rom the individual things; for number is units,Andrew Cogliano Tröjor, and the unit is precisely a certain kind of one.
But (B) if there is a unity-itself and a being itself, unity and being must be their substance; for it is not something else that is predicated universally of the things that are and are one, but just unity and being. But if there is to be a being-itself and a unity-itself, there is much difficulty in seeing how there will be anything else besides these,-I mean, how things will be more than one in number. For what is different from being does not exist,Ryan Miller Tröjor, so that it necessarily follows,Nathan MacKinnon Tröjor, according to the argument of Parmenides, that all things that are are one and this is being.
There are objections to both views. For whether unity is not a substance or there is a unity-itself, number cannot be a substance. We have already said why this result follows if unity is not a substance; and if it is, the same difficulty arises as arose with regard to being. For whence is there to be another one besides unity-itself? It must be not-one; but all things are either one or many, and of the many each is one.
Further, if unity-itself is indivisible, according to Zeno’s postulate it will be nothing. For that which neither when added makes a thing greater nor when subtracted makes it less,Zach Bogosian Tröjor, he asserts to have no being,Dave Keon Tröjor, evidently assuming that whatever has being is a spatial magnitude. And if it is a magnitude,Gerry Cheevers Tröjor, it is corporeal; for the corporeal has being in every dimension,Thomas Vanek Tröjor, while the other objects of mathematics, e.g. a plane or a line, added in one way will increase what they are added to, but in another way will not do so, and a point or a unit does so in no way. But,Eric Lindros Tröjor, since his theory is of a low order, and an indivisible thing can exist in such a way as to have a defence even against him (for the indivisible when added will make the number, though not the size, greater),Duncan Keith Tröjor,-yet how can a magnitude proceed from one such indivisible or from many? It is like saying that the line is made out of points.
But even if ore supposes the case to be such that, as some say, number proceeds from unity-itself and something else which is not one, none the less we must inquire why and how the product will be sometimes a number and sometimes a magnitude, if the not-one was inequality and was the same principle in either case. For it is not evident how magnitudes could proceed either from the one and this principle,PJS Dameklær Kodiak Strøk, or from some number and this principle.
Book III Chapter 5
(14) A question connected with these is whether numbers and bodies and planes and points are substances of a kind, or not. If they are not, it baffles us to say what being is and what the substances of things are. For modifications and movements and relations and dispositions and ratios do not seem to indicate the substance of anything; for all are predicated of a subject, and none is a ‘this’. And as to the things which might seem most of all to indicate substance, water and earth and fire and air,NHL Mens Tampa Bay Lightning Black Rink Warrior Pullover Hoodie, of which composite bodies consist,Jacob Trouba Tröjor, heat and cold and the like are modifi
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