Omnipotence paradox

Could Jesus microwave a burrito so hot that he himself could not eat it? The omnipotence paradox refers to the apparently paradoxical ability of an omnipotent entity to both limit its powers and remain omnipotent.

The paradox is used both as an argument against the existence of an omnipotent god (and the Judeo-Christian God in particular) and against the concept of true omnipotence.

The paradox
The paradox highlights cases where, in performing an action, an omnipotent being would be limiting its abilities (therefore rendering it very firmly not omnipotent); conversely if it was unable to perform such an action, it would also not be omnipotent. The paradox represents a reductio ad absurdum, with the conclusion that a truly omnipotent being cannot exist.

The most classic example of the paradox, a Morton's fork, is the "Paradox of the Stone":


 * Can an omnipotent being create a stone so heavy that it cannot lift it?


 * If yes: the being's power is limited, because it cannot lift the stone.
 * If no: the being's power is limited, because it cannot create the stone.
 * Either way, the allegedly omnipotent being has proven not to be omnipotent due to the logical contradiction present in both possible answers.

The stone paradox can be substituted with similar examples. For example, could an omnipotent being create another being more powerful than itself? Could an omnipotent being destroy itself? Could he create a wall he cannot climb? Could he beat himself at arm-wrestling? And so on. The situation crops up numerous times in different wordings but all mean the same thing.

Some variations gives other useful consequences:

Can God create a cryptography/key exchange system so secure that he himself cannot crack/bypass?
 * If no: He does not have the ability to authenticate any of his revelations, and therefore he lacks omnipotence, and cannot authentically reveal anything to anyone.
 * If yes: He does not have the ability to bypass encryptions therefore he lacks omnipotence and omniscience.

Other paradoxes
Some have suggested that the concept of any paradox presents a challenge to the concept of omnipotence. For example, the thirteenth century theologian Thomas Aquinas pondered whether God could create a triangle (on a flat surface, no cheating with non-Euclidean geometry) in which the angles do not add up to 180 degrees. Or similarly, could God create a flat circle where π = 3? To do so would be to create a shape which cannot possibly exist in our universe - such a triangle can only exist on a curved surface and even warping space to do so is still placing the object on a curved surface. Yet if God cannot do so, then his powers must be limited by the laws of mathematics, and therefore he could not be fully omnipotent. This can be further complicated by asking "Can an omnipotent being create a triangle with four sides?" The issue here is that an object with four sides ceases to be a triangle and becomes a quadilateral - naturally, an omnipotent being could just rig up human language so that a four sided object was called "a triangle", or try to pass off a straight side as having a 180° corner in it. For the purposes of the paradox the aim is for the being to create such a thing, without resorting to such semantic trickery (and in spite of the semantic contradiction of asking for a three sided object with four sides)

Paradoxes do not necessarily have to ask for strange forces (like unmovable and unstoppable) and strange physics. Omnipotence can equally be limited by non-contradictory but very plain examples. For example consider an individual making the statement: "God cannot make me love him with my own free will". God could "miracle" some love in someone, but that wouldn't be an act of free will. God could torture someone until he "loved him", but similarly, that would be an act of force, morally indistinct from a criminal torturing someone in order to make them say something. God could argue that "he does not need X's love", however this would not remove the original problem that this represents a case where a mere mortal individual can limit God's omnipotence. Still, God could just win us over; after all, when we come to love another mere-mortal, due to that mortal's attempts to win our love, we usually consider that "loving them of our own free will".

Definition of omnipotence
Most repudiations of the omnipotence paradox usually concern the definition of omnipotence, reducing it to merely an argument about semantics. These refutations assert that the paradox misrepresents omnipotence and the nature of a particular omnipotent god, as in their view, omnipotence is not necessarily bound by the laws of logic, physics or mathematics (see Molly Hayes' resolution, below). Non-believers often have trouble ignoring the irrationality of this idea, but those happy to accept that such a god would be truly omnipotent regardless of how contradictory that may be have no trouble dealing with it. This is notable for being the single strongest case of special pleading in history of logic.

If the situations were really to occur
Another argument is that an omnipotent being does have every conceivable ability, including the ability to limit their own power (and hence stop being omnipotent). In this refutation, it is claimed that such a being is unlikely to make that move. Hence they could create a stone so heavy that they could not lift it; they just wouldn't.

The problem here is that the question then becomes "could the being complete the sequence of creating a stone too heavy for it to lift and then lifting it?" Taking into consideration the interpretation that "God makes a rock too heavy for him at the present moment, but gives himself the power to carry said rock after it was created" still solves nothing, as that means that he can only do either/or - he cannot do both at the same time. And that's not omnipotent by a longshot.

Christians do have a kind of answer to the rock question by bringing in the concept of existing as two beings at the same time (via their claim that Jesus Christ of Nazareth is God). This can be circumvented simply by adding "without existing as two beings at the same time".

Contradiction in the paradox itself
If the paradox is reworded slightly to the common variant of "what happens when an unstoppable force meets an unmovable object?" then we can clearly spot a contradiction in the paradox itself, a similar problem to creating a four sided triangle as mentioned above. Namely, that if there is an unstoppable force, then there is no unmovable object that could be met by it, as if there was such an unmovable object, there could be no unstoppable force. The two are therefore mutually exclusive in existence, and it is a logical contradiction for both to exist at the same time. However, as is often the case, there may be a much simpler resolution to this paradox which allows both an unstoppable force and an immovable object to exist. . . If they were to meet, they would simply pass through each other without interacting. This would allow an omnipotent being to create both an unstoppable force and an immovable object.

Within the bounds of logic
One solution of the omnipotence paradox is to define omnipotence within the laws of logic. So while said god could happily create matter out of absolutely nothing, violating conservation of energy, suddenly reverse the orbit of the planet Earth, violating conservation of momentum, this god would still be bound within the laws of logic. This response if often phrased as something similar to, "God is able to do all that is able to be done." This approach could be interpreted as skewering itself on the horns of a metaphysical version of the Euthyphro dilemma - why would such a god be the ultimate authority if there exist things even more fundamental, the laws of logic?

Liar's paradox
Parallels can be drawn to the liar paradox -- Is the statement "This statement is false" true? -- Most responses to the liar paradox can be applied to the omnipotence paradox:
 * 1) The self-referential aspect (Can God do something He cannot do) renders the entire statement nonsensical and meaningless; stringing words together into a query that is grammatically valid does not mean the resulting query, itself, is valid.
 * 2) It is a statement to which "true" and "false" (or "yes" and "no" or "being able to" and "being unable to") cannot be applied; the answer is as undefined as the answer to the question: "If you divide a pie among zero people, what portion does each person get?"
 * 3) It has a constantly shifting answer where the temporal delta between true and false reduces to zero resulting in the statement being both true and false at the same time (It thus doesn't matter if God creates a rock He cannot lift because He can lift it at that same time).
 * 4) Semantic trickery about the meaning of "true", "is" and/or "false" can equally be applied to "create", to "being able to" and/or to "lift".
 * 5) The answer involves descriptions of quantum super-positions and roughly equates to a response of "maybe" or "kinda".
 * 6) 

Practical examples
can, in fact, create a it cannot edit. But of course that is because vi is, sadly, far from omnipotent, unlike.

As demonstrated by Star Trek and the wise, the omnipotence paradox would also be useful in shutting down Roko's Basilisk or some other rogue AI. (Albeit, Molly later reactivated the AI by providing the obvious answer: "Yes, God could make a sandwich so big that He couldn't eat it . . . And then He would eat it, anyway.")