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.
A statement is logically impossible if you cannot derive it from axioms. But you can still choose the axioms. Which makes lots of things logically possible. And that makes it possible to do things that are physically impossible. Doing physically impossible things, potentiallities that either do not exist or that cannot be made actual, were proven to be impossible to do by God earlier in this series.
Hence, God cannot do certain logical possible acts, contrary to what is stated here.
Corrolary from the premisse. Next.
Infinity simply means “not finite.” In mathematics it sometimes means the largest possible number above which there can be no higher number but that’s absurd; no such thing can exist. I usually treat it to mean “unbounded”; being unbounded does not require to fill all that available space just that there’s plenty of room.
” usually treat it to mean “unbounded”; being unbounded does not require to fill all that available space just that there’s plenty of room.”
Begs the question what’s beyond the boundary.
usually treat it to mean “unbounded”; being unbounded does not require to fill all that available space just that there’s plenty of room.
Given that all the unavailable space isn’t filled!
About the only way that God can be said to have a “free” will is that there is nothing that can make Him “change His mind” or “do” other than what He eternally knows and desires or wills.
We say that God can do anything but contradict Himself. That is, He is not “free” to be what He is not and He is not “free” to not be what He is.
By extension, He is not “free” to not know all that there is to be known etc.
That brings us round to the notion of infinite (knowledge, power, will). I suggest that infinite, in this context, means that there is no more, no “beyond” or further or boundary… not quite like the imaginary endless progression of numbers, for example.
So, let’s say God wanted to make a universe. How does he go about that?
JMJ
“the divine intellect knows an infinite number of things.”
Do there exist “an infinite number of things” to be known?
Is the language about “infinite” attributes to God merely poetical or if literal, what does it exactly mean?
What does it mean to be “infinitely knowing” or “infinitely loving” or “infinitely intelligent”?
Can these “infinities” be operated on like mathematical infinities?
Won’t the term “unbounded” capture Aquinas’ meaning more than the pseudo-mathematical “infinity”?
Sander van der Wal,
“A statement is logically impossible if you cannot derive it from axioms”
a big NO here. Apart from anything else, consider Goedel’s theorem which states that nontrivial formal systems have true statements that can not be proved.
That is, there exists statements within formal systems, that
1) Are seen to be true
2) Can not be derived from axioms.
@Sander van der Wal:
“a big NO here.”
Sander’s argument is wrong but not in the way you seem to think. You say:
“Apart from anything else, consider Goedel’s theorem which states that nontrivial formal systems have true statements that can not be proved.”
First, this is not what Göedel’s theorem says as it misses the all-important technical qualifications. Second, the sense in which Göedelian sentences are true is *not* the usual, mathematical sense of being true in all models. But more importantly, this does *not* militate against what Sander is saying, because all he needs is that there is *some* theory (I will add the proviso: consistent, otherwise it collapses into triviality) from which the statement — call it P — is derivable. But if the theory {P} is consistent there is an obvious theory from which P is derivable: precisely {P}.
Apologies, but previous post is addressed to
@Mactoul:
and not Sander van der Wal as I mistakenly wrote.
JMJ, with a snap of finger!
JMJ, with a snap of fingers!
Wow, God does zen?
Maybe: with one hand clapping.
“Won’t the term unbounded capture Aquinas’ meaning more than the pseudo-mathematical infinity?”
It does so for me. Only in math is “infinite” really big. Semantically it simply means “not finite” so it could be anything at all, including really small but not measurable or, as you suggest, not bounded.
So it could be a small thing in a boundless box. It could fill all of everything, but the word does not convey that it must do so.
Jersey McJones “So, let’s say God wanted to make a universe. How does he go about that?”
The moment he thinks of it existence is instantaneous. Neither is there a time-line; one day he doesn’t think of it and the next day he does as if it is a progression. Therefore every thought he will ever have he has already had, every universe he will ever imagine he has already imagined.
A better question might be how you would go about creating a universe and the first thought that comes to my mind is to harness a black hole and turn it into a white hole.
Jersey McJones
April 25, 2016 at 1:40 am
“So, let’s say God wanted to make a universe. How does he go about that?”
The proposition assumes a progression from not wanting to wanting and from not making to making… only possible in the temporal realm where events are successive.
my problem is not that there are logical statements that cannot be shown to derive from a bunch of axioms. My issue is that you can always add that statement as an axiom to the bunch if axioms you already have. And by doing that this notion that God can do everything that is not logically impossible is meaningless.
A related issue. On a sphere it is possible to create triangles with the sum of the angles bigger than 180 degrees. So it is not logicaly impossible to create such angles. And because it is nog logically impossible God can make such triangles. Now, as the argument does not restrict God to the domain where the statement is logical, God is able to make triangles with the sum of the angles bigger than 180 degrees in a plane.
There are plenty more of such examples. God can make a fallen egg whole again. We can’t because it is very hard to put all the atoms back, but there is no logical reason for it to be impssible, it is just very hard.
Another example, solutions to Einstein’s equations that have speeds faster than light, tachyons. We don’t like the physics, but physics is not logics.
Summarizing, as there are lots of things that can logically be done, but which are physically impossible, this statement about Gods abilities cannot be true. Physical possibility is a proper subset of logical possibility, it is not the same set.
“On a sphere it is possible to create triangles with the sum of the angles bigger than 180 degrees.”
Yes, a different set of rules for a different geometry. Spherical geometry is not plane geometry.
“God is able to make triangles with the sum of the angles bigger than 180 degrees in a plane.”
Of course, I can do that too but don’t ask me to build a bridge and expect it to work.
Sander van de Wal,
“My issue is that you can always add that statement as an axiom to the bunch if axioms you already have.”
Now, you have a different formal system –one with the added axiom. Again, Goedel theorem applies and there is yet another proposition in this formal system that can be seen to be true but can not be derived from the set of enlarged axioms.
I’m more and more wordless. The comments make me cry. There is so much in this concept of God that can not be explained in a sensible way.
The way I see, there is no God. And humans are not ‘machines’, that is contructs of an intelligence, but emergent phenomena of mathematics that describes what we call the reality.
I don’t know what ism this is. I just know this has to be true, which is weird because people who appear to disagree seem to be equally certain. They also appear to equally intelligent and well informed. In principle.
I don’t think terms like creation make any sense. The universe exists in a way which is independent of the time we experience. We have things like ‘before’ and ‘after’, but I’m not confident these terms should be applied to all universe. The universe ‘exists’ outside of ‘time’ and I rather strongly believe the existence of our future is determined as of ‘now’ either as one future or an assembly of futures equally truely existing.
The true question is about the equations of physics. Are they the only, complete set of equations of existence, or are there an infinite collection of realities? If the latter, why our reality appears so simple? If the former, what logical reasons prevent a more complicated reality?
I believe physics can identify the laws of reality and I believe they appear to be more and more complex, until it is found we only can operate on approximate mathematical simplifications, very elegant ones but not reach the true description of nature.
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