previous next
[1088b] [1] Moreover, the matter of every thing, and therefore of substance, must be that which is potentially of that nature; but the relative is neither potentially substance nor actually.

It is absurd, then, or rather impossible, to represent non-substance as an element of substance and prior to it; for all the other categories are posterior to substance. And further, the elements are not predicated of those things of which they are elements; yet "many" and "few" are predicated, both separately and together, of number; and "long" and "short" are predicated of the line, and the Plane is both broad and narrow.If, then, there is a plurality of which one term, viz. "few," is always predicable, e.g. 2 (for if 2 is many, 1 will be few1), then there will be an absolute "many"; e.g., 10 will be many (if there is nothing more than 102), or 10,000. How, then, in this light, can number be derived from Few and Many? Either both ought to be predicated of it, or neither; but according to this view only one or the other is predicated.

But we must inquire in general whether eternal things can be composed of elements. If so, they will have matter; for everything which consists of elements is composite.Assuming, then, that that which consists of anything, whether it has always existed or it came into being, must come into being <if at all> out of that of which it consists; and that everything comes to be that which it comes to be out of that which is it potentially (for it could not have come to be out of that which was not potentially such, nor could it have consisted of it); and that the potential can either be actualized or not; [20] then however everlasting number or anything else which has matter may be, it would be possible for it not to exist, just as that which is any number of years old is as capable of not existing as that which is one day old. And if this is so, that which has existed for so long a time that there is no limit to it may also not exist.Therefore things which contain matter cannot be eternal, that is, if that which is capable of not existing is not eternal, as we have had occasion to say elsewhere.3 Now if what we have just been saying—that no substance is eternal unless it is actuality—is true universally, and the elements are the matter of substance, an eternal substance can have no elements of which, as inherent in it, it consists.

There are some who, while making the element which acts conjointly with unity the indeterminate dyad, object to "the unequal," quite reasonably, on the score of the difficulties which it involves. But they are rid only of those difficulties4 which necessarily attend the theory of those who make the unequal, i.e. the relative, an element; all the difficulties which are independent of this view must apply to their theories also, whether it is Ideal or mathematical number that they construct out of these elements.

There are many causes for their resorting to these explanations,

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 United States License.

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.

load focus Greek (1924)
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.

Download Pleiades ancient places geospacial dataset for this text.

hide References (5 total)
hide Display Preferences
Greek Display:
Arabic Display:
View by Default:
Browse Bar: