Talk:Omnipotence paradox/Archive 1

'''Of course, if one follows Wikipedia's rules, the entire article must be deleted, because nothing in philosophy is verifiable (it fails the verifiability rule of Wikipedia). And most of the statements in the article qualify as "original research" as well (although that is true for the bulk of articles in Wikipedia, so if one is to follow the rules strictly, just about everything has to go).''' Thanks, Agateller 20:03, 12 January 2006 (UTC)

Formulating the Paradox
I don't understand why the simple definition of "all-powerful" is "insufficient for the omnipotence paradox.". Certainly this claim is wrong:


 * This paradox cannot be formulated, for example, if one defines omnipotence as the ability to operate outside the constraints of any logical framework.

The reason why it's wrong can be very simply explained by formalizing it:


 * A. Assume that one defines omnipotence as the ability to operate outside the constraints of any logical framework.
 * B. It follows from A that the omnipotence paradox cannot be formulated.

Now, proposition B has to follow from A by using some logical framework. But proposition A already states that the constraints of logical frameworks do not apply. Therefore B cannot follow from A.

Or more succinctly, postulating freedom from logic does not free you from logic.

Ldo 20:57, 14 January 2006 (UTC)


 * If you were walking down a road and saw an animal that was all rabbit and all turtle at the same time would you say that "I am not seeing an all rabbit all turtle animal because if I was that would violate logic and thus it would be impossible to use logic to reach the conclusion that I am seeing it."

Resolving the paradox
I added a section that explains how the paradox can be resolved by removing temporal constraints, which is entirely reasonable when one is discussing an omnipotent being. I don't know why the rest of the article fails to cover this possibility, although it comes close to mentioning it in the "Pop culture" section. A truly omnipotent being cannot be omnipotent unless it can create everything, and that would necessarily include such things as time. Therefore an omnipotent being would logically be independent of time. Therefore paradoxes that exist only because they assume temporal constraints would not exist for the omnipotent being, and the omnipotence paradox ceases to exist.

Agateller 11:16, 12 January 2006 (UTC)

?
"One such solution is that a being can create the situation and do the impossible and impossible at the same time. For example:" Should this say impossible and possible? I'm scared to edit a feature article :)The-dissonance-reports 05:52, 9 January 2006 (UTC)

Really a Paradox?
the question.... can...     make a rock...       can't lift? or in fact any other question of this type

reduces to

the question....can...     do something....      cannot do?

which put another way means...

the question....can...      violate logic?

therefore

those criticizing Rene Descrete's answer are in the wrong because his response is the meaningful way to answer the question.

So the response can be 1. the question is invalid because second part basically states in one way or another that ....is not capable of everything... something is impossible for, arm wrestling robot can do things....cannot do etc etc

... which would mean that the (question) is incorrect as ....can do anything...

2. you accept his answer.

Problem solved

Stupid question, not a paradox
Can God Create a Stone that He Cannot Lift?

This question is more than 800 years old. At the time of asking this question, the questioner had already assumed the existence of gravity.because of the word “lift” in the question. What is “lift”? My definition for “lift” is: Moving an object to the opposite direction of gravity. By definition, God created everything. Hence, God created gravity. Since God can create gravity, he can certainly make it disappear. So God can “lift” any stone. Put another way, this question could become: if God were to have an arm wrestling match between his left arm （gravity）and right arm (to “lift” the stone), which one would win? Both arms belong to God. This is not a contest; there is no winning or losing. Therefore this is a stupid question.

If God is omnipotent, then God must be everything, everything must be God. There is nothing outside God, not even empty space, because God created space and time. The fact is, “Outside God” is an oxymoron: if there is God, then there will be no “outside”; if there is an “outside”, then there will be no God. There is no gravity “outside” God. God doesn’t live in a gravitational field. For an omnipotent God, there is no such concept as “lift”. “Lift” only exists in human experience. Gravity, like everything else, exists inside God. An ant looks at you when you are talking, it could see your lips and tongue are moving. It asks you: “How did you lift your lips and tongue?” You answer: “This is a stupid question.” A man sees that the Moon is moving, he asks God: “How did you lift the Moon?” God says: “This is a stupid question.”

By Teng Wang    tengwang777@hotmail.com My website:   http://www3.telus.net/public/t5837479/index1.htm
 * you just saidi "in god's lexicon, there is no such a word as "lift"". wow, if that's the case, god is even LESS POTENT then we thought.  your paragraph does not contain any coherent set of premises.  you have simply dismissed the paradox with the miscellaneous (and ill-conceived) remark "This is not a contest."  you've missed the whole point.128.119.237.54 02:44, 10 January 2006 (UTC)


 * Erm. How about this question:  "Can God create Himself an arm which can defeat all others in arm-wrestling?"


 * Or this one: "Can God create a natural law (like gravity) so compelling that He is unable to cancel it?"


 * Or, "Can God create an axiom system so thorough and careful that it must necessarily have no contradictions or undecideable statements?" Sure, right after He makes a Euclidean triangle with three right angles. . ..


 * Whoops. My signature got zapped somewhere along the line.  You can blame this last passage on me, back on 16 Jul 2004. &mdash;Anville.


 * Actually this is not a stupid question, you simple did not understand the paradox. Our Assumption is, God is omnipotent. But as you said "God can lift any stone", but if he can do that, he violates the first part of a statment. If he can lift everything, than its not possible for him/her to "create a stone, he cannot lift'". If this is the case he is not omnipotent, which was our basic assumption in the first place. trin 4 Aug 2005


 * Replied Stupid question, not a paradox
 * The Logic process is, we make an assumption, if the statment is unsatisifiable (all other variable part of the statment had tried but all lead to a false statment(normaly contradiction) ). we proved the assumption statment to be false, which in this case "omnipotent being exist" is proved to be false. This is called proof by contradiction. (Check on formal logic for more info on this) --Zektonic 05:50, 11 August 2005 (UTC)


 * Gravity is irrelevant. Even without gravity, the megalomaniac would have to overcome the rock's inertia to lift it--and inertia is an intrinsic property of an object, based solely on its mass.  Kurt Weber 12:31, 28 November 2005 (UTC)

"ALMIGHTY GOD DOES NOT EXIST"
The Wikipedia article is biased in favor of assuming that &#8216;god&#8217; is possible i.e. a non-zero probability. This has not been demonstrated at all. Show that god is possible, (and the best way to do this is to produce at least one &#8216;god&#8217; in a show and tell) and then we can discuss the properties this &#8216;god&#8217; may possess.

The best way to discuss the &#8220;paradox&#8221; is to recognize that it IS a matter of logic and not material reasoning, that is, it is a matter of abstract structure, not semantic content. The best way is the same way logician Louise Carroll approached the matter.

Can an all-powerful being do &#8216;A&#8217; so Jabberwocky that he can&#8217;t &#8216;B&#8217; it?

This way we&#8217;re not speaking of gravity or extra arms. ;-)

Yes, it is a fact that parts of this query are incompatible with other parts, but there is nothing inherently wrong with lifting rocks (or &#8216;B&#8217;) or creating rocks (or &#8216;A&#8217;) but there IS something wrong with the idea of an object with unlimited properties and is what has to go.

If theorem-G leads to existential paradoxes, then theorem-G is false. It is incorrect to say that, &#8216;we like theorem-G, therefore asking questions that shows that theorem-G leads to existential paradoxes is disallowed.&#8217;

That&#8217;s a crock.

There CAN NOT be any omnipotent being i.e. a being with unlimited properties. This is not opinion, it is a logical fact.

This is no more a paradox than the law of impossible antecedent is a paradox.

If 'A' leads to 'B', and 'A' leads to not 'B', then not 'A'.

Omnipotent (all-powerful, almighty) 'god' does not exist.

QED

LOGOS

65.114.23.4 00:08, 16 Aug 2004 (UTC)


 * Just to correct any misapprehensions, I didn't write the passage above by 65.114.23.4. My signature got displaced from the text above it. Anville 16:05, 16 Aug 2004 (UTC)

It seems to me that the article is not biased. In order to discuss the "omnipotence paradox" at all, it is necessary to take the existence of God (or some omnipotent being whom we might as well call God) as a given, in the sense of a mathematical demonstration, much as it is necessary to ignore any God one happens to believe in, in order to usefully discuss evolution or cosmology from a scientific point of view. Sturgeonslawyer 10:14 AM PDST, 4 My 05


 * Of course the idea that ignoring the God you believe in is necessary for scientific debate is a controversial thing to say ;) But your point still stands. There is a guideline about when it is reasonable to assume something controversial. Arguments about the existence of God should be redirected to Talk:Existence of God if anywhere (and even then only if they are well known). Hairy Dude 04:01, 9 January 2006 (UTC)

A Paradox ???
If God is omnipotent, then the rock can not be made to be heavier than God because this unliftable rock would have limitations, ie: physical weight, mass, energy, etc. All of this has already put limitations on the rock, therefore the rock paradox can be obscured easily and can not be used to define/compare to God's omnipotence.

However, a clearer picture of this paradox could be explained.

If God is omnipotent and he was to make this unliftable rock, this would imply by the statement that "the rock" is greater/grander than God. Since God is omnipotent, the only other thing greater/grander than God would be himself, if he so chooses this. The question then would be, could he lift this grander version of Himself (or the rock)? Yes, he could. Since God is omnipotent, he could lift himself and would not contradict anything. The contradiction exist only when we're limiting his omnipotence or comparing it to something of a much lesser nature, ie: a rock. In general, a rock (real rock) heavier than God can not exist in physical reality. This would violate many reality/universal laws. If this rock was to exist outside of physical reality, then it's not a rock. This unliftable rock would fall short of contradicting God's omnipotence.

A better example would be, to liken God to infinity and let's say the unliftable rock to infinity + 100. The question then would be, could God (infinity) be more (lift) than infinity + 100 (the rock). Yes, because since: God = infinity and The rock = infinity + 100 and infinity = infinity + 101 = God

This takes us back to the assumption that if God so desires to create an unliftable rock (something greater than himself) and be able to lift it, then he could because this greater thing would still be himself, this unliftable rock would be God, the Omnipotent.

Comparing God's omnipotence with the unliftable rock is like comparing infinity to the set of numbers between the integers 1 and 10. You can't. I'd say, this isn't a paradox at all. Just some bad comparison/interpretations on God the Omnipotent and an unliftable rock. &mdash; Say Yang, July 28-29, 2004


 * Say Yang, the talk pages aren't really for debate over whether a principle or point of view is valid or not. But have no doubt that many philosophers and particularly (obviously) atheists consider the strong, literal, plain or usual meaning of omnipotence to be logically inconsistent and thus the paradoxical.  Many Christians also accept this conclusion with the proviso that God transcends logic and it is rational to accept His incomprehensible transcendance. Regardless of whether the examples and analogies are very good or not, any argument you proffer that there is no inconsistency, incoherency or paradox is going to fall on deaf ears amongst many logicians, philosophers, atheists and Christians. Although most people don't know how to read formal logic, if I care enough, maybe I'll add in an example written in formal logic to demonstrate the logical inconsistency. Frankly, I think the traditional examples work well enough although the Homer Simpson example is my favorite.   &mdash;B|Talk 19:34, 29 Jul 2004 (UTC)


 * I'm always wary of arguments which rely upon the properties of infinity, particularly the idea that all infinite quantitites have the same size. This is demonstrably untrue (e.g., the set of all subsets of the integers is larger than the set of integers).  Saying that "infinity + 1 = infinity" is true if we understand "infinity" to mean Cantor's $$\aleph_0$$, but false if we interpret it as a surreal number, $$\omega$$. &mdash;Anville 20:54, 10 Aug 2004 (UTC)


 * How About "Can god create a rock so heavy he can't make a machine that can lift it?"

JedG

Unstoppable forces and immovable objects
I've never cared for the unstoppable/immovable paradox, and I'm curious if the article could be reworded to avoid it. To me, the conclusion that they are incompatible is a rather Aristotelian way of looking at it. I first encountered this puzzler in the Mindtrap game, where it was posed with an unstoppable cannonball and a wall that nothing could knock down. Mindtrap gave the same solution that this article does, namely that presupposing one entity logically disallows the existence of the other.

Now, consider the Mindtrap version, as a person sitting on the wall would view it. This observer rests in an inertial frame, and all experiments he can perform indicate that he is effectively at rest. An observer riding on the cannonball, however, must come to the same conclusion: since nothing can change the cannonball's state of motion, this observer also finds himself in an inertial reference frame that nothing can disrupt. Both entities are objects of infinite inertia; they merely start off in motion relative to each other.

I can make hand-waving arguments that a solid cannonball is not necessary (although it certainly appears to be the image commonly associated with "unstoppable force"). In classical mechanics, energy is the result of a force acting on an object moving through a distance, and by Einstein's relation $$E = mc^2$$ energy and mass are essentially equivalent. . . yadda yadda, handwave. (Going all the way into general relativity, an object of infinite mass would have an event horizon at an infinite distance, and the curvature of spacetime would be infinite at all points&mdash;which is pretty darn weird. GR has enough problems with singularities as it is, I suppose.)

Given the precepts of Aristotelian physics, yes, the situation is a paradox, analagous to the omnipotence conundrum. However, we left Aristotle behind a long time ago, and the idea of two unshakeable reference frames (in Newtonian mechanics) doesn't sound that bad to me. As the limiting case of arbitrarily large finite masses, it's not any worse than the idealizations we do of infinitely long wires, say, or flat planes of infinite extent. (Remember all those old Gauss's Law problems?)

Anville 21:11, 10 Aug 2004 (UTC)

René Descartes
I am by no means a historian of philosophy, but it was my impression that Descartes claimed God could make a man believe that 2 + 2 = 5, not necessarily changing the truth of the assertion itself. James Burke raises this point in his book The Day the Universe Changed, where he describes Descartes's search for the undoubtable. He can doubt the physical world, his own senses, and even mathematics&mdash;but he cannot question doubt itself. This leads to his axiom cogito, ergo sum&mdash;the one which Feynman scoffed and Deep Thought used to deduce the existence of rice pudding. . ..

Anville 17:10, 13 Aug 2004 (UTC)

Matter of basic logic: bivalence
Anville, the "paradox" "is a rather Aristotelian way of looking at it" because the paradox was recognized in the era of Aristotelian logic and perpetuated to the present because of its simplicity. However just because logic has become more sophisticated does not mean that the "paradox" is resolved. It is also erroneous to state that "we left Aristotle behind a long time ago"; while Aristotle's physics has long since been discarded, logic still forms the backbone of science, mathematics and all sound reasoning. Intuitionistic logic aside, the principle of bivalence in classical logic is no less an axiom of logic now as it was in Aristotle's time. Given that this "paradox" is just as subject to bivalent parsing as any other proposition, as 65.114.23.4 implies above, this "paradox" is really only a paradox for those who reject the principle of bivalence because the strict definition of an omnipotent being is illogical under that principle. Sure a more modern version of the paradox can be phrased in predicate logic...but that doesn't avoid the principle of bivalence. Also the physics examples that you give more or less demonstrate intuitionistic principles of logic or modal logic, and why a bivalence parsing may not tell the whole story...but your examples also reflect why rejecting bivalence is problematic. Because of the assumption of intuitionistic logic this "paradox" becomes intertwined with unsettled theories about the nature of truth and unsettled issues in the philosophy of mind. Until those issues are settled, mathematical objects (object of infinite mass, infinitely long wires, flat planes of infinite extent, etc) are interesting possibilities to consider in relation to this "paradox" but far from being proved to have any ontological existence outside of the mind or outside of a mathematical formula. &mdash;B|Talk 23:55, 19 Sep 2004 (UTC)


 * Granted, granted. You can't make the "paradox" go away by throwing in some Galilean relativity.  My real point (insofar as anything I say in a talk page has a point) is that stating the problem in a way which depends on outdated physics is probably a bad idea&mdash;especially when the more recent physical ideas which change the interpretation are very important ones: inertia, relative motion, and reference frames.


 * I'm glad that people have invented words for this sort of thing: bivalence is a useful one to know. Isn't it great that the same word applies to arguments about God and to atoms which have lost electrons?


 * Anville 14:20, 20 Sep 2004 (UTC)


 * It probably makes more sense to avoid presenting the paradox with any physics example because the paradox is primarily a logical problem and a physics example may only confuse the issue. Consider that in your handwaving example "unshakeable reference frames . . . [do]n't sound that bad to [you]" because it examines whether there really is an "unshakeable reference frame" in the first place.  But that conclusion merely drives home the point of the paradox: an omnipotent being (as that concept is traditionally defined in a strict sense) has the power to create what does not exist...an unshakeable reference frame.  If unshakeable reference frames really do exist, then how could an omnipotent being create more than one, etc. etc.  As I said before, modern physics presents some interesting things to consider along with this "paradox", but a modern physics version of the paradox does not avoid the bivalence issue.  With all of that said, at a minimum, the classic examples should be stated in the article since that is how the paradox first arose, but the "paradox" should also be stated in formal logic for clarity's sake.   &mdash;B|Talk 22:30, 20 Sep 2004 (UTC)


 * Sometimes I wonder: can God make a Wikipedia article so perfect that it invites no discussion? After all, the perfect Wikipedia article should have, among its many excellent attributes, the attribute of existence.


 * Anville 23:05, 20 Sep 2004 (UTC)


 * But Kant's assertion - existence is not a predicate. -- Anon. Dec. 30, 2004

Religious response
I started to get confused. Does the article say that the orthodox religious (rather than philosophical) response is that God could create an unmoveable stone, and having done so God could then move it? It should. See and University of Paris (Condemnations). The arguement goes that it doesn't matter whether humans think this is logically possible or not, since one of the things that makes humans describe God as God is the ability to do what seems impossible to human minds (known as a miracle). Not that God would do anything like this, as providing entertainment to philosophers is probably not one of God's aims.--Henrygb 14:30, 2 Feb 2005 (UTC)

That is an answer to the paradox I saw published by Alvin Plantinga. He argued that if God can do one impossible thing - make a rock he is incapable of lifting, given that he is omnipotent - then he can do another, lift it. The problem comes when we consider what this says about God. Miracles are merely physical impossibilities - that is, they violate the ordinary physical laws of the universe - not LOGICAL impossibilities. If God can do the logically impossible then he has an impossible property. Any being with an impossible property is by definition impossible - cannot exist. When this crosses into the region of metaphilosophy is when we ask if perhaps the logically impossible could exist: in a round-the-houses not-really-but-I-see-where-you're-coming-from way, yes but by definition no. If the omnipotence paradox is solved in the manner you suggest one must conceed that God is impossible, i.e. cannot exist. A belief in the existence of the impossible requires a suspension of rationality and thus forfeiture of one's status as an agent. Essentially, if you believe the impossible exists then you are no longer capable of engaging in meaningful discussion.

Removed section
I snipped the following paragraph from the end of the article.


 * An omnipotent being can be considered an infinite one, since there are no limits on what the being is able to do. Therefore by asking the question if 'an infinite being can create a stone that the being can not lift' contains the impossible of doing operations on infinities: 'can the infinity of the being be less than the infinity of the stone?'. Of course such question can not be formulated, since infinity + infinity is undefined. Therefore, is does not make sense to ask that question.

My reasons:


 * Wikipedia is not a forum for personal thoughts on philosophical matters (well, not in the articles, anyway), as per the "no original research" policy.
 * If I define the weight of an object to be a surreal number, then it is perfectly permissible to have a stone weighing &omega; ("infinity") which can be lifted by a being of strength 2&omega; ("infinity plus infinity"). What paradoxes this leads to I haven't figured out:  God would have to be an entity whose strength is greater than all constructible surreals, etc.

Anville 21:43, 11 Mar 2005 (UTC)

logical validity or fallacy
I understand it is hard to get a conclusion. However, I think it is not appropriate to simply set a head line to make conclusing. It prevents anyone to add a counter argument and violate the spirit of wikipedia.


 * The above user is simply changing the heading "logical fallacy" to "logical validity", which makes no sense in relation to the content of that section. Read the article on logical fallacy, and the section in question. 24.76.141.220 04:04, 13 Apr 2005 (UTC)


 * The section discusses the validity of the statement. Logical fallacy imply the question is in logical fallacy. I don't think it is fair to conclude here. I did not simply change the heading and I have stated the reason: let the heading neutual!. I know the article logical fallacy well. But there are a counter arguement to state the question not logical fallacy. It is still controversal to see if it is logical fallacy. Just refer to a article means nothing. Please respect the wikipedia here. It is not a religious home page.
 * Wake up and smell whatever roses need smelling, or something. The section called "Logical Fallacy/Validity" is talking about one arguement (among the many on this article), that states that the "God can create something he can not lift" is a logical fallacy. The arguement does not state that it is a "logical validity", as that makes no sense. Sheesh, "Proof by Contradiction", by your arguement, should be called "Possible Contradition", which is stupid. 24.76.141.237 03:10, 19 Apr 2005 (UTC)
 * logical validity, in my original sense, means the status whether it is valid or invalid. It is neutral and left to discuss. "God can create something he can not lift" is a logical fallacy by no means. But the debate is on what causes the fallacy: The action - creating something himself cannot left or omnipotence? The action alone is feasible as said before. How about Omnipotence(I don't like the word God), it can make many many contradict sentence as the last section of the article. Ok. I can't say I am right but please use the neutral topic --203.112.80.139 03:12, 20 Apr 2005 (UTC)


 * Also, read this: "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,". That's in the section of the article. It clearly states that it's a "fallacy", so hiding it with "validity" does nothing. 24.76.141.237 03:10, 19 Apr 2005 (UTC)

--203.112.80.139 03:12, 20 Apr 2005 (UTC)
 * the statement you quoted just stated it is a fallacy but without any point to make his statment supportive. It is just an assertion. It can't make any conclusion by no means.
 * And it's changed again. Does this one appease you? 24.76.141.237 03:12, 19 Apr 2005 (UTC)


 * I will add a seperate sub-topic to show arguments against the assertion of fallacy on which not all agrees. It will make the article in a more neutral view.--203.112.80.139 05:41, 20 Apr 2005 (UTC)
 * That's fine, it's just that the section that you kept renaming argued for logical fallacy, and so it was originally named as such. 24.76.141.237 21:18, 25 Apr 2005 (UTC)

Removal of the "proof by contradiction"
I have just removed the following section:


 * ==== Proof by contradiction ====
 * One response is to use proof by contradiction:
 * 1) Assumption: An omnipotent body exists
 * 2) From 1: An omnipotent can create any stones.
 * 3) From 1: There are no stones too heavy to lift up for an omnipotent.
 * 4) From 2 and 3, an omnipotent cannot create a stone too heavy to lift up.
 * 5) A non-omnipotent body can create a stone too heavy to lift up.
 * 6) From 4 and 5, a non-omnipotent is superior to an omnipotent, which is contradictory.


 * The result is an omnipotent body cannot exists.

This "proof" is completely irrelevant, and flawed also. Nothing is said anywhere in the paradox formulation about superiority of omnipotence or non-omnipotence, and "superiority" is not defined. The paradox does not attempt to demonstrate anything; it's a clever contradiction only.

It is clear, also given the above discussion and the tone of the "logical fallacy" argument and counterargument, that is has turned into a discussion about the Christian God's supposed attributes. The "logical fallacy" issue simply cannot be addressed that way.

--Pablo D. Flores 11:16, 4 May 2005 (UTC)

Removed text
I have removed the following section from the article, since it does not seem to add enough content (and brims with mechanical errors anyway).


 * 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.
 * Such definitions need to be further clarifed, or run the risk to make the term omnipotence void.

I also nixed the following sentence, which was placed after the discussion of Averroes.


 * 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.

If I ask, "What is the sum of the internal angles of a triangle?", one could guess a wide variety of answers. Only one of them is correct&mdash;provably correct, given Euclidean geometry&mdash;but before doing the proof, who's to say what the answer should be? The mere fact that there exists only one correct answer does not make the question meaningless. Note that Averroes never asked for a four-sided triangle, which would be a contradiction in terms. Instead, he asked if God could evade the consequences of defining a triangle in a particular way.

One could formulate an analagous conundrum for any theorem in mathematics, I suppose. Can God draw a circle whose ratio of circumference to diameter is not &pi;? If God decides that the only appropriate tools are compass and straightedge, can He construct a square with the same area as a given circle, in a finite number of steps? God can make Abraham sacrifice Isaac, but can He trisect an angle?

I recall a line from Donald Knuth's novella Surreal Numbers, which goes something like this: "The difference, as I see it, is between proof and calculation.  We can prove that $$2\times\pi = \pi + \pi$$, but we can't calculate $$\pi + \pi$$ in a finite number of steps.  Only God can finish the calculations, but we can finish the proofs." (I lent my copy and never got it back, so this quote is probably somewhat garbled.)

Anville 02:09, 5 May 2005 (UTC)

Modified "Philosophical discussions," Removed "The argument from will"
I have modified "Philosophical discussions" by adding in various sections categorized by definitions of omnipotence (since that seems to be upon what the entire paradox depends). Each of these sections can be expanded to further discuss that particular way of treating the omnipotence paradox. Some more references would be a good idea too.

I've also removed "The argument from will" section because most of it discusses what I placed in the "Logical impossibility" section, and otherwise was duplicating a lot of content that belongs near to the beginning of the article. I haven't touched the "Logical fallacy" section because I don't grasp the concept well enough to be rewritten, but it needs to be rewritten because the paragraphs are lengthy and need more wikilinks, in my opinion. Ben Babcock 13:07, 5 May 2005 (UTC)


 * The logical fallacy section should be removed, if only because it's horribly confusing, and also rather transparently POV. Power is not ability? To me they are synonyms, but I'd like to see the difference explained somewhere. Myself, I'll give it a few days, unless somebody can come up with a better explanation of this "fallacy". --Pablo D. Flores 14:27, 7 May 2005 (UTC)
 * I agree with your, Pablo. Although I have seen a distinguishment between power and ability (Power should be distinguished from ability. Power is ability plus opportunity), the Logical Fallacy section makes it even more confusing, breaks the coherence of the article, and unless someone can seriously rewrite it, I'd rather it is just removed. Ben Babcock 16:04, 7 May 2005 (UTC)


 * 'Tis done. The "power vs. ability" issue, BTW, is extremely interesting. It should appear somewhere, though not here (it doesn't have to do with the paradox, and more importantly, it refers to maximally powerful beings, not to absolutely omnipotent beings as the definition of omnipotence suggests). --Pablo D. Flores 10:31, 9 May 2005 (UTC)

Another block of removed text

 * Criticism to this view


 * However, the above argument cannot have no weakness. Using the similar induction above, one can also prove that the paradox Is A Squared Triangle Being Is Triangular? can be resolved and a squared triangle exists too. The squared triangle being is essentially of the shape of a squared triangle, and therefore it is impossible for it to be of the shape of a non-squared triangle.Furthermore, the squared triangle being cannot do what is logically impossible.A squared triangle being is triangular would be an impossibility, and therefore the squared triangle being is not required to be triangular. The squared triangle being cannot be triangular, but nevertheless retains the shape of Squared Triangle.The flaw of the argument results from Begging the question, so does the original argument. It assumes the concept of omnipotence valid and then asserts the consequence(contradiction) invalid by the assumption itself. If the argument is valid, every proof by Reductio ad absurdum is void.The critics claim that the concept of omnipotence is being questioned, like the squared triangle. We cannot use it to disprove/resolve the difficulty(paradox) by the assumption(cause) itself.The concept of Essential Omnipotence remains self-contradictory, just like a squared triangle.

Neither Averroes, Tempier, Burke or I spoke of a "squared triangle". A criticism should, ideally, be phrased using the same terms in which the original view was stated. If I am correctly parsing the sentence "It assumes the concept of omnipotence valid ...", then this paragraph is denying the validity of all proofs by contradiction. Euclid would not be pleased.

I have no problem with providing counterarguments to Averroes's little puzzle. That's what this article is here for, after all. Those counterarguments, however, should be renditions of the arguments which were, historically, presented to buttress the Church's position against such devilishly logical infidels. Cite a source? Quote a source?

Anville 11:58, 22 May 2005 (UTC)

Do you mean that every view here shoud be quoted? I doubt. Even so, it is just the view of someone and the view cannot be said as truth. Why can you said another view is false and remove them? If the argument of Essential Omnipontence, "The omnipotent being is essentially omnipotent, and therefore it is impossible for it to be non-omnipotent. ", this sentence make any induction meaningless. An analog, which is non-sense too, can be that " I am the most clever persion in the world, so no one can be clever than me. Any view that I am not the most clever must be made by someone which is more stupid than me. So I am still the most clever. "

For the sentence he asked whether God could create a triangle whose internal angles did not add up to 180 degrees., is it something like "squared trangle"? 61.10.7.173 12:30, 16 Jun 2005 (UTC)

I have to agree with Anville's removal of this section. Firstly, the grammatical structure of that text is horrendous&mdash;a transistion word should not be used to begin a paragraph. "Cannot have no weakness" is a double negative. I would fix the article myself, but have really no clue what it is trying to say.


 * To say "cannot have no weakness" is terrible grammar, but I think that they are trying to say that it "cannot be without weakness", or something along those lines. --Kirk Surber 15:36, 11 January 2006 (UTC)


 * "Do you mean that every view here shoud be quoted? I doubt. Even so, it is just the view of someone and the view cannot be said as truth. Why can you said another view is false and remove them?" (61.10.7.173 12:30, 16 Jun 2005 (UTC))

Er. . . yes, every view should be sourced from other material. According to No original research: "In fact, all articles on Wikipedia should be based on information collected from primary and secondary sources. This is called source-based research, and it is fundamental to writing an encyclopedia." No one is saying the view is false, just that it lacks the proper sources to be included in the article, Wikipedia is not the place to espouse one's own philosophical postulates. If the same counter-argument can be included along with some sources, then that would be great. Also, please sign your posts. Ben Babcock 13:04, 21 Jun 2005 (UTC)


 * A "squared triangle" might be one of two things:
 * A triangle somehow constructed with four equal sides, or
 * A square constructed with the same area as a given triangle.
 * The first possibility is meaningless, by definition. An omnipotent being would have to pretty damn omnipotent to make one of these, i.e., strong enough to survive a logical contradiction.  The article already discusses this.  The second possibility is a bit stranger, grammatically, but it seems a valid way to use the words, by analogy with "squaring the circle".  One "squares" a circle by constructing a square with the same area as the circle given (&pi;r2).  Since &pi; is a transcendental number, this cannot be done in a finite number of compass-and-straightedge manipulations&mdash;that is, it is impossible within the realm of classical Euclidean tools.  (It is possible with higher-order mathematics, involving curves like the quadratrix, but it takes an infinite number of steps to construct such curves.  See Petr Beckmann's History of Pi.)  One statement of the omnipotence paradox might be the following:
 * If God restricts Himself to using only compass and straightedge, in the manner of Euclid, can He square a circle in a finite number of steps?
 * This is an interesting re-statement, I think, but it is not what the paragraph in question seems to discuss.
 * I find it hard to believe that no one in the last several centuries has tried to resolve or dismiss Averroes's paradox using traditional Christian thinking. Surely all those bishops and clerics would have taken a few days off debating how many angels could dance on a pinhead to set down their thoughts.  Such a rebuttal, translated from Latin, would fit nicely into this article.
 * Anville 01:25, 22 Jun 2005 (UTC)

Pop culture and humorous responses section
I've tried to cleanup this section as it was the most unprofessional part of the article. I gave it a slightly stronger lead and then organised the references into a list. Then I removed some of the information because it was extremely informal (used the first person) and did not seem to be in the right place. Lastly, I am not sure if the point about quantum superposition belongs there, since the title is "pop-culture and humorous" responses, not just "responses."


 * Humorous to a physicist or a student of physics, no doubt. Doesn't all humor depend upon the audience? 18.53.6.239 21:39, 11 July 2005 (UTC)

P.S. I think the article is almost ready to move to the closed issues part of the taskforce. We can still work on it but I think the major cleanup issues have been dealt with, as long as the dispute over the "Another block of removed text" is resolved. Ben Babcock 01:00, 24 Jun 2005 (UTC)

Distinction of GOD and Omnipotence Being
In Christianity, GOD is an omnipotence. However, in other religions, their gods are not omnipotent. In this sense, GOD and Omnipotence Being are not intercheagable. The topic is talking about the Omnipotence paradox. If we use the word GOD here, it will fall into the debate about religions.--61.10.7.2 17:53, 14 May 2005 (UTC)

Suggest removal of "neutrality disputed" banner
I am of the opinion that the "Neutrality is disputed" banner on this article should be removed now, as I can't find anything that could be construed as a particular POV in terms of the content of the article. If no one raises any objections, I shall remove the banner. --NicholasTurnbull 3 July 2005 01:51 (UTC), Cleanup Taskforce

Simple solution.
An omnipotent being can control everything, being "all-powerful", correct? So why is the flow of logic outside of his/her/it's sphere of control? An omnipotent being lift the unliftable rock simply because it can alter the flow of logic to make it liftable and unliftable at the same time. There.
 * Well if God lifts the "unliftable rock", no matter what logic you apply, than its not an "unliftable rock" anymore, isn't it? There is no such thing as a liftable "unliftable rock". Its a question of definition.
 * What is "no such thing"? In your logic, "liftable" and "unliftable" is mutually exclusive.  Using a logic which allow these two properties coexist would be okay then.Billyswong 07:33, 9 January 2006 (UTC)


 * Also, if he lifts the "unliftable rock", it would prove that he is NOT almighty, because he cannot create a rock, that he can't lift. As you have proven yourself.

God is not the author of absurdity.


 * While reading the article I realizied some things and though "Hey, let's put this into a talk page...". Then I found many similar things already mentioned... So I just decided to put it anywhere... I'll add another formulation or interpetation (if you wish) of Descartes view:


 * Human languge is relative to, well, human perceptions and observed laws of nature. Assuming that omnipotent being can improve itself or change the laws of nature (well, is it omnipotent or what?) at a point in time then whatever is "true" at one moment does no longer need to hold for long. In the "stone" example, the omnipotent being can truly create it can not lift at the moment (for example). They it can change the laws of nature as necessary or even redefine humans and their language to make it possible to "lift" the stone. Of course, this has some flaws by itself, such as:


 * it deals with imprecise wording of the paradox statement. We can add specifics such as "never", for example. That too, however, can be changed if omnipotent being can change time. We can say that it cannot lift the stone but it can lower the earth away from it which gives the same effect. Another example is can at any instant create as stone that noone can lift and that does not make me incapable at all. Want an example? Here it is - stone. It is a stone - I'm thinking of it. Now go lift it. Stupid example, I know, but omnipotent being would be much better equipped than I am :).


 * it assumed that omnipotent being can at least temporarily be not omnipotent.


 * it avoids the crux of the paradox


 * It is arguable, however, that omnipotent being is infinitely smarter and more capable than us. Therefore, regardless of how much effort we put into defining conditions one can always find a way out. Example: take a helicopter 2000 years into the past. Get surrounded by locals who will not let you escape in any direction... other than "up".


 * What would be interesting to, well, just interesting, is whether one omnipotent being can create a challenge it (or another omnipotent being) cannot solve. However, answering that one brings us nowhere. Because of vague human definition of omnipotent we would not be able to relate any answers to omnipotent abilities.


 * Finally, one YES/NO question fot you: "Is your answer to this question "NO"?


 * Have phun, --Aleksandar Šušnjar 17:23, 19 January 2006 (UTC)

Points raised on peer review
For quick reference, the following is a list of points raised on this article's peer review. The next time I have to procrastinate on something important, I'll try knocking them down, unless someone beats me to it.


 * Expand lead by at least one more paragraph.
 * Use the semantics and logical positivism we have as "see also" items, and elaborate upon modern approaches to the problem, e.g., Wittgenstein.
 * I have added some Wittgenstein (and also Ethan Allen), but whether I did the Tractatus justice I can't really say. Anville 16:38, 14 November 2005 (UTC)


 * The quantum-mechanical "joke response" is confusingly written. Fix it up.
 * The picture of Averroes needs source information.
 * It originally came from http://www.ibn-rushd.org/English/BiographicalInfoIbnRushd.htm, and was used as "public domain" on the French Wikipedia. The original picture is a detail from a fourteenth-century Florentine painting; I have found a color version and put the source info in its description page.  Anville 09:57, 14 November 2005 (UTC)

More will follow if other people post to peer review. Anville 09:21, 14 November 2005 (UTC)

Final Answer
Can God create a stone so heavy that He cannot lift it? This question is asking if God has the power to make Himself powerless. The answer is no. God's inability to be powerless is precisely what makes Him All-Powerful; lacking weakness is not a weakness. Lacking powerlessness means "having all power".


 * Can an omnipotent being create a stone too heavy to lift? The answer is yes.  An omnipotent being can only logically exist in the absence of anything else, since the moment any one alternative is chosen over others, all alternative not chosen can no longer be chosen.  In other words, an omnipotent being can make the choice to create a stone too heavy to lift, and will then no longer be omnipotent.  Taken further, an omnipotent being can create the universe as we know it at the expense of it's own omnipotence!  "Atheism The Case Against God" by George H. Smith (ISBN 0840211155 and ISBN 087975124X) provides the argument that an omnipotent being cannot exist in a rational world, creation dilemma covered somewhat by Alston in response to Hartshorne, Mr. Bene 18:30, 6 December 2005 (UTC)

Tomorrow's Featured Article discussion
Wikipedia talk:Tomorrow's featured article/Omnipotence paradox discussion

Whoa. Kudos to Brian0918 for suggesting it in the first place, and showing just how touchy an issue philosophy can be! Anville 18:43, 10 December 2005 (UTC)

Need for references
This article leaves me gasping for references to the discussions in Averroes and Aquinas, and the other unnamed 'medieval philosophers' referred to. I can try and find the relevant Aquinas passages myself as I know ST is on the web - but doesn't anyone have more primary sources?Bengalski 19:53, 11 December 2005 (UTC)


 * I believe Augustine addresses something very much like this question in The City of God, and decides that God cannot do anything to reduce his own power because it would be logically incosistent - something like the Aquinas position mentioned in the article. A quick search: Book 5, chapter 10  - scroll down to chapter 10.  See also  for some leads.  --Reuben 05:06, 19 December 2005 (UTC)

God/omnipotent being
The article says "Could an omnipotent being create a rock so heavy that even that being could not lift it?" The only way I've ever heard that used is "Could God creat a rock so heavy the even He could not lift it?" Can I change the quote? The current version seems awkward and unnecessarily PC.--Kuciwalker 18:04, 2 January 2006 (UTC)


 * Well, there are many kinds and varieties of gods worshipped throughout the world, and not all of them are believed to be omnipotent. The paradox wouldn't apply to a non-omnipotent deity.  For instance, in Norse, Greek, and Hindu mythology, gods struggle with each other, each meeting success at times and failure at other times.  For wikipedia to use the term "god", singular, in this article would very clearly be granting special consideration to the Judeo-Christian-Islamic deity.  -Kasreyn 00:29, 9 January 2006 (UTC)


 * God with a capital G is usually used to refer to the Judeo-Christian or Muslim deity, or occasionally a deity in another religion like Buddhism that (as far as I understand) occupies a similar place. Particularly in English it usually refers to the Judeo-Christian deity, with the Muslim one referred to as Allah.  I don't see anything particularly POV about including the most common version of a quote rather than a more awkward but PC version, especially when it claims to be the classic example.--Kuciwalker 05:37, 10 January 2006 (UTC)