The omnipotence paradox reduces to the omniidiota dilemma
…sed evanuerunt in cogitationibus suis et obscuratum est insipiens cor eorum dicentes enim se esse sapientes stulti facti sunt.
There is an old—perhaps ancient—“puzzle” or “paradox” that is quite often used by atheists—even today—to prove that the concept of omnipotence is self-contradictory; ergo the existence of omnipotent being is logically impossible. One of the cornerstones of this reasoning is the paradox of the stone.
The paradox of the stone
Can God create a stone so heavy that He cannot lift it?
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If He can, then He is not omnipotent because of inability to lift such a stone.
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If He cannot create such a stone, then He is not omnipotent because of inability to create such a huge object
In either case, the conclusion is straightforward: an omnipotent being (God) cannot exist, it is a logically contradictory concept.
St Thomas Aquinas did not address the paradox of the stone directly. Hist treatment of the omnipotence (Summa Theologiae I Q XXV) is much more abstract, detailed and deeper than the stone paradox caricature. Nonetheless, St Thomas concedes that “Sed rationem omnipotentiae assignare videtur difficile.” (It is difficult to account omnipotence). Moreover, St Thomas considers whether negation capacities like “deny Himself” are consistent with omnipotence, e.g. (2) "… Sed Deus non potest peccare, neque seipsum negare, ut dicitur II Tim. 2,13. Ergo Deus non est omnipotens.” (… But God cannot sin, nor deny Himself as it is said in 2 Tim. 2:13. Therefore He is not omnipotent), and further, in (5) “Utrum Deus possit facere quae non facit” (Can God do what He does not?).
Moreover, further, he clearly states “Hoc enim omnipotentiae non subditur, non propter defectum divinae potentiae; sed quia non potest habere rationem factibilis neque possibilis. Quaecumque igitur contradictionem non implicant, sub illis possibilibus continentur, respectu quorum dicitur Deus omnipotens. Ea vero quae contradictionem implicant sub divina omnipotentia non continentur: quia non possunt habere possibilium rationem. Unde convenientius dicitur quod non possunt fieri, quam quod Deus non potest ea facere …” (For this is not submitted to omnipotence, not because of a lack of divine power; but because it cannot have a reason that is feasible or possible. All things, therefore, which do not imply a contradiction, are contained under those things which are possible, in respect of which God is said to be omnipotent. But those things which imply a contradiction are not contained under the divine omnipotence: because they cannot have the reason of the possible. Hence it is more appropriate to say that they cannot be done, than that God cannot do them.) Incidentally, there is a close similarity between this omnipotence attribute following St. Thomas and the concept of positive qualities—purely positive qualities that are not limited or negated—used by Kurt Gödel as the principal element in hist modal version of the “ontologisk bevis” (see Gödel, 1995, pp. 389, 401, 403).
The paradox of the stone stone has been considered by many modern philosophers, including Mavrodes (1963), Frankfurt (1964), Cowan (1965,1974), Plantinga (1967), Schrader (1979), Anderson (1984) and more recently Cogburn (2004), Hill (2014), Beall & Cotnoir (2017), Wreen (2022), Bassford (2023). The treatment of the paradox by these authors seems overtly inkhorn, over-complicated, confusing and deliberately verbose. The Wikipedia (2024) description of the “omnipotence paradox” follows the confusing line of the modern philosophy. It looks like the philosopher’ job is to make trivial things fully unintelligible. Basically, if one dares to make a winding way through the thicket of quantum entangled reasoning, the principal argument nearly repeats that in the St. Thomas’ wording: omnipotence does not entail arbitrary, logically impossible and contradictory things: inability to do a self-contradictory task does not imply that the agent is limited. [An alternative is the Cartesian view that God is above and not subject to logic, so free from any contradiction, (see Bassford, 2023), but this position is incoherent (Geach, 1973)].
Some go much further by arguing that there must be truth-value gaps not accounted for by classical logic (Beall & Cotnoir, 2017), that the omnipotence concept is useless in theology (Cowan, 1974), that the solution to the stone paradox is that “it proves nothing” (Schrader, 1979) or that God is not omnipotent even if we do not deny His perfections and power (Hill, 2014).
However, the simplest and best solution to the stone paradox in my view was provided by (Savage, 1967): “God can create stones of any poundage, and God can lift stones of any poundage” (p. 79). Strangely, this transparent phrase does not look like the conclusions most philosophers like to come to.
However, the paradox of the stone can be reduced to a trivial form which I call “the omniidiota dilemma,” with an instructive corollary. The argument is as follows.
The omniidiota dilemma
Definition. Idiot is defined as someone suffering from (in certain cases, perhaps enjoying) extreme intellectual disability, primarily an utmost form of acalculia.
Comments. Dyscalculia describes a deficit in processing numerical information, learning and recalling arithmetic, as well as making calculations (American Psychiatric Association, 2022). Its extreme form is well described in the psychiatric and psychological literature as acalculia (Dehaene, 1997; Nieder, 2025). A person with acalculia suffers from extreme challenges with even the most basic arithmetic operations, often as a consequence of severe brain damage or extreme developmental disorder. For example, if asked to add one to a given number, the he/she is unable to do such elementary calculation. It is important to note that the term “idiot” should not be understood pejoratively. The original meaning of ἰδιώτης in Greek is just a normal person. There is also a large literature on idiot savants who combine extreme deficit in one cognitive capacity or many diverse capacities with much above the average achievement in certain specific intellectual domain (Dehaene, 1997).
The omniidiota dilemma:
Can a person make such a big number that he/she cannot imagine a number greater than that?
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If he/she can imagine such a number, then it proves he/she is an idiot, since the task of guessing a number that is greater than the given number (without any other conditions or restrictions) is trivial. It can be solved in any of many different ways, e.g. adding one or two to the big number, or just doubling this number. Incapacity to increase a number (big or small) points to severe cognitive deficit.
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If he/she cannot imagine such a number, then he/she is an idiot, because just imagining any number is a trivial task: take any number and then imagine an even bigger number using any of the elementary arithmetic operations. Incapacity to create a number therefore points to severe cognitive deficit.
It follows from the omniidiota dilemma that you (the reader) and I (the writer) are all idiots: Being not an idiot is a logically contradictory proposition. The dilemma is then simple: everyone is either an idiot or … an idiot: tertium non datur.
Corollary. It follows from The paradox of the stone and The omniidiota dilemma that, if God’s omnipotence is considered self-contradictory, then everyone is necessarily an idiot.
References
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American Psychiatric Association, ed (2022). Diagnostic and statistical manual of mental disorders: DSM-5-TRTM. American Psychiatric Association Publishing, Washington, DC, Fifth revised edition.
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Anderson, C.A. (1984). Divine omnipotence and impossible tasks: An intensional analysis– Int J Philos Relig 15: 109–124.
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Bassford, A.D. (2023). God and the problem of logic. Cambridge University Press.
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Beall, J. & Cotnoir, A.J. (2017). God of the gaps: a neglected reply to God’s stone problem– Analysis 77: 681–689.
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Cogburn, J. (2004). Paradox lost– Can. J. of Philosophy 34: 195–216.
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Cowan, J.L. (1965). The paradox of omnipotence– Analysis 25: 102–108.
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Cowan, J.L. (1974). The paradox of omnipotence revisited– Can. J. of Philosophy 3: 435–445.
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Dehaene, S. (1997). The number sense: how the mind creates mathematics. Oxford University Press.
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Frankfurt, H.G. (1964). The logic of omnipotence– Philosophical Review 73: 262–263.
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Geach, P.T. (1973). Omnipotence– Philosophy 48: 7–20.
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Gödel, K. (1995). Collected Works: Volume III: Unpublished essays and lectures– (S. Feferman, J. W. D. Jr., W. Goldfarb, C. Parsons, & R. Solovay, Eds.). Oxford University Press
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Hill, S. (2014). Giving up omnipotence– Can. J. of Philosophy 44: 97–117.
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Mavrodes, G.I. (1963). some puzzles concerning omnipotence– The Philosophical Review 72: 221.
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Nieder, A. (2025). The calculating brain– Physiological Reviews 105: 267–314.
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Plantinga, A. (1967). God and other minds. Cornell University Press.
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Savage, C.W. (1967). The paradox of the stone– The Philosophical Review 76: 74-79.
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Schrader, D.E. (1979). A solution to the stone paradox– Synthese 42: 255–264.
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Wikipedia (2024, November 7). Omnipotence paradox. https://en.wikipedia.org/wiki/Omnipotence_paradox.
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Wreen, M. (2022). The contradiction approach to solving problems about omnipotence– TheoLogica 6: 52533.
