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Xenocrates (; el, Ξενοκράτης; c. 396/5314/3 BC) of Chalcedon was a Greek philosopher,
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
, and leader ( scholarch) of the
Platonic Academy The Academy (Ancient Greek: Ἀκαδημία) was founded by Plato in c. 387 BC in Classical Athens, Athens. Aristotle studied there for twenty years (367–347 BC) before founding his own school, the Lyceum (classical), Lyceum. The Academy ...
from 339/8 to 314/3 BC. His teachings followed those of
Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
, which he attempted to define more closely, often with mathematical elements. He distinguished three forms of being: the sensible, the intelligible, and a third compounded of the two, to which correspond respectively,
sense A sense is a biological system used by an organism for sensation, the process of gathering information about the world through the detection of Stimulus (physiology), stimuli. (For example, in the human body, the brain which is part of the cen ...
,
intellect In the study of the human mind, intellect refers to, describes, and identifies the ability of the human mind to reach correct conclusions about what is true and what is false in reality; and how to solve problems. Derived from the Ancient Gree ...
and
opinion An opinion is a judgment, viewpoint, or statement that is not conclusive, rather than facts, which are true statements. Definition A given opinion may deal with subjective matters in which there is no conclusive finding, or it may deal with f ...
. He considered unity and duality to be gods which rule the
universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. Acc ...
, and the soul a self-moving
number A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers c ...
. God pervades all things, and there are daemonical powers, intermediate between the
divine Divinity or the divine are things that are either related to, devoted to, or proceeding from a deity.divine
and the
mortal Mortal means susceptible to death; the opposite of immortality, immortal. Mortal may also refer to: * Mortal (band), a Christian industrial band * The Mortal, Sakurai Atsushi's project band * Mortal (novel), ''Mortal'' (novel), a science fiction ...
, which consist in conditions of the soul. He held that mathematical objects and the
Platonic Ideas Platonic realism is the philosophical position that universals or abstract objects exist objectively and outside of human minds. It is named after the Greek philosopher Plato who applied realism to such universals, which he considered ideal for ...
are identical, unlike Plato who distinguished them. In
ethics Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and wrong behavior".''Internet Encyclopedia of Philosophy'' The field of ethics, along with aesthetics, concerns m ...
, he taught that
virtue Virtue ( la, virtus) is moral excellence. A virtue is a trait or quality that is deemed to be morally good and thus is valued as a foundation of principle and good moral being. In other words, it is a behavior that shows high moral standard ...
produces
happiness Happiness, in the context of Mental health, mental or emotional states, is positive or Pleasure, pleasant emotions ranging from contentment to intense joy. Other forms include life satisfaction, well-being, subjective well-being, flourishin ...
, but external goods can minister to it and enable it to effect its purpose.


Life

Xenocrates was a native of Chalcedon. By the most probable calculation he was born 396/5 BC, and died 314/3 BC at the age of 82. His father was named Agathon ( grc, Ἀγάθωνος) or Agathanor ( grc, Ἀγαθάνορος).Suda Encyclopedia, xi,42
/ref> Moving to
Athens Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is both the capital and largest city of Greece. With a population close to four million, it is also the seventh largest city in the European Union. Athens dominates ...
in early youth, he became the pupil of
Aeschines Socraticus Aeschines of Sphettus ( grc, Αἰσχίνης Σφήττιος, c. 425 BC – c. 350 BC) or Aeschines Socraticus ( grc, Αἰσχίνης Σωκρατικός), son of Lysanias, of the deme Sphettus of Athens, was a philosopher who in his youth ...
, but subsequently joined himself to
Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
, whom he accompanied to
Sicily (man) it, Siciliana (woman) , population_note = , population_blank1_title = , population_blank1 = , demographics_type1 = Ethnicity , demographics1_footnotes = , demographi ...
in 361. Upon his master's death, he paid a visit with
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
to Hermias of Atarneus. In 339/8 BC, Xenocrates succeeded
Speusippus Speusippus (; grc-gre, Σπεύσιππος; c. 408 – 339/8 BC) was an ancient Greek philosopher. Speusippus was Plato's nephew by his sister Potone. After Plato's death, c. 348 BC, Speusippus inherited the Academy, near age 60, and remained ...
in the presidency of the school, defeating his competitors
Menedemus of Pyrrha Menedemus of Pyrrha (Lesbos) ( grc-gre, Μενέδημος; fl. c. 350 BC, was a member of Plato's Academy, during the time of Speusippus. Upon the death of Speusippus in 339 BC, an election was held for the next scholarch of the Academy. Menedem ...
and
Heraclides Ponticus Heraclides Ponticus ( grc-gre, Ἡρακλείδης ὁ Ποντικός ''Herakleides''; c. 390 BC – c. 310 BC) was a Greek philosopher and astronomer who was born in Heraclea Pontica, now Karadeniz Ereğli, Turkey, and migrated to Athens. He ...
by a few votes. On three occasions he was member of an Athenian legation, once to
Philip Philip, also Phillip, is a male given name, derived from the Greek (''Philippos'', lit. "horse-loving" or "fond of horses"), from a compound of (''philos'', "dear", "loved", "loving") and (''hippos'', "horse"). Prominent Philips who popularize ...
, twice to
Antipater Antipater (; grc, , translit=Antipatros, lit=like the father; c. 400 BC319 BC) was a Macedonian general and statesman under the subsequent kingships of Philip II of Macedon and his son, Alexander the Great. In the wake of the collaps ...
. Xenocrates resented the
Macedon Macedonia (; grc-gre, Μακεδονία), also called Macedon (), was an ancient kingdom on the periphery of Archaic and Classical Greece, and later the dominant state of Hellenistic Greece. The kingdom was founded and initially ruled by ...
ian influence then dominant at Athens. Soon after the death of
Demosthenes Demosthenes (; el, Δημοσθένης, translit=Dēmosthénēs; ; 384 – 12 October 322 BC) was a Greek statesman and orator in ancient Athens. His orations constitute a significant expression of contemporary Athenian intellectual prow ...
(c. 322 BC), he declined the citizenship offered to him at the insistence of Phocion as a reward for his services in negotiating peace with
Antipater Antipater (; grc, , translit=Antipatros, lit=like the father; c. 400 BC319 BC) was a Macedonian general and statesman under the subsequent kingships of Philip II of Macedon and his son, Alexander the Great. In the wake of the collaps ...
after Athens' unsuccessful rebellion. The settlement was reached "at the price of a constitutional change: thousands of poor Athenians were disenfranchised," and Xenocrates said "that he did not want to become a citizen within a constitution he had struggled to prevent". Being unable to pay the tax levied upon resident aliens, he is said to have been saved only by the courage of the orator
Lycurgus Lycurgus or Lykourgos () may refer to: People * Lycurgus (king of Sparta) (third century BC) * Lycurgus (lawgiver) (eighth century BC), creator of constitution of Sparta * Lycurgus of Athens (fourth century BC), one of the 'ten notable orators' ...
, or even to have been bought by Demetrius Phalereus, and then emancipated. In 314/3, 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 Crantor ( el, Κράντωρ, ''gen''.: Κράντορος; died 276/5 BC) was a Greek philosopher and scholarch (leader) of the Old Academy, probably born around the middle of the 4th century BC, at Soli in Cilicia (modern-day Turkey). Life Cra ...
, the Stoic Zeno and
Epicurus Epicurus (; grc-gre, Ἐπίκουρος ; 341–270 BC) was an ancient Greek philosopher and sage who founded Epicureanism, a highly influential school of philosophy. He was born on the Greek island of Samos to Athenian parents. Influenced ...
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 Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
and
ethics Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and wrong behavior".''Internet Encyclopedia of Philosophy'' The field of ethics, along with aesthetics, concerns m ...
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 Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
,
Dialectic Dialectic ( grc-gre, διαλεκτική, ''dialektikḗ''; related to dialogue; german: Dialektik), also known as the dialectical method, is a discourse between two or more people holding different points of view about a subject but wishing ...
and
Ethics Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and wrong behavior".''Internet Encyclopedia of Philosophy'' The field of ethics, along with aesthetics, concerns m ...
.


Writings

With a comprehensive work on
Dialectic Dialectic ( grc-gre, διαλεκτική, ''dialektikḗ''; related to dialogue; german: Dialektik), also known as the dialectical method, is a discourse between two or more people holding different points of view about a subject but wishing ...
() there were also separate treatises ''On
Knowledge Knowledge can be defined as awareness of facts or as practical skills, and may also refer to familiarity with objects or situations. Knowledge of facts, also called propositional knowledge, is often defined as true belief that is distinc ...
'', ''On Knowledgibility'' (), ''On Divisions'' (), ''On Genera and Species'' (), ''On Ideas'' (), ''On the Opposite'' (), and others, to which probably the work ''On Mediate Thought'' () also belonged. Two works by Xenocrates on Physics are mentioned (), as are also books ''On the Gods'' (), ''On the Existent'' (), ''On the One'' (), ''On the Indefinite'' (), ''On the Soul'' (), ''On the Emotions'' () ''On
Memory Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembered, ...
'' (), etc. In like manner, with the more general Ethical treatises ''On
Happiness Happiness, in the context of Mental health, mental or emotional states, is positive or Pleasure, pleasant emotions ranging from contentment to intense joy. Other forms include life satisfaction, well-being, subjective well-being, flourishin ...
'' (), and ''On
Virtue Virtue ( la, virtus) is moral excellence. A virtue is a trait or quality that is deemed to be morally good and thus is valued as a foundation of principle and good moral being. In other words, it is a behavior that shows high moral standard ...
'' () there were connected separate books on individual Virtues, on the Voluntary, etc. His four books on
Royalty Royalty may refer to: * Any individual monarch, such as a king, queen, emperor, empress, etc. * Royal family, the immediate family of a king or queen regnant, and sometimes his or her extended family * Royalty payment for use of such things as int ...
he had addressed to Alexander (). Besides these he had written treatises ''On the State'' (), ''On the Power of Law'' (), etc., as well as upon
Geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
,
Arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...
, and
Astrology Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of Celestial o ...
. Besides philosophical treatises, he wrote poetry () and paraenesis.


Philosophy


Epistemology

Xenocrates made a more definite division between the three departments of philosophy, than
Speusippus Speusippus (; grc-gre, Σπεύσιππος; c. 408 – 339/8 BC) was an ancient Greek philosopher. Speusippus was Plato's nephew by his sister Potone. After Plato's death, c. 348 BC, Speusippus inherited the Academy, near age 60, and remained ...
, but at the same time abandoned Plato's heuristic method of conducting through doubts (), and adopted instead a mode of bringing forward his doctrines in which they were developed dogmatically. Xenocrates recognized three grades of cognition, each appropriated to a region of its own: knowledge, sensation, and opinion. He referred knowledge () to that essence which is the object of pure thought, and is not included in the phenomenal world; sensation () to that which passes into the world of phenomena; opinion () to that essence which is at once the object of sensuous perception, and, mathematically, of pure reason - the essence of
heaven Heaven or the heavens, is a common religious cosmological or transcendent supernatural place where beings such as deities, angels, souls, saints, or venerated ancestors are said to originate, be enthroned, or reside. According to the belie ...
or the
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s; so that he conceived of in a higher sense, and endeavored, 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 () 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 The Fates are a common motif in European polytheism, most frequently represented as a trio of goddesses. The Fates shape the destiny of each human, often expressed in textile metaphors such as spinning fibers into yarn, or weaving threads on a ...
:
Atropos Atropos (; grc, Ἄτροπος "without turn") or Aisa, in Greek mythology, was one of the three Moirai, goddesses of fate and destiny. Her Roman equivalent was Morta. Atropos was the oldest of the Three Fates, and was known as "the Inflex ...
, Clotho, and
Lachesis Lachesis ( ; grc, Λάχεσις, Lákhesis, disposer of lots; from , 'to obtain by lot, by fate, or by the will of the gods'), in ancient Greek religion, was the second of the Three Fates, or Moirai; the others were her sisters, Clotho and A ...
. We know nothing further about the mode in which Xenocrates carried out his
dialectic Dialectic ( grc-gre, διαλεκτική, ''dialektikḗ''; related to dialogue; german: Dialektik), also known as the dialectical method, is a discourse between two or more people holding different points of view about a subject but wishing ...
, 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 Category, plural categories, may refer to: Philosophy and general uses *Categorization, categories in cognitive science, information science and generally *Category of being *Categories (Aristotle), ''Categories'' (Aristotle) *Category (Kant) ...
.


Metaphysics

We know from
Plutarch Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for his ''P ...
that Xenocrates, if he did not explain the Platonic construction of the world-soul as
Crantor Crantor ( el, Κράντωρ, ''gen''.: Κράντορος; died 276/5 BC) was a Greek philosopher and scholarch (leader) of the Old Academy, probably born around the middle of the 4th century BC, at Soli in Cilicia (modern-day Turkey). Life Cra ...
after him did, nevertheless drew heavily on the ''
Timaeus Timaeus (or Timaios) is a Greek name. It may refer to: * ''Timaeus'' (dialogue), a Socratic dialogue by Plato *Timaeus of Locri, 5th-century BC Pythagorean philosopher, appearing in Plato's dialogue *Timaeus (historian) (c. 345 BC-c. 250 BC), Greek ...
''; and further that he was at the head of those who, regarding the universe as unoriginated and imperishable, looked upon the chronological succession in the Platonic theory as a form in which to denote the relations of conceptual succession. Plutarch unfortunately, does not give us any further details, and contented himself with describing the well-known assumption of Xenocrates, that the soul is a self-moving number. Probably we should connect with this the statement that Xenocrates called unity and duality (''monas'' and ''duas'') deities, and characterised the former as the first male existence, ruling in heaven, as father and
Zeus Zeus or , , ; grc, Δῐός, ''Diós'', label=Genitive case, genitive Aeolic Greek, Boeotian Aeolic and Doric Greek#Laconian, Laconian grc-dor, Δεύς, Deús ; grc, Δέος, ''Déos'', label=Genitive case, genitive el, Δίας, ''D ...
, 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, 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. 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 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 file:Greek - Procession of Twelve Gods and Goddesses - Walters 2340.jpg, upright=1.8, Fragment of a Hellenistic relief sculpture, relief (1st century BC1st century AD) depicting the twelve Olympians carrying their attributes in procession; from ...
. As a sublunary daemonical power (as
Hera In ancient Greek religion, Hera (; grc-gre, Ἥρα, Hḗrā; grc, Ἥρη, Hḗrē, label=none in Ionic and Homeric Greek) is the goddess of marriage, women and family, and the protector of women during childbirth. In Greek mythology, she ...
,
Poseidon Poseidon (; grc-gre, Ποσειδῶν) was one of the Twelve Olympians in ancient Greek religion and myth, god of the sea, storms, earthquakes and horses.Burkert 1985pp. 136–139 In pre-Olympian Bronze Age Greece, he was venerated as a ch ...
,
Demeter In ancient Greek religion and mythology, Demeter (; Attic: ''Dēmḗtēr'' ; Doric: ''Dāmā́tēr'') is the Olympian goddess of the harvest and agriculture, presiding over crops, grains, food, and the fertility of the earth. Although s ...
), 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 Scalene may refer to: * A scalene triangle, one in which all sides and angles are not the same. * A scalene ellipsoid, one in which the lengths of all three semi-principal axes are different * Scalene muscles of the neck * Scalene tubercle The sc ...
. 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 until we get to the sphere of the separate daemonical powers of
nature Nature, in the broadest sense, is the physics, physical world or universe. "Nature" can refer to the phenomenon, phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. ...
that the opposition between
good and evil In religion, ethics, philosophy, and psychology "good and evil" is a very common dichotomy. In cultures with Manichaean and Abrahamic religious influence, evil is perceived as the dualistic antagonistic opposite of good, in which good shoul ...
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 Eudaimonia (Greek: εὐδαιμονία ; sometimes anglicized as eudaemonia or eudemonia, ) is a Greek word literally translating to the state or condition of 'good spirit', and which is commonly translated as 'happiness' or 'welfare'. In wor ...
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 Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
, 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 Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
, in his ''
Metaphysics Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
'', recognized amongst contemporary Platonists three principal views concerning the ''ideal'' numbers, and their relation to the ideas and to ''mathematical''
number A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers c ...
s: #those who, like Plato, distinguished ''ideal'' and ''mathematical'' numbers; #those who, like Xenocrates, identified ''ideal'' numbers with ''mathematical'' numbers #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 ideal numbers are 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.


Ethics

The information on his Ethics is scanty. He tried to supplement the Platonic doctrine at various points, and at the same time to give it a more direct applicability to life. He distinguished from the good and the bad something which is neither good nor bad. Following the ideas of his Academic predecessors, he viewed the good as that which should be striven after for itself, that is, which has value in itself, while the bad is the opposite of this. 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 opposite 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) would not accept that these intermediate things, such as
health Health, according to the World Health Organization, is "a state of complete physical, mental and social well-being and not merely the absence of disease and infirmity".World Health Organization. (2006)''Constitution of the World Health Organiza ...
, beauty, fame, good
fortune Fortune may refer to: General * Fortuna or Fortune, the Roman goddess of luck * Luck * Wealth * Fortune, a prediction made in fortune-telling * Fortune, in a fortune cookie Arts and entertainment Film and television * ''The Fortune'' (1931 film) ...
, 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.


Mathematics

Xenocrates is known to have written a book ''On Numbers'', and a ''Theory of Numbers'', besides books on
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
.
Plutarch Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for his ''P ...
writes that Xenocrates once attempted to find the total number of syllables that could be made from the letters of the alphabet. According to Plutarch, Xenocrates result was 1,002,000,000,000 (a "
myriad A myriad (from Ancient Greek grc, μυριάς, translit=myrias, label=none) is technically the number 10,000 (ten thousand); in that sense, the term is used in English almost exclusively for literal translations from Greek, Latin or Sinospher ...
-and-twenty times a myriad-myriad"). This possibly represents the first instance that a combinatorial problem involving
permutations In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...
was attempted. Xenocrates also supported the idea of "indivisible lines" (and magnitudes) in order to counter Zeno's paradoxes.Simplicius, ''in Arist. Phys.''


See also

*'' On Indivisible Lines''


References


Bibliography

* Bartninkas, V. (2023).
Traditional and Cosmic Gods in Later Plato and the Early Academy
' Cambridge: Cambridge University Press, 211–238. * * * * * * Attribution *


External links

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{{Authority control 4th-century BC Greek philosophers Academic philosophers Ancient Athenian philosophers Ancient Chalcedonians Ancient Greek mathematicians Ancient Greek metaphysicians Greek educators Metic philosophers in Classical Athens 390s BC births 310s BC deaths Philosophers and tutors of Alexander the Great 4th-century BC mathematicians