[1002b] [1] at one time, when they are joined one surface is instantaneously produced, and at another, when they are divided, two. Thus when the bodies are combined the surface does not exist but has perished; and when they are divided, surfaces exist which did not exist before. (The indivisible point is of course never divided into two.) And if they are generated and destroyed, from what are they generated?It is very much the same with "the present moment" in time. This too cannot be generated and destroyed; but nevertheless it seems always to be different, not being a substance. And obviously it is the same with points, lines and planes, for the argument is the same; they are all similarly either limits or divisions.1

In general one might wonder why we should seek for other entities apart from sensible things and the Intermediates:2 e.g., for the Forms which we Platonists assume.If it is for the reason that the objects of mathematics, while differing from the things in our world in another respect, resemble them in being a plurality of objects similar in form, so that their principles cannot be numerically determined (just as the principles of all language in this world of ours are determinate not in number but in kind—unless one takes such and such a particular syllable [20] or sound, for the principles of these are determinate in number too—and similarly with the Intermediates, for in their case too there is an infinity of objects similar in form), then if there is not another set of objects apart from sensible and mathematical objects, such as the Forms are said to be, there will be no substance which is one both in kind and in number, nor will the principles of things be determinate in number, but in kind only.Thus if this is necessarily so, it is necessary for this reason to posit the Forms also. For even if their exponents do not articulate their theory properly, still this is what they are trying to express, and it must be that they maintain the Forms on the ground that each of them is a substance, and none of them exists by accident.On the other hand, if we are to assume that the Forms exist, and that the first principles are one in number but not in kind, we have already stated3 the impossible consequences which must follow.4

(12.) Closely connected with these questions is the problem whether the elements exist potentially or in some other sense.If in some other sense, there will be something else prior to the first principles.

1 For arguments against the substantiality of numbers and mathematical objects see Aristot. Met. 13.1-3, 6-9; Aristot. Met. 14.1-3, 5, 6.

4 This problem is not stated in ch. 1., but is akin to problems 5. and 8., which see.

An XML version of this text is available for download, with the additional restriction that you offer Perseus any modifications you make. Perseus provides credit for all accepted changes, storing new additions in a versioning system.

hide Places (automatically extracted)

View a map of the most frequently mentioned places in this document.

Visualize the most frequently mentioned Pleiades ancient places in this text.

hide References (7 total)