations of conceptual succession. Plutarch unfortunately presupposed, as known, that of which only a few obscure traces have been preserved, and contented himself with bringing forward the well-known assumption of the Chalcedonian, that the soul is a self-moving number (l.c. ; comp. Arist. de Anima, 1.2, 4, Anal. Post. 2.4, ib. Interp.). Probably we should connect with this the statement that Xenocrates called unity and duality (μονάς and δυάς) deities, and characterised the former as the first male existence, ruling in heaven, as father and Zeus, as uneven number and spirit; the latter as female, as the mother of the gods, and as the soul of the universe which reigns over the mutable world under heaven (Stob. Ecl. Phys. 1.62), or, as others have it, that he named the Zeus who ever remains like himself, governing in the sphere of the immutable, the highest; the one who rules over the mutable, sublunary world, the last, or outermost (Plut. Plat. Quaest. 9.1; Clem. Alex. Strom. 5.604). If, like other Platonists, he designated the material principle as undefined duality (ἀόριστος δυάς), 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 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. 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 Here, 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 (Stob. l.c. ; Plut. de Orac. defect. p. 416c. ; Cic. de Nat. Deor. 1.13). 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 (Stob. Ecl. Phys p. 62), 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 eudaemonia is the indwelling of a good daemon, the opposite the indwelling of a bad one (Plut. de Isid. et Os. p. 360d., 361, a., de Orac. defect. p. 419a. ; Arist. Top. 2.2; Stob. Serm. 104.24). How Xenocrates endeavoured to establish and connect scientifically these assumptions, which appear to be taken chiefly from his books on the nature of the gods (Cic. l c.), 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 also he appears to have maintained that as far as consciousness extends, so far also extends and intuition of that all-ruling divine power, of which he represented even irrational animals as partaking (Clem. Alex. Strom. 5.590). But neither the thick nor the thin (πυκνὸν καὶ μανόν), to the different combinations of which he appears to have endeavoured to refer the various grades of material existence, were regarded by him as in themselves partaking of soul (Plut. de Fac. in orbe lunae, p. 943f.); 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 (Nemesius, p. 31, Ant.). But what more precise conception he formed of the material principium, the twofold infinite, or the undefined duality, or which of the different modes of expression attributed by Aristotle to the Platonists (Metaph. N, 1. p. 1087b., p.1088. 15.100.2,p. 1088b., 28. 100.5, p. 1092. 35) belonged to him, can hardly be determined with certainty. As little can we ascertain which of the three assumptions, noticed by Aristotle, respecting the primal numbers, and their relation to the ideas and to mathematical numbers (Metaph. M, 6. p. 1080b., 11. 100.9, p. 1086. 2. 100.8, p. 1083. 27., comp. N, 5. p. 1090b., 31, &c) was his. We can only assume as probable, that, after the example of Plato, he designated the divine principium as alone indivisible, and remaining like itself (ταὐτόν); the material, as the divisible, partaking of multiformity, and different (θάτερον), 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. It is also probable that, like Speusippus, he gave up the distinction between primal numbers and ideas, and did not even separate mathematical number from primal number. Then, going back to the Pythagoreans, he appears to have made use of his elementary numbers in the first instance as exponents of relations with reference to the different grades as well of the divine activity as of material existence. In the derivation of things according to the series of the numbers he seems to have gone further than any of his predecessors (Theophrast. Met. 100.3). He approximated to the Pythagoreans again 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 in so far 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 (Aristot. de Lin. insec. Phys. Ausc. 6.2 ; comp. Simpl. in Arist. Phys. f. 30). In them he thought he had discovered what, according to Plato (Tim. p. 53c.), 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 (Simpl. in Arist. de Caelo ; Schol. in Arist. p. 510. 35), 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 (de Anima, 1.4, extr.) should perhaps be referred to him.

Our information with regard to the Ethic of Xenocrates is still more scanty than that respecting his Dialectic and Physic. We only see that here, also, he endeavored to supplement the Platonic doctrine in individual points, and at the same time to give it a more direct applicability to life. He distinguished from the good and the bad a something which is neither good nor bad (Sext. Emp. ad v. Math. 11.4). In his view, as in that of the older Academy generally, the good is that which should be striven after for itself, that is, which has value in itself, while the bad is the opposite of this (Cic. de Leg. 1.13). Consequently, that which is neither good nor bad is what in itself is neither to be striven after nor to be avoided, but derives value or the contrary according as it serves as means for what is good or bad, or rather, is used by us for that purpose. While, however, Xenocrates (and with him Speusippus and the other philosophers of the older Academy appear to have coincided, Cic. de Fin. 4.18, &c) would not allow that these intermediate things, such as health, beauty, fame, the gifts of fortune, &c were valuable in themselves, he did not allow that they were absolutely worthless or indifferent (Cic. de Leg. 1.21). 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. (Cic. Tusc. 5.10, 18.)

Still he appears to have maintained in the most decided manner that virtue alone is valuable in itself, and that the value of every thing else is conditional (Cic. ll. cc., comp. Acad. 1.6). According to this, happiness should coincide with the consciousness of virtue (Arist. Top. 2.6, 7.1, ib. Alex.), 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 (Cic. Tusc. 5.13, comp. 17, de Fin. 2.11; Senec. Epist. 85). 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 (πράξεις, ἕξεις, καὶ διαθέσεις), those movements and relations (σχέσεις) also without which external good things cannot be attained (Clem. Al. Strom. ii. p. 419; comp. Cic. de Fin. 4.7, 5.9, Acad. 2.44, 45, Tusc. 4.10, 26, 31), 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 men (Clem. Al. Strom. ii. p. 369; Cic. Ac. 2.44, 45), and therefore seems to have regarded this human wisdom as at the same time exerted in investigating, defining, and applying (θεωρητικὴ καὶ ὁριστική, Arist. Top. 6.3). 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 (Aelian, Ael. VH 14.42). His moral earnestness is also expressed in the warning that the ears of children should be guarded against the poison of immoral speeches. (Plut. de Audit. p. 38a.)

Comp. Van de Wynpersee, Diatribe de Xenocrate Chalcedonio, Lugd. Batav. 1822, with the review in the 1824, p. 275, &c. by the writer of this article.