2. Objections

223. And because stubbornness is possible about relations, by conceding that they are not the same really as their foundation but that they are not different realities, and by denying that they are certain things by saying that a relation exists only in the act of the comparing intellect [Henry of Ghent] - there are arguments against this view: first that it destroys the unity of the universe, second that it destroys all substantial and accidental composition in the universe, third that it destroys all causality of second causes, and fourth that it destroys the reality of all the mathematical sciences.

224. The first is easily proved, because, according to Aristotle Metaphysics 12.10.1075a11-15, the unity of the universe exists in the order of the parts to each other and to the first thing, as the unity of an army exists in the order of the parts of the army to each other and to the leader; and from this can be asserted, against those who deny that a relation is a thing outside the act of the intellect, the word of the Philosopher, Metaphysics 12.10.1075b37-6a3, that the sort of people who speak thus “are disconnecting the substance of the universe.”

225. The proof of the second is that nothing is composite without the union of composable parts, such that, when the parts are separated, the composite does not remain; but nothing real depends on what is merely a matter of reason (and precisely of reason caused by an act of our intellect), or at any rate the sort of real that is not a product of art; therefore no ‘whole’ will be a natural real thing if for its being is necessarily required a relation and if this relation is nothing but a being of reason.

226. The proof of the third is that the causing of a real being does not require a being of reason in the cause, and because second causes cannot cause unless they are proportioned and nearby; therefore, if this being nearby is only a being of reason, causes under this being nearby will not be able to cause anything real. Because without this being nearby they cannot cause, and this being nearby (which is a relation) is no real thing, according to you [n.223, Henry] -     therefore a second cause contributes nothing to a being able to cause.

227. The proof of the fourth is that all mathematical conclusions demonstrate relations of subjects. The point is clear first from the authority of the Philosopher, Metaphysics 13.3.1078a31-b2, who says, “Of the good the species most of all are order [common measure and the definite] etc     ... and these are shown most of all by the mathematician,” because a mathematician’s art lies in proportion and the measures of certain things with each other. Secondly, this same thing is plain from experience by running through mathematical conclusions, in all of which some relative property is commonly predicated; as is plain beginning from the first conclusion of geometry, where the equality of the sides of a triangle is shown, or the predicate ‘able to be the base or side of an equilateral triangle’ is shown of a straight line; and so in all the rest, as that a triangle has three angles equal to two right angles (the property demonstrated of the three angles of a triangle is this, namely ‘equal to two right angles’), and so in other cases.

228. But if the stubbornness is still continued, that although relations are not formally beings of reason but something outside the intellect and not the same as the foundation, yet they are not a thing different from the foundation but are only proper modes of the thing - this objection seems to be a contention only about the term ‘mode of a thing’; for although the mode of a thing is not a thing other than the thing of which it is the mode, yet it is not no thing (just as neither is it no being), because then it would be nothing; and therefore relation falls under the division of being per se, according to the Philosopher Metaphysics 5.7.1017a24-27. Nor is everything into which ‘being per se’ is divided an equally perfect being; on the contrary, quality in respect of substance can be called a ‘mode’ and yet quality is in itself a true thing. Thus relation, although it is a mode (though one more imperfect still than quality), yet if it is outside the intellect (and not a mode intrinsic to the foundation, as infinity is in God and the infinity of all the essentials in God, as was said in 1 d.8 nn.192, 220-221 [d.3 n.58, d.10 n.30, d.19 n.15, d.31 n.19]) it follows that such a mode, being from the nature of the thing other than the thing, is a different thing from the foundation, taking ‘thing’ in its most general sense as divided into the ten categories.

229. And if it be said that the genus of relation is a thing, not because of the mode that is a disposition to something else, but because of the thing to which the being toward another belongs - this is not true; because just as every ‘being for itself’, conceived under an absolute idea, can pertain essentially to some absolute genus provided it is per se one (for no mode of conceiving, along with which the concept ‘per se unity’ [or: the per se unity of a concept] can stand, and which concept is absolute, takes away from the thing thus conceived its belonging to an absolute concept, because what is thus conceived includes something absolute asserted of it in its whatness and something said of it in its what-sortness, whereby it is distinguished from other absolute concepts - as its genus and difference, outside the intellect), so every such respect, or disposition or relation (or however it is named, for these are synonyms), can be per se conceived as per se one, having some quidditative predicate asserted of it in its whatness (as it is outside the mind, as was proved [nn.224-227]), and distinct from that in which it is founded, as was proved in the first article [nn.200-222]; therefore a proper genus can be had of those respects as they are respects without including their foundations essentially - and so the reality of the things that are in this genus is not precisely such because of the foundations, formally speaking, because the foundation is outside the per se idea of them as they have the complete of idea of a being in a real genus.