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Xenocrates (Ξενοκράτης) of Chalcedon (396 – 314 B.C.E.) was a Greek philosopher and third scholarch or rector of the Academy from 339 to 314 B.C.E. His thought is known to us only through the commentaries of Aristotle, Proclus, Themistius and other Greek philosophers. He was loyal to the ideas of Plato, and responsible for formulating them in way that influenced later Platonists. He is credited with organizing the topics of philosophy into logic, physics and ethics, and with elaborating a more logical and complete cosmology than other Platonists, postulating the generation of number, then soul (as a self-moving number), then all the succeeding intangible and material levels of the universe.

In his biography of Xenocrates, Diogenes Laertius recounts several anecdotes to illustrate his humble, consistent and incorruptible character. He was teacher to a number of important Greek thinkers, including Polemon, the statesman Phocion, the academic Crantor, Crates, the Stoic Zeno and Epicurus.


Xenocrates was born in Chalcedon around 396 B.C.E. Moving to Athens in early youth, he became the pupil of Aeschines Socraticus, and then a disciple of Plato, whom he accompanied to Sicily in 361 B.C.E. According to Diogenes Laertius, Xenocrates was lazy by nature, and when comparing him with Aristotle, Plato used to say, "The one requires the spur, and the other the bridle." Diogenes also relates that Xenocrates was always solemn and grave, and that Plato often told him, "Xenocrates, sacrifice to the Graces."

After Plato’s death, Xenocrates went with Aristotle to visit Hermias at Atarneus. In 339 B.C.E., Xenocrates succeeded Speusippus as president of Plato’s Academy, defeating his rivals Menedemus and Heraclides Ponticus by only a few votes. Xenocrates's earnestness and strength of character won him the respect of the people of Athens. Three times he was sent as a member of an Athenian legation, once to Philip, and twice to Antipater. On these occasions he refused to be corrupted by gifts and lavish banquets. Diogenes Laertius reports several stories about Xenocrates' refusal to keep more wealth then he needed for his living expenses. He also had the habit of meditating in silence for an hour every day.

Xenocrates resented the Macedonian influence then dominant in Athens. Soon after the death of Demosthenes (flourished 322 B.C.E.), 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 sold as a slave by the city of Athens. A man named Demetrius Phalereus purchased him and gave him his freedom.

After twenty-five years as president of the Academy, Xenocrates died in 314 B.C.E. and was succeeded as scholarch by Polemon, whom he had reclaimed from a life of profligacy. Besides Polemon, Crates the Cynic, the statesman Phocion, Chaeron (tyrant of Pellene), the academic Crantor, the Stoic Zeno and Epicurus are said to have frequented his lectures.

Thought and Works

Diogenes Laertius lists 70 works by Xenocrates on a wide variety of topics; none of them have survived even as fragments embedded in other works. References and responses to his ideas in the writings of other Greek philosophers such as Aristotle, Theophrastus, Proclus and Asclepius, however, are numerous, and indicate that his thought played an important role in the development of Greek philosophy. Aristotle wrote several criticisms of Xenocrates without mentioning him by name, but commentators on Aristotle, such as Alexander of Aphrodisias, verify that these passages were directed towards him. His role seems to have been to clarify and formalize the teachings of Plato rather than to promote original ideas of his own.

Xenocrates is said to have invented, or at least to have emphasized, the division of philosophy into physics, logic and ethics.


Xenocrates held that being originated with the two ultimate principles, the One and the Indefinite Dyad (plurality, the everflowing, or the many) which generated the form-numbers from which arose lines, planes, solids, solids in motion (astronomical bodies) and ultimately perceptible things. He interpreted the concept of generation as simply a pedagogical device. Plato had distinguished between ideal (formal) numbers, which were essential concepts or ideals, and the mathematical numbers which are used for arithmetic calculations and measurements in the material world. Xenocrates thought that the formal numbers and mathematical numbers had the same nature, and that therefore it was unnecessary to distinguish between them. Aristotle attacked this concept, pointing out that, if forms (ideals) are numbers made up of arithmetical units, they not only cease to be principles, but also become subject to arithmetical operations. In his Metaphysics, Aristotle distinguishes between three groups of Platonists; those who, like Plato, distinguished between mathematical and ideal numbers; those who, like Xenocrates, identified them; and those who, like Speusippus, postulated mathematical numbers only.

Xenocrates's theory of inorganic nature was substantially identical with the theory of the elements which is propounded in Plato's 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, thus suggesting something closer to atomism. He also added the ether to the tetrad of the classical elements (fire, air, water, and earth).

According to Proclus, Xenocrates rejected the existence of forms (ideals) for objects manufactured by man (artifacts) and for individual beings.

Xenocrates proposed that there were certain lines that were indivisible and therefore primary, and certain primary planes and solids composed of them. Aristotle attributed this concept to Plato, but passages in the works of Alexander and several other commentators indicate that Xenocrates was a much stronger proponent of this idea. Several commentators suggested that Xenocrates was speaking of the form (ideal) of such a line rather than its physical or geometric magnitude.

In his Metaphysics, Theophrastus complains that the Platonists and Pythagoreans fail to give a complete description of the structure of the universe, but that Xenocrates presents a coherent world order which encompasses perceptibles, mathematicals and the divine. Aristotle also credited Xenocrates’ explanation of the universe with showing continuity.


His cosmology, which is drawn almost entirely from Plato’s 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, the one and the Indefinite Dyad (plurality, the everflowing, or the many), from where 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.

In a passage from his commentary on Aristotle’s De anima, Themistius refers to an account from a work by Xenocrates called On Nature, which describes how the soul is composed from the formal numbers 1, 2, 3 and 4. Both Themistius and Aristotle explain that, since the universe is derivative from those numbers, the soul derived from those same numbers can know about the universe on the principle that like recognizes like. The soul, a self-moving number, was capable of understanding the universe which was derived from the same number.

Xenocrates saw the One and the Dyad as gods, the One as male and the Dyad as female. He also thought of the heavenly bodies as gods, and identified intermediary beings between man and god, called daimones, who existed in the sublunary world. Plutarch says that Xenocrates associated each type of being with a different type of triangle; gods with equilateral triangles, daimones with isosceles triangles (intermediate between equilateral and scalene), and men with scalene triangles. Plutarch also said that according to Xenocrates, there were good and bad types of daimones.

Cognition and Ethics

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.

Xenocrates valued philosophy chiefly for its influence upon conduct. Diogenes Laertius’ catalog of his works shows that he had written largely on ethics; but few traces of his doctrine have survived. Things are goods, ills or neutrals. Goods are of three types—mental, bodily, or external; 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 only in his actions, but also in heart. Philosophy offers the greatest assistance to the attainment of virtue; for the philosopher does of his own accord what others do under the compulsion of law. There is a distinction between speculative wisdom and practical wisdom.

Of Xenocrates' logic we know only that he rejected the Aristotelian list of ten categories as too long, and sided with Plato’s distinction between things that are “by virtue of themselves” and things that exist “relative to something.” He associated things which exist in themselves with the One and things that exist relative to something with the many (plurality).

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This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.

Commentaries on Xenocrates

  • Babbitt, F. C. Plutarch's Moralia, Vol. V: 351C-438E. Cambridge, MA: Harvard University Press; London: William Heinemann Ltd., 1936, rpr. 1969.
  • Bury, R. G. Sextus Empiricus, 4 Vols. Vol II: Against the Logicians. Cambridge, MA: Harvard University Press; London: William Heinemann Ltd., 1935.
  • Dooley, William E. and Arthur Magdigan (trans.). Alexander of Aphrodisias on Aristotle's Metaphysics 1. Ithaca, NY: Cornell University Press, 1992. ISBN 0801427401
  • Morrow, Glenn R., and John Dillon. Proclus' Commentary on Plato's Parmenides. Princeton, NJ: Princeton University Press, 1987. ISBN 0691020892
  • Pines, S. “A New Fragment of Xenocrates and Its Implications.” Transactions of the American Philological Association 51 (1961): 3-34.
  • Ross, W. D., & F. H. Fobes. 1929. Theophrastus: Metaphysics. Reprint edition, 1967. Hildesheim: Georg Olms.
  • Todd, Robert B. Themistius on Aristotle's On the Soul. Ithaca, NY: Cornell University Press, 1996. ISBN 0801432812

Works About Xenocrates

  • Cherniss, Harold. 1945. The Riddle of the Early Academy. Reprint edition, 1962. New York: Russell & Russell. ISBN 0846201526
  • Dillon, John. 2003. The Heirs of Plato: A Study of the Old Academy (347-274 B.C.E.). New edition, 2005. New York: Oxford University Press. ISBN 0199279462
  • Furley, David. Two Studies in the Greek Atomists. Princeton, NJ: Princeton University Press, 1967.
  • Heinze, Richard. 1892. Xenocrates. Reprint edition, 1965. Hildesheim: G. Olms.
  • Hicks, R. D. Diogenes Laertius: Lives of Eminent Philosophers, 2 vols. Cambridge, MA: Loeb Classical Library, 1925. ISBN 0674992040

External links

All links retrieved May 20, 2023.

General Philosophy Sources


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