Is it correct to assume that if something can create a paradox, this something itself cannot exist nor be created? That sounds logical, because a paradox leads to a senseless conclusion, it's unquestionably impossible so it cannot exist. The anthropomorphic omnipotent God can create a paradox, for example "Can God make something he cannot lift?". His omnipotence should allow him to break scientific laws, so I would assume God can't coexist with the totality of the universe.
5 Answers
You're conflating things a bit, so let me try to parse what you're trying to say.
Statements that lead to contradictions can't possibly be true
This is true. By the principle of explosion, if we were to allow for contradictions, anything can follow (e.g. 
). So the system is meaningless.
The existence of God leads to contradictions, so it can't possibly be true
Essentially, you're arguing that because God can create "square circles" -- a logical impossibility -- he cannot exist. Conversely, if he can't create "square circles," God really isn't omnipotent so, again, God can't exist. This argument doesn't work due to a very old distinction between (what Avicenna) called particulars, universals, imaginaries, and impossibles.
A "square circle" is a logical impossibility so God couldn't create it by virtue of its meaninglessness rather than God's lack of power.
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But there is a level of internal contradiction that is more essential than the analytic one of 'square circles'. Russel's paradox or Kant's antinomies about the start and end of time are not internally meaningless, they point up real problems within natural human logic. The irresistible force/immoveable object contradiction falls in that class, not the one you would like to put it in.– user9166Commented Mar 21, 2016 at 15:33
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According to Aquinas (and Avicenna), you're wrong: www3.nd.edu/~jspeaks/courses/2009-10/20229/LECTURES/… -- the omnipotence paradox is, essentially, analytic in nature. Commented Mar 21, 2016 at 18:33
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And Kant made no improvement on Aquinas...– user9166Commented Mar 21, 2016 at 19:22
1) A paradox is a phenomenon which contradicts our usual experience, and therefore also our expectation and our intuition. But it is our task to find a way how to resolve the paradox. Any successful resolution improves our thinking.
An old example is Zeno's arrow-paradox. It can be resolved by the methods from calculus, see Why does Zeno's paradox seem valid but remain obviously wrong?
2) Different from a paradox is a logical contradiction, often named an antinomy. A logical contradiction consists of two statements which contradict each other. Here one has to abandon at least one of the statements.
Classical logic has no way to deal with two contradicting statements. This principle has been formalized by the law of non-contraction "not A and non-A".
I consider your example of an omnipotent being creating a stone, which he cannot lift, a logical contradiction. The contradiction is "omnipotent" versus "cannot lift".
Such examples do not prove anything about the existene or non-existence of God. Instead, they prompt us to recall the rules of logic and to improve our logical thinking.
3) I know that the example has occupied some medieval Christian theologicans.
answered Mar 21, 2016 at 7:57
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But Zeno's paradox is also Kant's antinomy of basic particles -- either everything is subdivisible, or something isn't. And calculus captures a compromise, but does not solve the question. We can evade it with limits, or create special rules for infinitesimals, but we are left with questions as to the propriety of such things. So the division you are proposing is knowable only after-the-fact, when we do or do not find a way around the impasse and then we either get used to the compromise, or we do not.– user9166Commented Mar 21, 2016 at 16:15
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@jobermark I do not understand why you consider a compromise the resolution of the arrow-paradox by calculus. It is our task to correct our intuition from dealing with finite sets. The mathematical realm of infinite sets follows different rules which we have to investigate and then to accept. - A similar reasoning holds for Kant's 2nd antinomy: Continued subdivision of particles finally requires a huge energy which serves to create new particles. We must not neglect the required energy which stops the whole process of subdivison. Metaphysics should be based on the state of the art in physics. Commented Mar 21, 2016 at 16:48
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So something that is on its surface to be an antinomy becomes, in modern physics, a resolved paradox. And something that was on its surface a resolved paradox for Cauchy became an antinomy and then again was resolved... Would it will again be unresolved if we accept quantum foam and the idea that our space is very locally not Hausdorff? Science changes too fast to base metaphysics on in any detail.– user9166Commented Mar 21, 2016 at 16:58
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@ jobermark I expect that our concept of spacetime will undergo a further change due to quantum gravity. But at the moment, we do not ave a generally accepted physical theory. Neither superstring theory nor loop quantum gravity has already evolved into a mature theory. - I think that the whole concept of Hausdorff spaces looses its importance in the context of lattice structures. They favour discrete structures. - If you emphasize the fast change in science: What about suspending metaphysics for a while? :-) Commented Mar 21, 2016 at 17:10
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Because there is a point of knowing how human intuition naturally works even when it is wrong.... My degrees/careers have been Math and Psychology. So physics is really secondary to my worldview.– user9166Commented Mar 21, 2016 at 17:17
Kant addresses this kind of notion with his Antinomies: https://en.wikipedia.org/wiki/Kant%27s_antinomies.
His conclusion is that human logic is essentially limited in at least these four ways. Russell's paradox introduces a fifth. If it cannot resolve the ultimate nature of something like the start of time, or definition of a set, it also cannot decide the issue of God. We simply have to give up.
The argument here is an antinomy like those, there is a problem with our ability to combine the notion of mass or force, which, as quantities, are implicitly limited, with the notion of perfection, which is implicitly unlimited.
This is a limitation of our intuition, which means we can't use that intuition to decide whether or not God exists. After all, God's involvement is secondary, right? You can remove him entirely and still have the problem. The question "What is the outcome of an irresistible force acting on an immovable object?" is not about God.
Your question is interesting because many people tend to draw the opposite conclusion: If a paradox is shown to exist, then this supports the idea of the existence of God. Keep in mind that they don't claim that paradoxes are in themselves knockdown proofs of God's existence, just that they are arguments in favor of the idea. Their reasoning tends to follow the below pattern:
- The existence of paradoxes means that logic and math can't prove everything.
- Somethings are true that can't be proved by logic and math, a) therefore the only other possible explanation for such things is God or b) The existence of God is one of those things that can't be proven using logic or math.
See for example the following article, by Marko Vojinovic:"Reductionism, emergence, and burden of proof" — part I and part II , and the SEP article on Godel's incompleteness theorems - section 6.5 and the reference therein.
On the other hand the physicist Mario Gleiser offers an argument related to yours in his book "A Tear at the Edge of Creation" (I will need to find my copy and then I will provide a more complete reference). His argument is physics based, not logic based, and goes something like:
The search for a unified theory of everything is useless, empirical evidence indicates that there is no such theory. (His implication here is that there will always be paradoxes that arise in the natural science, for example those that arise from the conflict of Relativity and Quantum Mechanics - note Gleiser doesn't believe that String Theory is going anywhere).
The lack of a single unified theory disproves monotheism, since the idea that one scientific theory should be able to explain all natural phenomenon is really just a form of monotheism in itself.
In conclusion, the existence of a logical paradox wouldn't really say one thing or the other about God's existence, and as Jobermark pointed out, we simply have to give up.
answered Mar 21, 2016 at 16:48
I think the paradox reveals the senselessness of God being omnipotent not of his existence. Not being omnipotent is no proof of inexistence. We people are not omnipotent, but we exist.
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Or one may argue that humans are the actual creators of paradox... Welcome to Philosophy SE! Commented Jul 5, 2019 at 5:42