Editing Xenocrates (section)

===Metaphysics===
We know from [[Plutarch]]<ref>Plutarch, ''de Animae procreat. e Tim.''</ref> that Xenocrates, if he did not explain the Platonic construction of the [[Anima mundi|world-soul]] as [[Crantor]] after him did, nevertheless drew heavily on the ''[[Timaeus (dialogue)|Timaeus]]''; and further<ref>Aristotle, ''de Caelo'', i. 10, 32, ''Metaph.'' xiv. 4</ref> 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.<ref>Plutarch, ''de Animae procreat. e Tim.'', comp. Aristotle, ''de Anima'', i. 2, 4, ''Anal. Post.'' ii. 4, ''ib.'' Interp.</ref> 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]], 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,<ref>Stobaeus, Ecl. Phys. i. 62</ref> 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.<ref>Plutarch, ''Plat. Quaest.'' ix. 1; Clement of Alexandria, ''Stromata'', v. 604</ref>

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 [[Twelve Olympians|Olympic gods]]. As a sublunary [[Daemon (mythology)|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 [[Triangle#Types of triangle|scalene]].<ref>Stobaeus, Ecl. Phys. i. 62; Plutarch, ''de Orac. defect.''; Cicero, ''de Natura Deorum'', i. 13</ref> 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]] that the opposition between [[good and evil]] begins,<ref>Stobaeus, ''Ecl. Phys.''</ref> 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.<ref>Plutarch, ''de Isid. et Os.'', ''de Orac. defect.''; Aristotle, ''Topica'', ii. 2; Stobaeus, ''Serm'', civ. 24</ref>

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,<ref>Cicero, ''de Natura Deorum'', i. 13</ref> 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.<ref>Clement of Alexandria, ''Stromata'', v. 590</ref> 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;<ref>Plutarch, ''de Fac. in orbe lunae''</ref> 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.<ref>Nemesius, ''De Natura Hominis''</ref>

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]], in his ''[[Metaphysics (Aristotle)|Metaphysics]]'',<ref>Aristotle, ''Metaph.'' vii.2.1028</ref> recognized amongst contemporary Platonists three principal views concerning the ''ideal'' numbers, and their relation to the ideas and to ''mathematical'' [[number]]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.<ref>Theophrastus, ''Met.'' c. 3</ref> 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.<ref>Aristotle, ''de Lin. insec. Phys. Ausc.'' vi. 2; comp. Simplicius, ''in Arist. Phys.'' f. 30</ref> In them he thought he had discovered what, according to Plato,<ref>Plato ''Timaeus''</ref> 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,<ref>Simplicius, ''in Arist. de Caelo''</ref> 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<ref>Aristotle, ''de Anima'', i. 4, extr.</ref> should perhaps be referred to him.