Omnipotence paradox
The paradox arises, for example, if one assumes that an omnipotent being has no limits and is capable of realizing any outcome, even a logically contradictory one such as creating a square circle.
Atheological arguments based on the omnipotence paradox are sometimes described as evidence for countering theism.
[3] Pseudo-Dionysius the Areopagite (before 532) has a predecessor version of the paradox, asking whether it is possible for God to "deny Himself".
Alternative statements of the paradox include "If given the axioms of Euclidean geometry, can an omnipotent being create a triangle whose angles do not add up to 180 degrees?"
[7] Some modern approaches to the problem have involved semantic debates over whether language—and therefore philosophy—can meaningfully address the concept of omnipotence itself.
Omnipotence, they say, does not mean that God can do anything at all but, rather, that he can do anything that is logically possible; he cannot, for instance, make a square circle.
[11] Essentially, Mavrodes argues that it is no limitation on a being's omnipotence to say that it cannot make a round square.
[12]If a being is accidentally omnipotent, it can resolve the paradox by creating a stone it cannot lift, thereby becoming non-omnipotent.
[6] On the other hand, the ability to voluntarily give up great power is often thought of as central to the notion of the Christian Incarnation.
There has been considerable philosophical dispute since Mackie, as to the best way to formulate the paradox of omnipotence in formal logic.
Suppose the objector insists that it's a coherent question, then we reply by affirming that God can create such a stone.
The conclusion which the objector wishes to draw from an affirmative answer to the original question is itself the required proof that the descriptive phrase which appears there is self-contradictory.
C. S. Lewis argues that when talking about omnipotence, referencing "a rock so heavy that God cannot lift it" is nonsense just as much as referencing "a square circle"; that it is not logically coherent in terms of power to think that omnipotence includes the power to do the logically impossible.
While this does not quite make complete sense, Lewis wished to stress its implicit point: that even within the attempt to prove that the concept of omnipotence is immediately incoherent, one admits that it is immediately coherent, and that the only difference is that this attempt is forced to admit this despite that the attempt is constituted by a perfectly irrational route to its own unwilling end, with a perfectly irrational set of 'things' included in that end.
This implies for the debate on omnipotence that, as in matter, so in the human understanding of truth: it takes no true insight to destroy a perfectly integrated structure, and the effort to destroy has greater effect than an equal effort to build; so, a man is thought a fool who assumes its integrity, and thought an abomination who argues for it.
It is easier to teach a fish to swim in outer space than to convince a room full of ignorant fools why it cannot be done.
The philosopher Ludwig Wittgenstein is frequently interpreted as arguing that language is not up to the task of describing the kind of power an omnipotent being would have.
In his Tractatus Logico-Philosophicus, he stays generally within the realm of logical positivism until claim 6.4—but at 6.41 and following, he argues that ethics and several other issues are "transcendental" subjects that we cannot examine with language.
[20] Wittgenstein's work expresses the omnipotence paradox as a problem in semantics—the study of how we give symbols meaning.
(The retort "That's only semantics," is a way of saying that a statement only concerns the definitions of words, instead of anything important in the physical world.)
The final proposition of the Tractatus gives Wittgenstein's dictum for these circumstances: "What we cannot speak of, we must pass over in silence".
In the 6th century, Pseudo-Dionysius claims that a version of the omnipotence paradox constituted the dispute between Paul the Apostle and Elymas the Magician mentioned in Acts 13:8, but it is phrased in terms of a debate as to whether God can "deny himself" a'la 2 Tim 2:13.
[24] In the 11th century, Anselm of Canterbury argues that there are many things that God cannot do, but that nonetheless he counts as omnipotent.
[25] Thomas Aquinas advanced a version of the omnipotence paradox by asking whether God could create a triangle with internal angles that did not add up to 180 degrees.
Modern physics indicates that the choice of phrasing about lifting stones should relate to acceleration; however, this does not in itself of course invalidate the fundamental concept of the generalized omnipotence paradox.
Ethan Allen's Reason addresses the topics of original sin, theodicy and several others in classic Age of Enlightenment fashion.
In Principles of Philosophy, Descartes tried refuting the existence of atoms with a variation of this argument, claiming God could not create things so indivisible that he could not divide them.
