The omnipotence paradox is an apparent contradiction in the notion of an omnipotent (all-powerful) being (such as God, or Superman, or the government). An omnipotent being can do absolutley anything. So can an omnipotent being create a stone that is too heavy for him to lift? If he can create it, then there is one thing he can't do: lift the stone. If he can't create it, then there is one thing he can't do: create such a stone. Either way, there is something he can't do, which contradicts the assumption that he is omnipotent. This is a paradox. It has been taken by some to show that there cannot be an omnipotent being, and by others to show merely that the concept of omnipotence is misunderstood (for example, that it does not involve the power to bring about logical impossibilities).

Philosophical Responses

One common response points out that this question makes implicit assertions that are inconsistent and self-contradictory. The phrase omnipotent being implicitly states that any phrase such as a stone too heavy for him to lift is meaningless. Thus, one solution to this type of paradox is to say that it is logically impossible for both entities to exist at the same time. So, there cannot be both an omnipotent God and an unliftable rock.
  1. Extraction: Therefore, a response is available if it is already accepted that God cannot do what is logically impossible
  2. Logical Conclusion: God cannot do what is logically impossible.
  3. Assumption: It is logically impossible for there to be a stone God cannot move.
  4. Logical Result: God cannot create such a stone.
This necessarily accepts the view that even an omnipotent God cannot violate the laws of logic, and indeed this whole paradox can be seen as a strong reason for such a view. The philosopher Averroes advanced the omnipotence paradox for this reason (for which he was condemned by Bishop Tempier), although instead of phrasing it in terms of stones, he asked whether God could create a triangle whose internal angles did not add up to 180 degrees. (Note that the later discovery of non-Euclidean geometry does not resolve this question. One might as well ask, "If given the axioms of Riemannian geometry, can God create a triangle whose angles do not add up to less than 180 degrees?" In either case, the real question is whether, once God has decided to establish a system of axioms, can He evade the consequences which follow logically from them?)
However, the answer above can be restated even if one does not already accept that God cannot do logically impossible things: one can answer that the question is literally meaningless, and therefore there is not even a logically impossible task being set.
This is a useful distinction if one wants to hold (as some, including René Descartes, have held), that God can do even some logically impossible things, such as making 2+2=4 false, although not everyone believes that God can mess with math.
Another solution is simply that an omnipotent being can create a stone too heavy for him to lift. The being's omnipotence depends on the nonexistence of such a stone, but his omnipotence also implies that the being can give up his unlimited power if he wishes. If he were to create such a stone, then he would in effect be relinquishing his omnipotence, but no logical contradiction would arise. (But in this "solution" may lie yet another problem: if God is omnipotent at any given point in time, he must also be omnipotent at any other time since he can manipulate the time axis arbitrarily without losing his omnipotence. Thus, God cannot choose to give up his omnipotence at any time.)
Yet another solution would be to say that creating a stone too heavy for God to lift is impossible, as God can do anything. But because God can do anything he must therefore be able to create a stone so heavy that he cannot lift it: God must be able to do the impossible if he is truly omnipotent. Once the stone is created, logically, it is impossible for God to lift. However, God can do the impossible, so he can lift a stone so heavy that he cannot lift it. In the words of Harry Frankfurt, "If an omnipotent being can do what is logically impossible, then he can not only create situations which he cannot handle but also, since he is not bound by the limits of consistency, he can handle situations which he cannot handle."
It could also be argued that with omnipotence comes omniscience. If God knew that he would be needing to lift the stone in the future, why would he create that stone?

Proof By Contradiction

One response is to use proof by contradiction:
  1. Assumption: An omnipotent body exists
  2. Extraction: An omnipotent can create any type of stone.
  3. Extraction:There are no stones too heavy to lift up for an omnipotent.
  4. Logical Conclusion: An omnipotent cannot create a stone too heavy to lift up.
  5. Assumption: A non-omnipotent body can create a stone too heavy to lift up.
  6. Extraction: A non-omnipotent is superior to an omnipotent, which is contradictory.
  7. Logical Result: (An) omnipotent bod(y/ies) cannot exist.

The "Logical Fallacy" Arguement

Another response to those positing these questions of omnipotence and alleged conflict is that the questions of super heavy stones, along with all the other ability-based arguments etc., are actually a clever logical fallacy, and are false straw man arguments. The reason being is that power is not ability, or knowledge, therefore being all-powerful [omnipotent], logically says nothing about knowledge or ability. To assume [wrongly] that an omnipotent [all-powerful] being is also limitless in ability is not only moving the proverbial goal posts, it is specifically setting up a false straw man to argue upon, by saying they [power and ability] go together when there is no logical or rational basis for this assumption. A simple illustration can be demonstrated, in the fact that mankind has the power to destroy most of life on earth, but still hasn't the ability or knowledge to design and create from scratch simple life forms, such as a flower, a microbe, or a housefly. Ability and knowledge are not the same as raw power. Therefore an omnipotent being, would not necessarily have unlimited abilities at all, and to posit such is a logical fallacy as they [ability and power] are not necessarily linked at all. One other point brought up in regard to the Biblical God's claimed omnipotence, is that is it not a linked prerequisite with ability, in as much as God (in the Bible) is described as being immortal, and incorruptible, therefore it is impossible for Him to die and impossible to for Him to be corrupted, but this has no logical effect on His omnipotence, as has been illustrated. Power is not ability, nor knowledge, they are separate categories, and not mutually exclusive if [power] were unlimited. Therefore for a being to be omnipotent would not logically mean that this being would need to also have unlimited abilities, like the ones proposed above in regard to lifting immovable heavy stones that were just created by the same being. These argument do not affect the position of an omnipotent being because the falsely linked "unlimited ability" is a straw man, and has been inserted to alter the meaning of omnipotence, to then give a false argument for dismissal, as if the omnipotent being is logically untenable due to its omnipotence being in conflict. It is important to be aware of logical fallacies inserted like we see with the false assumption that a being or God that is omnipotent must also somehow be unlimited in abilities. This is not logical, nor rational, and is a straw man argument.

The "Logical Fallacy" Counter Argument:

Some have another view. It is said it is totally different from a case of a squared triangle.The logical fallacy is not due to the action of creating a stone too heavy to lift up. A squared triangle is seft-contractory and drawing it is logically impossible. However, It is not a illogical or difficult task to create a stone too heavy to lif up even for a layman. The logical difficulty is due to the term omnipotence. If someone attributes the action as a fallacy for a omnipotent, he forgets that the term omnipotence is being investigated. There is another logical fallacy: begging the question. Although some try to defend the existance of an omnipotent being by defining other meanings to the term omnipotence, the new definitions deviate from the common perception of the term and are hard to understand. For example,
Power is not ability, nor knowledge, they are separate categories, and not mutually exclusive if [power] were unlimited.
Definitions like that needs to be further clarifed or make the term omnipotence void, especially for non-christians, otherwise.

Willpower Argument

It has been suggested in recent years that the resolution lies in how one understands the word "omnipotent." The paradox dissolves if one accepts this reasonable definition: "An omnipotent being is one who can do anything he (or she or it) wants to." If this is accepted, then "God" can make an unliftable stone at will. If at some later time, God wants to lift that stone, then he can do so. The obvious flaw with this argument can be stated succinctly by rephrasing the paradox: "Can God create a stone so heavy that he will never be able to lift it?" (The religionist in turn might rejoin that God's will never changes, and so on into as many iterations as you choose.)

Another example of a paradox like this is the Heaven hotter than Hell Paradox.

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