Henry Jackson

“ In his ontology Xenocrates built upon Plato's foundations: that is to say, with Plato he postulated ideas or numbers to be the causes of nature's organic products, and derived these ideas or numbers from unity (which is active) and plurality (which is passive) . But he put upon this fundamental dogma a new interpretation. According to Plato, existence is mind pluralized: mind as a unity, i.e. universal mind, apprehends its own plurality as eternal, immutable, intelligible ideas; and mind as a plurality, i.e. particular mind, perceives its own plurality as transitory, mutable, sensible things. ”

“ What is the single element which underlies the apparent plurality of the material world? their answers, Parmenides conceived, by attributing to the selected element various and varying qualities, reintroduced the plurality which the question sought to eliminate. If we would discover that which is common to all things at all times, we must, he submitted, exclude the differences of things, whether simultaneous or successive. ”

“ Yet men imagine gods to be born, and to have raiment and voice and body, like themselves. Even so the gods of the Ethiopians are swarthy and flat-nosed, the gods of the Thracians are fair-haired and blue-eyed. ”

“ Hence the theory of the unity of nature is necessarily followed by a theory of its seeming plurality, that is to say, of the variety and mutation of things. The theory of plurality cannot indeed pretend to the certainty of the theory of unity, being of necessity untrustworthy, because it is the partial and inconstant representation of that which is partial and inconstant in nature. ”

“ Happiness consists in the possession of virtue, and consequently is independent of personal and extraneous advantages. The virtuous man is pure, not in act only, but also in heart. To the attainment of virtue the best help is philosophy; for the philosopher does of his own accord what others do under the compulsion of law. Speculative wisdom and practical wisdom are to be distinguished. Meagre as these statements are, they suffice to show that in ethics, as elsewhere, Xenocrates worked upon Platonic lines. ”

“ Soul is a self-moving number, derived from the two fundamental principles, unity (ἕν) and plurality (δυὰς ἀόριστος) , whence 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. ”

“ The Greek gods being the powers of nature personified, pantheism lay nearer to hand than monotheism. Xenophanes was, then, a pantheist. Accordingly his assertion of the unity of God was at the same time a declaration of the unity of Being, and in virtue of this declaration he is entitled to rank as the founder of Eleaticism, inasmuch as the philosophy of Parmenides was his forerunner's pantheism divested of its theistic element. ”

“ In other words, Zeno re-affirmed the dogma, “The Ent is, the Non-ent is not.”
If tradition has not misrepresented these paradoxes of time, space and motion, there is in Zeno's reasoning an element of fallacy. It is indeed difficult to understand how so acute a thinker should confound that which is infinitely divisible with that which is infinitely great, as in (1) , (2) , (5) , and (6) ; that he should identify space and magnitude, as in (3) ; that he should neglect the imperfection of the organs of sense, as in (4) ; that he should deny the reality of motion, as in (7) ”

“ Thirdly, when Xenophanes himself says that theories about gods and about things are not knowledge, that his own utterances are not verities but verisimilitudes, and that, so far from learning things by revelation, man must laboriously seek a better opinion, he plainly renounces the “disinterested pursuit of truth.” ”

“ The idea, inasmuch as it is a law of universal mind, which in particular minds produces aggregates of sensations called things, is a “determinant” (πέρας ἔχον) , and as such is styled “quantity” (ποσόν) and perhaps “number” (ἀριθμός) ; but the ideal numbers are distinct from arithmetical numbers. Xenocrates, however, failing, as it would seem, to grasp the idealism which was the metaphysical foundation of Plato's theory of natural kinds, took for his principles arithmetical unity and plurality, and accordingly identified ideal numbers with arithmetical numbers. ”

“ No man hath certainly known, nor shall certainly know, that which he saith about the gods and about all things; for, be that which he saith ever so perfect, yet doth he not know it; all things are matters of opinion. ”

“ The silence of the extant fragments, which have not one word about the unity of Being, favours the one view; the voice of antiquity, which proclaims Xenophanes the founder of Eleaticism, has been thought to favour the other.
Of Xenophanes's utterances about (1) God, (2) the world, (3) knowledge, the following survive: (1) “There is one God, greatest among gods and men, neither in shape nor in thought like unto mortals. ”

“ Further, the information thus obtained is the sum total of "truth"; for, as “existence” in the strict sense of the word cannot be attributed to anything besides the universal element, so nothing besides the universal element can properly be said to be "known."
If Parmenides’s poem had had “Being” for its subject it would doubtless have ended at this point. Its subject is, however, “Nature”; and nature, besides its unity, has also the semblance, if no more than the semblance, of plurality. ”

“ As then the Ent is one, invariable and immutable, all plurality, variety and mutation belong to the Nonent. Whence it follows that all things to which men attribute reality, generation and destruction, being and not-being, change of place, alteration of colour are no more than empty words. ”

“ For, while Parmenides had recognized, together with the One, which is, and is the object of knowledge, a Many, which is not, and therefore is not known, but nevertheless becomes, and is the object of opinion, Zeno plainly affirmed that plurality, becoming and opinion are one and all inconceivable. ”

“ Two bodies moving with equal speed traverse equal spaces in equal time. But, when two bodies move with equal speed in opposite directions, the one passes the other in half the time in which it passes it when at rest. These propositions appeared to Zeno to be irreconcilable. In short, the ordinary belief in plurality and motion seemed to him to involve fatal inconsistencies, whence he inferred that Parmenides was justified in distinguishing the mutable movable Many from the immutable immovable One, which alone is really existent. ”

“ Great as was the importance of these paradoxes of plurality and motion in stimulating speculation about space and time, their direct influence upon Greek thought was less considerable than that of another paradox—strangely neglected by historians of philosophy—the paradox of predication. ”

“ Of Xenocrates's logic we know only that with Plato he distinguished τὸ καθ’ αὑτό and τὸ πρός τι, rejecting the Aristotelian list of ten categories as a superfluity.
Valuing philosophy chiefly for its influence upon conduct, Xenocrates bestowed especial attention upon ethics. The catalogue of his works shows that he had written largely upon this subject; but the indications of doctrine which have survived are scanty, and may be summed up in a few sentences. Things are goods, ills or neutrals. Goods are of three sorts—mental, bodily, external ”

“ But an infinite distance (which Zeno fails to distinguish from a finite distance infinitely divided) cannot be traversed in a finite time. Consequently, the goal can never be reached. (6) If the tortoise has the start of Achilles, Achilles can never come up with the tortoise; for, while Achilles traverses the distance from his starting-point to the starting-point of the tortoise, the tortoise advances a certain distance, and while Achilles traverses this distance, the tortoise makes a further advance, and so on ad infinitum. ”

“ The Platonic testimony, if it proved anything, would prove too much, namely, that the doctrine of the unity of Being originated, not with Xenophanes, but before him; and, in fact, the passage from the Sophist no more proves that Plato attributed to Xenophanes the philosophy of Parmenides than Theaetetus, 160 D, proves that Plato attributed to Homer the philosophy of Heraclitus. Again, Aristotle's description of Xenophanes as the first of the Eleatic unitarians does not necessarily imply that the unity asserted by Xenophanes was the unity asserted by Parmenides ”

“ This again was followed by a psychology, which made thought [as well as sensation, which was conceived to differ from thought only in respect of its object] depend upon the excess of the one or the other of the two constituent elements, fire and night. “Such, opinion tells us, was the generation, such is the present existence, such will be the end, of those things to which men have given distinguishing names.”
In the truism “the Ent is, the Nonent is not,” ὄν ἔστι, μὴ ὄν οὐκ ἔστι, Parmenides breaks with his predecessors, the physicists of the Ionian succession. ”

“ He must learn all things, she tells him, both truth, which is certain, and human opinions; for, though in human opinions there can be no"true faith, " they must be studied notwithstanding for what they are worth. ”

“ In “Opinion” he propounded a theory of the world of seeming and its development, pointing out however that, in accordance with the principles already laid down, these cosmological speculations do not pretend to anything more than probability. In spite of the contemptuous remarks of Cicero and Plutarch about Parmenides’s versification. Nature is not without literary merit. ”

“ In like manner the Many must be numerically both finite and infinite—numerically finite, because there are as many things as there are, neither more nor less; numerically infinite, because, that any two things may be separate, the intervention of a third thing is necessary, and so on ad infinitum. ”

“ Of the paradoxes used by Zeno to discredit the belief in plurality and motion, eight survive in the writings of Aristotle and Simplicius. They are commonly stated as follows. [1] (1) If the Existent is Many, it must be at once infinitely small and infinitely great—infinitely small, because the parts of which it consists must be indivisible and therefore without magnitude ”

“ The philosophical system is expounded and discussed by E. Zeller, D. Philosophie d. Griechen (5th ed., Leipzig, 1892; Eng. trans., London, 1881) ; by T. Gomperz, Griechische Denker (Leipzig, 1896; Eng. trans., London, 1901) ; and by J. Burnet, Early Greek Philosophy (London, 1908) . For the cosmology, see A. B. Krische, D. theologischen Lehren d. griechischen Denker (Göttingen, 1840) . On the relations of Eleaticism and Platonism, see W. H. Thompson, “On Plato’s Sophist,” in the Journal of Philology viii. ”