23 Facts About Xenocrates

1.

Xenocrates's teachings followed those of Plato, which he attempted to define more closely, often with mathematical elements.

2.

Xenocrates distinguished three forms of being: the sensible, the intelligible, and a third compounded of the two, to which correspond respectively, sense, intellect and opinion.

3.

Xenocrates considered unity and duality to be gods which rule the universe, and the soul a self-moving number.

4.

Xenocrates held that mathematical objects and the Platonic Ideas are identical, unlike Plato who distinguished them.

5.

Xenocrates's father was named Agathon or Agathanor.

6.

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".

7.

Xenocrates was succeeded as scholarch by Polemon, whom he had reclaimed from a life of profligacy.

8.

Xenocrates adhered closely to the Platonist doctrine, and he is accounted the typical representative of the Old Academy.

9.

Xenocrates is said to have made more explicit the division of philosophy into the three parts of Physics, Dialectic and Ethics.

10.

Xenocrates made a more definite division between the three departments of philosophy, than Speusippus, 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.

11.

Xenocrates recognized three grades of cognition, each appropriated to a region of its own: knowledge, sensation, and opinion.

12.

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.

13.

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.

14.

Xenocrates 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.

15.

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.

16.

Xenocrates approximated to the Pythagoreans in this, that he regarded number as the conditioning principle of consciousness, and consequently of knowledge ; he thought it necessary 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.

17.

Xenocrates 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.

18.

Xenocrates tried to supplement the Platonic doctrine at various points, and at the same time to give it a more direct applicability to life.

19.

Xenocrates distinguished from the good and the bad something which is neither good nor bad.

20.

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.

21.

Xenocrates is known to have written a book On Numbers, and a Theory of Numbers, besides books on geometry.

22.

Plutarch writes that Xenocrates once attempted to find the total number of syllables that could be made from the letters of the alphabet.

23.

Xenocrates supported the idea of "indivisible lines" in order to counter Zeno's paradoxes.