Such profound doctrines occupied the first book of the poem of Parmenides; in the second he treated of opinion, which, as we have said, is altogether dependent on the senses, and therefore untrustworthy, not, however, that it must necessarily be absolutely false. It is scarcely possible for us to reconstruct from the remains of his works the details of his theory, or to show his approach to the Ionian doctrines by the assumption of the existence in nature of two opposite species--ethereal fire and heavy night; of an equal proportion of which all things consist, fire being the true, and night the phenomenal. From such an unsubstantial and delusive basis it would not repay us, even if we had the means of accomplishing it, to give an exposition of his physical system. In many respects it degenerated into a wild vagary; as, for example, when he placed an overruling dæmon in the centre of the phenomenal world. Nor need we be detained by his extravagant reproduction of the old doctrine of the generation of animals from miry clay, nor follow his explanation of the nature of man, who, since he is composed of light and darkness, participates in both, and can never ascertain absolute truth. By other routes, and upon far less fanciful principles, modern philosophy has at last come to the same melancholy conclusion. [Sidenote: Doctrines of Parmenides carried out by Zeno;] The doctrines of Parmenides were carried out by Zeno the Eleatic, who is said to have been his adopted son. He brought into use the method of refuting error by the _reductio ad absurdum_. His compositions were in prose, and not in poetry, as were those of his predecessors. As it had been the object of Parmenides to establish the existence of "the One," it was the object of Zeno to establish the non-existence of "the Many." Agreeably to such principles, he started from the position that only one thing really exists, and that all others are mere modifications or appearances of it. He denied motion, but admitted the appearance of it; regarding it as a name given to a series of conditions, each of which is necessarily rest. This dogma against the possibility of motion he maintained by four arguments; the second of them is the celebrated Achilles puzzle. It is thus stated: "Suppose Achilles to run ten times as fast as a tortoise, yet, if the tortoise has the start, Achilles can never overtake him; for, if they are separated at first by an interval of a thousand feet, when Achilles has run these thousand feet the tortoise will have run a hundred, and when Achilles has run these hundred the tortoise will have got on ten, and so on for ever; therefore Achilles may run for ever without overtaking the tortoise." Such were his arguments against the existence of motion; his proof of the existence of One, the indivisible and infinite, may thus be stated: "To suppose that the one is divisible is to suppose it finite. If divisible, it must be infinitely divisible.