15. Another form which the Pythagoreans employed to express their principle was the expression μονὰς, the one, and ἀόριστος δυὰς, the indeterminate or indefinite two. Of these terms, the latter, in particular, is very obscure, and has been very insufficiently explained. I will endeavour to throw what light upon them I can out of my own reflections. First of all, these terms seem to be merely another form of expression for the πέρας and the ἄπειρον; the μονὰς; or one is the πέρας or limit; the ἀόριστος δυὰς is the ἄπειρον, the unlimited and indeterminate. Everything in being limited is one. This is expressed by the term μονὰς, which stands for the sameness or identity in things; but the diversity of things is inexhaustible; and this capacity of infinite diversity is indicated by the term ἀόριστος δυὰς, indefinite difference; so that, according to the Pythagoreans, the general scheme of the universe, as regarded by pure reason, is identity, combined with a capacity of infinite diversity. Neither of the terms has any meaning out of relation to the other. But let us for a moment consider each term by itself; ἀόριστος δυὰς, taken by itself, stands for absolute diversity. Everything in the universe is absolutely different from every other; all things are particular, and they are held together by no universal. The ἀόριστος δυὰς, in short, signifies, when taken by itself, the unbounded and inexhaustible particular. The μονὰς, again, taken by itself, stands for their unity; it signifies their feature of agreement. In a word, it is their genus, just as the ἀόριστος δνὰς is a
