I remember asking an adult if God can make 2 + 2 = 5 when I was 8. “How could God possibility do that?” I asked. I’ve since come to the conclusion that, no, God cannot make 2 + 2 = 5. The thought has received a lot of intellectual discussion though, and it draws out some interesting confusions:
From “Impossible Omnipotence” by Mike Almeida over at Prosblogion:
Many students think that anything that is omnipotent could make 2+2 = 5 or create a round-square, or square-circle or the like. Now these sorts of claims are often dismissed as naive or not well thought out since they amount to the claim that an omnipotent being could do the impossible.
I’m now less sanguine about this sort of response, though I’ve given it before. I don’t think that students or others who claim that an omnipotent being could create a round-square are in fact claiming that an omnipotent being could do the impossible. What they are claiming, I think, is that round-squares would not be impossible were there omnipotent beings or the state of affairs that p & ~p would not be impossible were there an omnipotent being.
It seems like Mike is saying that any “omnipotent being” could do anything, including those things which are inherently contradictory.
But, what kind of “inability” is it to be unable to build a statue of David and not build a statue of David at the same time? Is such an inability incapable of something? Ok, enough rhetorical questions:
Lets suppose that W represents the quality of being a round square. Any being with such a quality has W-ness. Is it necessary that God could create something with W-ness in order to have omnipotence?
Nothing could ever have W-ness. Therefore, W-ness is no thing. Since God has the quality of being capable of creating all things, he is omnipotent despite being unable to create something with W-ness. Again, this is because W-ness is no thing since nothing could possibly have W-ness.
A related problem comes up later in his post. It is best discussed in this comment:
Fascinating discussion; it reminds me of disputes about Descartes’s position on eternal truths. Descartes would agree enthusiastically with the claim that what is impossible is impossible, and what is necessary is necessary, because God wills it to be — and due to omnipotence he could have willed otherwise:
“…God cannot have been determined to make it true that contradictories cannot be true together, and tehrefore…he could have done the opposite….And even if God has willed that some truths should be necessary, this does not mean that he willed them necessarily; for it is one thing to will that they be necessary, and quite another to will this necessarily, or to be necessitated to will it.” (AT IV, 118; CSMK 235)
According to Descartes, God could have willed otherwise in cases of necessity. It is necessary that 2 + 2 = 4, but God could have willed otherwise. He could have made it 5 or 6. Since everything is merely as God willed it, including cases of necessity, then 2 + 2 could have equaled π.
But, wait a second. This is absurd. Every time a couple and another couple formed a group together, they could have had π total people in their group, if only God had willed it necessary? That seems ridiculous. It sounds like the punch line to a reductio ad absurdum argument.
I’ve run out of clever arguments. Necessary means it could never have been any other way. And it is necessary that 2 + 2 = 4. Does anyone have any plausible arguments which refute this? Descartes was happy, at least in the passage quoted above, to merely assert that it is false. I want to ask “What coherent conception of reality allows for Descartes’s position?” but coherent usually entails non-contradictory. And Descartes is allowing God to have had the power to make contradictions true.
if it is contradictory for 2 and 2 to equal 5, and god can do all things, then its not an issue. For he does it, and thus it is not contradictory to do such a thing.
Simple.
I argued above that contradictory notions are nothing (and 2 + 2 = 5 is a contradictory notion given what is meant by the number 2 and addition). So the fact that God cannot make it true is not a limitation, because he can still do all things.
As Mike pointed out in his post, no being can do the impossible. The conclusion to follow from that is that God (if he exists) cannot do the impossible. This, too, causes trouble for your plausible refutation of the necessity of 2 + 2 = 4, since the principle of contradiction is the bedrock of refutations. There would be nothing to refute if contradictory positions did not entail that one was false.
“There would be nothing to refute if contradictory positions did not entail that one was false.”
Exactly, thanks for making my point.
What I was trying to get at in the post is a question about the truth-makers for necessary truths. There are lots of positions one can take on this, including the common Platonist position. It is Platonism that most people think is obviously true and basically the show stopper. But there are also Augustinian views on which the truth-makers are concepts (not independently existing forms) in the mind of God, still again there are those like Descartes (on some interpretations), Leftow (and I think C. Menzel) who take the truth-makers to be determined by God’s will. I agree that it sounds radical, but it is not incoherent. I tried to illustrate in the post a clear way to see how a necessary truth might fail to be such. Bivalence fails to be necessary in paraconsistent logics, for instance, and the necessary truths in S5 are not (not all, that is) necessary in S4, al the more so for S2. The idea that there is some absolute, system independent notion of necessary truth is mistaken. So, we can give sense to the idea that what is necessary is nonetheless dependent on one’s choice (of logical system). Plantinga wrote about the post to say that he discusses this same thing in _Does God have a Nature?_ p. 94ff., and indeed the discussion there is very interesting. Anyway, for what it’s worth.
So the question that arises, at least as I understand what has transpired in this conversation, if there are no necessary (objective truths independent of God)what is it that prevents God from doing these things that we are saying cannot be done, God? If there is no objective truth, but truth that is subject to God’s will, then nothing is ever impossible for God, nor paradoxical, because it can be done if God wills it, since God creates truth. So God can make 2+2= 5, or God can make a round square.
If however there are things which God cannot do, like the inablity to create a round square, because a round square is not a thing (which in saying it or imagining we make it a thing, much like an Anselm argument) we are saying that there are things outside of God, to which God has no say over, these may be necessary objective truths, however this completely reworks the notion of God as not being the Creator, but allows for God to be more logically possible, because there are things God cannot do but God can do all things that are logically possible (a slightly diluted since of omnipotence).
Mike:
Thanks for the response. I’m studying Plato’s metaphysics this semester, and I’m still not sure I’ve got a great grasp on it yet. How does God and necessity fit in with Plato’s brand of metaphysics?
I’ll look into Bivalence, paraconsistent logics, and “Does God Have a Nature?” This sounds like my kind of rabbit hole.
Zack:
You took a swing at what I thought was the most contestable idea in the post – that contradictory notions are nothing. Since we can conceive of them, and talk about them, they aren’t nothing. If we can conceive of a round square, then an Omnipotent God should be able to create it.
My contention is that you cannot actually conceive of a round square. What does it look like? What dimensions? We have two contradictory ideas – roundness and squareness – and we can form a phrase by writing “a round square”, but that doesn’t mean that we know what “a round square” is.
You might object “it is easy to conceive of a round square – it is a square in which all points are equidistant to the center”. But I will always come back with “and what does that look like?”. My claim is that you cannot answer this question because you don’t know what you mean when you assert a contradictory notion.
So, I have to ask, do you think that there are Truths outside of God? If there are not, and all truths are contingent on God- that he creates them- then Chris seems to be right. God can simply rewrite the rules to make 2+2=5 or make a round square. Nothing is inherently contradictory, simply temporaly contradictory.
However, if there are necessary truths not contingent on God, but independent, that changes the nature of the common conception of God. And God cannot do quite a few things.
I do think Truths exist apart from God. And necessary truths exist necessarliy, and God cannot do anything about that. It is nonsense to suppose that what is necessary could be any other way. C.S. Lewis wrote, “nonsense remains nonsense even if we talk it about God”.
I maintain that being able to make 2 + 2 equal 5 is no ability. It is nonsense.
What is your view on the matter, Zack?
Thanks for the response. I’m studying Plato’s metaphysics this semester, and I’m still not sure I’ve got a great grasp on it yet. How does God and necessity fit in with Plato’s brand of metaphysics?
If you’re a Platonist, you think that forms are abstratc objects that have an independent existence. They do not depend on God for their existence. But this is in violation of God’s aseity, or so say many theists. So there is the form of triangularity in virtual of their participation in which, triangles are tirangles; there is the form of a horse (effectively horseness itself) in virtual of their participation in which horses are horses. And this whole ideal realm of abstract objects (forms) constitutes an ideal world that exists independently of the typical theistic God.
I maintain that being able to make 2 + 2 equal 5 is no ability. It is nonsense.
I don’t think it’s nonsense, but I agree it’s not easy to be clear about. Descartes says at one point that God not only brings it about that 2 + 2 = 4, but he also brings it about that we could not see how it could fail. That is, God brings it about that we see “clearly & distinctly” that 2+2 = 4. So God is reponsible for modal truths and for modal epistemology. For a very strong view on God’s aseity in these matters, look for Brian Leftow’s _God & Necessity_ (OUP forthcoming).
Buy:Actos.Accutane.100% Pure Okinawan Coral Calcium.Zovirax.Zyban.Arimidex.Mega Hoodia.Petcam (Metacam) Oral Suspension.Lumigan.Prednisolone.Prevacid.Retin-A.Valtrex.Human Growth Hormone.Nexium.Synthroid….
steadicam http://zremotehxuts6.ABABYCLOTHES.INFO/tag/Prices+steadicam+Steadicam/ : Prices…
Steadicam…