24. There are, therefore, according to Pythagoras, two worlds, one intelligible which has the monad as its beginning, but the other the perceptible. This last is the Tetractys containing Iota,[88] the one tittle, a perfect number. [Sidenote: p. 272.] Thus the Iota, the one tittle, is received by the Pythagoreans as the first and chiefest, and as the substance of the Intelligible both intelligibly and perceptibly. Belonging to which are the nine bodiless accidents which cannot exist apart from substance, (viz.) Quantity, Quality, Wherefore, Where, and When, and also Being, Having, Doing and Suffering.[89] There are therefore nine accidents to substance reckoned in with which they comprise[90] the perfect number, the 10. Wherefore the universe being divided, as we have said, into an intelligible and a perceptible world, we have also reason from the intelligible in order that by it we may behold the substance of the intelligible, the bodiless and the divine. But we have, he says, five senses, smell, sight, hearing, taste and touch. By these we arrive at a knowledge of perceptible things, and so, he says, the perceptible world is separated from the intelligible; and that we have an organ of knowledge for each of them, we learn from this. None of the intelligibles, he says, can become known to us through sense: for, he says, eye has not seen that, nor ear heard, nor has it become known, he says, by any other of the senses whatever. Nor again by reason can one come to a knowledge of the perceptible; [Sidenote: p. 273.] but one must see that a thing is white, and taste that it is sweet, and know by hearing that it is just or unjust; and if any smell is fragrant or nauseous, that is the work of the sense of smell and not of the reason. And it is the same with the things relating to touch. For that a thing is hard or soft or hot or cold cannot be known through the hearing, but the test of these things is the touch. This being granted, the setting in order of the things that have been and are is seen to come about arithmetically. For, just as we, beginning by addition of monads (or dyads) or triads and of the other numbers strung together, make one very large compound number, and on the other hand work by subtracting from the total strung together and by analysing by a fresh calculation what has been brought together arithmetically;--so, he says, the cosmos is bound together by a certain arithmetical and musical bond, and by its tightening and slackening, its addition and subtraction, is ever and everywhere preserved uncorrupted. 25. For instance in some such fashion as this also do the Pythagoreans describe the duration of the world:-- [Sidenote: p. 274.] “For it was before and will be. Never I ween Will the unquenchable aeon be devoid of these two.”