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But it is necessary, that there should either be one principle or more than one: and if one, that it should either be immoveable, as Parmenides and Melissus say, or moved, as the natural philosophers assert, some of whom say, that the first principle is air, and others water. But if there are more principles than one, it is necessary that they should be either finite or infinite. And if finite, and more than one, that they should be either two, or three, or four, or some other number. But if infinite, it is requisite that either they should be, as Democritus asserts, one in genus, but different in figure or species, or also contraries. In a similar manner likewise they enquire, who investigate the number of beings: for they enquire in the first place, whether the things from which beings consist, are one or many; and if many, whether they are finite or infinite. So that they enquire, with respect to principle and element, whether they are one or many. To consider, therefore whether being is one and immoveable, does not belong to the speculation concerning nature. For just as a geometrician can no longer discourse with him who subverts the principles of geometry, but this is either the province of another science, or of that which is common to all the sciences; so neither can he who speculates concerning physical principles, discourse with him who denies those principles. For there is no longer a principle, if there is only one thing, and if it is thus one. For principle is either the principle of a certain thing, or of a certain number of things. To consider, therefore, in this manner, whether there is one principle resembles a discourse against any thesis whatever, which is advanced for the sake of argument; such as against the Heraclitean thesis; or if any one should say that being is one man. It also resembles the solution of the litigious argument which the assertions both of Melissus and Parmenides contain: for they assume that which is false, and are unsyllogistic. But the argument of Melissus is more troublesome, and is not the subject of doubt. One absurdity, however, being admitted, other things happen as the consequences; but this is attended with no difficulty. We, indeed, suppose, that with respect to things which have a natural subsistence, either all or some of them are moved. And this is manifest from induction. At the same time, however, it is not proper to solve all the arguments, but those only, in which some one, demonstrating from principles, concludes falsely: for such as do not thus conclude are not to be solved. Thus, for instance, with respect to the quadrature of lunulas, that which is effected through segments, it is the business of a geometrician to solve; but it is not the province of geometrician to solve that of Antiphon. However, though Parmenides and Melissus do not discourse concerning nature, yet as it happens that their assertions are attended with physical doubts, it will perhaps be well to speak a little concerning these: for the consideration of these is philosophic.