This may be proved in three ways. The first…
Last week was meatier, showing God cannot do the logically impossible; this week our saintly guide shows God can do what isn’t.
Chapter 26 That the divine intellect is not constrained to certain determined effects (alternate translation)
[1] FORASMUCH as it has been proved that the divine power is not limited to certain determined effects, and this because He acts not by a necessity of His nature, but by His intellect and will; lest some one perhaps should think that His intellect or knowledge can only reach to certain effects, and that consequently He acts by a necessity of His knowledge, although not by a necessity of His nature: it remains to be shown that His knowledge or intellect is not confined to any limits in its effects.
[2] For it was proved above that God comprehends all other things that can proceed from Him, by understanding His essence, in which all such things must necessarily exist by a kind of likeness, even as effects are virtually in their causes. If, then, the divine power is not confined to certain definite effects, as we have shown above, it is necessary to pronounce a like opinion on His intellect.
[3] Further. We have already proved the infinity of the divine intellect. Now, no matter how many finite things we add together, even though there were an infinite number of finite things, we cannot equal the infinite, for it infinitely exceeds the finite, however great.
Now it is clear that nothing outside God is infinite in its essence: since all else are by the very nature of their essence included under certain definite genera and species. Consequently, however many and however great divine effects be taken, it is always in the divine essence to exceed them: and so it can be the ratio of more. Wherefore the divine intellect, which knows the divine essence perfectly, as we have shown above, surpasses all finitude of effects. Therefore it is not necessarily confined to these or those effects.
Notes Not for the first time Aquinas gets his math right; and recall there are infinities and infinities, one larger than the next. Mathematicians have an idea of a final or largest infinity, and perhaps not uncoincidentally it is strikingly similar to Anselm’s ontological statement “we believe that thou art a being than which nothing greater can be conceived.”
[4] Again. It was shown above that the divine intellect knows an infinite number of things. Now God brings things into being by the knowledge of His intellect. Therefore the causality of the divine intellect is not confined to a finite number of effects.
Notes Numbering the hairs on your head, or all the quarks in the universe is nothing for God, because these are all finite in number, and anything finite is infinitely far from infinity.
[5] Moreover. If the causality of the divine intellect were confined to certain effects, as though it produced them of necessity, this would be in reference to the things which it brings into being. But this is impossible; for it was shown above that God understands even those things that never are, nor shall be, nor have been. Therefore God does not work by necessity of His intellect or knowledge.
Notes God has choice, free will.
[6] Further. God’s knowledge is compared to things produced by Him, as the knowledge of the craftsman to his handiwork. Now every art extends to all the things that can be comprised under the genus subject to that art: thus the art of building extends to all houses. Now the genus subject to the divine art is being: since God by His intellect is the universal principle of being, as we have proved. Therefore the divine intellect extends its causality to whatever is not incompatible with the notion of being: for all such things, considered in themselves, are of a nature to be contained under being. Therefore the divine intellect is not confined to certain determined effects…
Notes Appropriate here to remind us that metaphysics is the subject of being, a subject about which science is necessarily silent.
Chapter 27 That the divine will is not confined to certain effects (alternate translation)
[1] IT may also be proved from the foregoing that neither is His will, by which He works, necessitated to produce certain determinate effects.
[2] For it behoves the will to be proportionate to its object. Now the object of the intellect is a good understood, as stated above. Hence the will has a natural aptitude to extend to whatever the intellect can propose to it under the aspect of good. If, then, the divine intellect is not confined to certain effects, as we have shown, it follows that neither does the divine will produce certain determinate effects of necessity.
[3] Further. Nothing acting by will produces a thing without willing. Now it was proved above that God wills nothing other than Himself of absolute necessity. Therefore effects proceed from the divine will not of necessity but by its free ordinance.
Notes The same goes for us in N=nothing acting by will produces a thing without willing, of course.