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From Wikipedia:

The omnipotence paradox is a family of semantic paradoxes that explores what is meant by 'omnipotence'. If an omnipotent being is able to perform any action, then it should be able to create a task that it is unable to perform. Hence, this being cannot perform all actions (i.e. it is not omnipotent), a logical contradiction.

The paradox of the stone:

Could an omnipotent being create a stone so heavy that even he could not lift it?

I posit that:

"Creating a boulder that one can't lift" isn't a logically inconsistent demand. Humans do it all the time (make stuff that they cannot lift). This argument actually shows how omnipotence is logically inconsistent.

I've used it in many forums but the general counter-arguments I get claim that this is not a logically consistent argument. The most clearly worded counter-argument I got is as follows:

If God is omnipotent, then there is no boulder that cannot be lifted by him. If God is omnipotent, he can create anything. You're not disproving omnipotence, you're disproving the possibility of such a boulder existing. Something which can both exist, and therefore be lifted by God by definition, and its un-liftability by God are in direct conflict with each other.

Many even say that, the general definition of Omnipotence is wrong (saying that God can only do things that are logically possible) and later go on to claim that the existence of such a boulder isn't possible since an object not lift-able by God can't exist. I was never convinced by these arguments.

I've asked similar questions in other forums where people explained to me that there can't exist both an unstoppable force and an immovable object in the same Universe which I understood. But nobody explained why creating/building stuff that aren't lift-able is not logically possible. Humans and some animals do it all the time. We build stuff that we alone can't lift like furniture, houses, cars etc.

Creating/Building something that one can't lift alone isn't logically impossible. It becomes logically impossible only when considering God, doesn't it? Is my reasoning correct or am I missing out something?

What is the conclusion one should draw from this argument - Omnipotence can't exist OR an Immovable object can't exit? If its the latter, what are some sound arguments for it?

TL;DR

What is logically incoherent about God creating an object that he can't lift/move?

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    Err.. can you edit this down to just your question about philosophy that we can answer. I'm having a little trouble deciphering what that is. Best I can guess "What's logically incoherent about God creating an object he can't move?" – virmaior May 22 '16 at 7:34
  • @virmaior Yes, That's it. I'll add a TL;DR – UrsinusTheStrong May 22 '16 at 7:40
  • @virmaior Am I not making sense here? I just wanted to give a background and have a detailed response in return. – UrsinusTheStrong May 22 '16 at 7:42
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    We (our mind) are able to "create" many concepts, like those of unicorns, round squares and omnipotent beings. The fact that we may "imagine" them does not implies that they must be instantiated, i.e. that there exists some objects having the properties inherent to the corresponding concept. – Mauro ALLEGRANZA May 22 '16 at 7:56
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    If the concept of "omnipotent being" produce a contradiction, then there is no "object" instantiating it. – Mauro ALLEGRANZA May 22 '16 at 8:15
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I guess I'd answer the question in two parts.

The first issue is to parse out what is meant by "an object Q cannot move."

Here, you give the helpful example of whether we humans (or we bears?) can create objects that we ourselves cannot move. The answer to this is obviously yes. But this merely means the object is relatively immovable.

When referring to an object that God cannot move, this is synonymous with an object that nothing can move. In other words, it's something absolutely immovable. This seems to be a substantially different sort of thing and not something attested to merely by the fact that we can create relatively immovable objects (where their immovability is relative to us).

Second, with this distinction in hand, we can look at the claim more directly as you word it:

Can God create an immovable object God cannot move?

As you note this is a question about the nature of omnipotence. Moreover, the framing of the question has us looking at the Abrahamic monotheisms -- particularly Christianity and Islam. In both of these religions, this was dealt with philosophically in the Medieval period (inter alia).

I think there's three basic positions that were taken (I'm not an expert on medieval philosophy):

  1. The notion of an absolutely immovable physical object is logically incoherent. Here, the argument would be that to be a physical object is to be the sort of thing subject to physical forces and that being so would mean there's some amount of mass or hardness or other feature that the object has. By definition, anything that could exceed that could move or alter the object. Ergo, the concept of an object that is unliftable would be self-contradictory (See SEP "Omnipotence") (This seems to be the view of Thomas Aquinas).
  2. That any limitation on God is a form of self-restraint rather than fundamental limitation. In other words, God can create an object God says God cannot move, and God won't move it -- but not because it is immovable per se but instead immovable per volens. (People that take this view and think there's a God would be committed to a form of voluntarism).
  3. That God can impose self limitations that stand permanently. In other words, God can make a rock God cannot lift. Again, the origin wouldn't be that the rock has infinite mass but that God can manufacture the rock and bind a condition on God's own self to not be able to pick up the rock.

My memory of it's all a little hazy, but you could read hundreds of pages on this in the late medieval philosophy literature in both the Christian and Islamic parts.

Obviously, outside of these options, you can say the incoherence is in the concept of God.

But I take the hinge that makes the unliftable rock incoherent vis-a-vis God to be the account I mention in 1 -- that also appears in the SEP article on omnipotence.

  • That 3rd position doesn't seem to go anywhere - wouldn't an omnipotent being be able to change their mind (religious stances aside), or break any sort of limitation (even self-imposed) due to the omni property? i.e. it's only shifting from unable to lift a rock to unable to remove a restriction - but both the rock and the restriction were created by an omni being, and by the definition of omni would also be able to then move/break those. – user2813274 May 22 '16 at 12:00
  • The third position does in fact exist in the medieval literature from what I can remember. It's also an important thought in "kenotic theology." After a sort, it creates problems such as the one you mention, but it also removes problems in the domain of moral metaphysics in that it makes morality real but created (whereas the pure voluntarist has to explain how God can change and say murder is cool tomorrow when it isn't today). – virmaior May 22 '16 at 12:19
  • The key is that it is self-limitation from a being that is resolute in will (even if able to change their mind). This seems less improbable if the being is taken to be both omnipotent and omniscient -- such that they could fully grasp what it would be to bind themselves to a position. – virmaior May 22 '16 at 12:20
  • The second/third idea is philosophically elaborated in the tradition of the Lurianic Kabbalah and called tzimtzum. This is Judaic philosophy and has strongly influenced e.g. Moses Mendelssohn. – Philip Klöcking May 23 '17 at 16:46
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I wrote a little something about this exact issue, over ten years ago. Here it is in full. If it's a little over the top, apologies— I was much younger and sillier then. Or maybe I'm sillier now. Pfah.


The Burrito Challenge

The hallmark of philosophical acuity is the ability to explain in rich detail and flawless clarity humanity's most commonly made logical errors. It requires philosophical genius to make these errors obvious to the lowest common denominator in any society. Thankfully, genius does not need to be housed within one individual, but can often result from the collective and faithful efforts of many individuals, accrued over centuries of recorded thought. However, many errors, once made obvious, are often easily passed over among later generations of thinkers, and are thus left without a decent explanation that may be vital to the philosophically apathetic.

One such easily ignored error of reasoning comes up easily among theological speculation, expressed always with some variant of the cliché question: "Can God make a burrito so hot, that He Himself cannot eat it?" (I much prefer this version to the agonizingly mindless one involving God lifting rocks; credit goes to Homer Simpson for posing it). Any student of first-order logic should be capable of answering the "Burrito Challenge", but too often the subtlety of the answer and its sweeping implications are beyond a student's explanatory power and beneath the dignity of a real scholar.

By the grace of God, burritos and all, I am neither of these. My goal is not only to fully explain the answer to the Burrito Challenge, but to make it possible for you, the reader, to do so as well. In actuality, that is a lie; my true goal is to further reduce, by every possible degree, the great cranial silences that afflict most representatives of humanity. Hopefully you, dear reader, will join me in this effort, and when confronted by this or similar challenges, you will dutifully roll your eyes and proceed to once again explain what should be collectively obvious: the answer is No.

Here's why.

1. Load The Question

First take note of the question itself; most people pose it in one of three general flavors. Because of the challenge's stock-in-trade use as a riddle designed to trip up the thoughtlessly faithful, it's most common appearance is as a weapon that neither party truly wishes answered. People otherwise reasonable in other discussions tend to throw out this challenge as an all-purpose 'get out of jail free' card when solicitors of faith come knocking on the door. The unfortunate fact is that most of the people posing the question rarely know the answer themselves, relying instead on the solicitor's own deficit of logic. In turn, these same solicitors who come to ignore the question by tacitly repeating that God can do anything, only reveal to their would-be converts the utter thoughtlessness of their own faith.

On the other hand, years of this kind of willful ignorance to the Burrito Challenge lead both the honestly religious and genuinely curious to pose the question in good faith to their teachers, parents, or peers, most of whom have no better explanation than that the challenge itself is simply wrong. Although this is true, once again the subtlety of the proper answer is lost, allowing the cycle to continue unabated. Normally I wouldn't consider this to be much of a problem, but I've come to believe that by letting such an obvious point of reason slide, we stunt the growth of human progress. There is simply no excuse for allowing this kind of easily-avoided stupidity to perpetuate itself.

2. Tacit Agreements (The Short Answer)

The Burrito Challenge includes in itself an implicit assumption: that the 'God' which it specifies is omnipotent, or simply all-powerful. The challenge rather loses its punch if this assumption is left out. Thus, anyone in their right mind will agree that we can rewrite the challenge to read: "Can He-who-can-do-anything (God) make a burrito so hot, that He Himself cannot eat it?" Even those without a degree in logic or philosophy should already begin to see that, phrased this way, though obviously identical to the original question, the challenge is a wee bit more specious.

That done, the harder part follows. We must ignore the first part of the question, in order to clearly rewrite its end in the same manner. It seems uneccessary, but often people are still hung up on the thought that God can do or make anything, which clouds reasoning through the second half. Instead, simply ask, "is there a burrito so hot that God cannot eat it?" Do not play the game of trying to answer this, because all it really asks is, "is there something that God cannot do?" We can rewrite this again, as we did the first half, replacing 'God' with 'He-who-can-do-anything'. What it becomes is: "is there something that He-who-can-do-anything cannot do?"

Strangely enough, there is a clear answer to this reformed question; something that an all-powerful being cannot do is, clearly, something that cannot be done. In the end, this is what a burrito-so-hot-that-God-Himself-cannot-eat-it is; something that cannot be done. It follows that what the Burrito Challenge is really asking is this: "Can He, who can do anything, do that which cannot be done?"

The answer, obviously, is "No".

3. Categorically Wrong (The Long Answer)

Don't be fooled into thinking that this is the end of the story. Those of you reading this, who think that this explanation serves to better support the Burrito Challenge as a valid weapon against avid monotheists have, once again, missed the subtlety in the argument. Feel free to blame me if you have, but let me be clear. The fault expressed in the Burrito Challenge has nothing to do with any imaginable limitations on divine power, but instead picks out a problem of vagueness in human language. Just because our language allows us to put together these words, which in turn refer to more complicated ideas, we will always have the ability to assign incompatible ideas together in grammatically correct statements.

Years ago a former teacher summed up this kind of fault in a simple, beautifully useless question: "why is a duck?"

The answer is, of course, that there is no answer; the question itself was simply formed wrong, a practice that first-year philosophy students learn to call 'categorical mistakes'. The Burrito Challenge is simply one of many examples of these, but like other questions that fall under this label, the flaw isn't readily apparent until the logical reasoning is followed up on. Thus a more religiously-minded thinker might like to point out that the true answer to the Burrito Challenge is: "No, God cannot make a burrito that hot.. but that's your problem, not His".

Once the two parties have managed to clear this little matter up, they can finally move on to far more interesting theological questions, like why bad things happen to good people, or why Christians, Jews, and Muslims all say they worship the same deity but still think everyone else is a heretic.

Now go convert some infidels!

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    Haha.. The problem is that many people who assert belief in some kind of omnipotent God will say that their God can even do logically inconsistent things, and when challenged on that will say that you cannot understand God, and then refuse to listen to any response. – user21820 May 22 '16 at 13:58
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    If they believe God is illogical (that is, if 'omnipotence' includes the ability for self-contradiction), then there's no use to using logic or argument in the first place, is there? – Ryder May 22 '16 at 14:11
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    Right. Attempting to use logical reasoning with them is futile, sadly. What I don't understand is how they can convince themselves to adopt their stance, because if contradictions can actually occur in our world then there is absolutely no basis for any order whatsoever. – user21820 May 22 '16 at 14:16
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    Who needs logic when you have faith? – Ryder May 22 '16 at 14:41
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    Yes that's what the argument always boils down to, but yet they use logic like picking cherries, because they 'need' logic to 'explain' why we must do/believe XXX according to their beliefs. For example, "Jesus must die for our sins. Why? Because ..." If it was purely based on faith they ought to preach "Jesus died for our sins. Why? No reason! Just believe!". Not all christians reject logic, though, but few ever think through carefully enough about the various concepts like omnipotence and omniscience. – user21820 May 22 '16 at 14:52
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Let me refer you to this post where I distinguish between a few possible definitions of omnipotence and omniscience, and which are self-contradictory and which are not. After you read that, let me address one of your (implicit) questions that hasn't been answered, namely whether or not the argument "If God is omnipotent, then there is no boulder that cannot be lifted by him." is valid. The answer is that it is valid but actually demolishes the validity of total omnipotence, as follows:

If there is no boulder that cannot be lifted by God, then God cannot create a boulder that cannot be lifted by himself, so God is not totally omnipotent.

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    @UrsinusTheStrong: You're welcome. As I hinted at in a comment to someone else, you need to be clear what you mean by a property being illogical. The property as a concept has no logical status. The concept exists. The claim that there exists an instance with that property, however, is a factual assertion that has a truth value. In this case, indeed the claim that there is a totally omnipotent entity is false, but the concept of omnipotence is still there, just like the concept of a flat Earth. The only reason I used "God" in my answer is because the theist assumes that God exists. – user21820 May 22 '16 at 17:00
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    @UrsinusTheStrong: In other words, when presenting a logical argument to a theist, we're free to use their assumptions to derive a contradiction, which then implies that at least one of their assumptions is false. In this case their assumption is that there is an entity that is totally omnipotent (that they call God). We're free to use their name for this entity to arrive at a contradiction. The only logical way out for them would be to change their definition of omnipotence if they still wish to claim there is an entity that has that property. – user21820 May 22 '16 at 17:07
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    @UrsinusTheStrong: Many people I've talked to take the illogical way out, which is to claim that God can do even contradictory things. In that case I give up. – user21820 May 22 '16 at 17:08
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    That actually becomes awkward in many cases. – UrsinusTheStrong May 22 '16 at 17:11
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    @UrsinusTheStrong: Yes, and that's despite the fact that they know that I'm not an atheist. They simply insist that (their) God is beyond all human logical reasoning. This actually sounds very reasonable to most people who are unfamiliar with logic. There are even verses in most religious texts to back this claim up, all of which say something like "God is beyond man's understanding.". Of course quoting from a text that hasn't been verified yet is begging the question, but many believers don't seem to notice... – user21820 May 22 '16 at 17:16
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I think that the main problem with this argument is that it is too vague and the words - 'can', mainly - are being employed too loosely. You're basically leaving the concept of omnipotence vague enough and then just finding contradictions of using 'can' too generously - that "God can then create a rock which he cannot lift" sentence looks to me like it is just another version of the liar paradox: it is roughly "(given that God can do anything, then) God can make it so that he cannot do everything".

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The question can be boiled down to:

Can an omnipotent god restrict his own omnipotence?

I would say, if he is truly omnipotent, then he certainly can do that. But of course if he ever actually did it, he'd cease to be omnipotent, and therefore it would be unwise for him to do it. And therefore if he's wise (another quality commonly attributed to god), he won't do it, not because he can't do it, but because he's wise enough not to do it.

Or specifically for the boulder:

Yes, an omnipotent god can create a boulder that he cannot lift. And yes, if he ever actually created that boulder, he'd no longer be omnipotent. But as long as, despite being able to create the boulder, he doesn't actually do so, he remains omnipotent.

  • Once we make an assertion that God is omni- this-or-that, it becomes unwise to make any further statements about God's wisdom, judgement, abilities etc. – christo183 Dec 21 '18 at 4:23
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We, as humans, cannot attribute such quality to God, because we cannot perceive or understand its entirety, integrity, wholeness. That would be equivalent for fools to define intelligence (yes, that happens on facebook, twitter, instantgram).

A lot of fools think of Kim Jong-un, Donald Trump or Hitler as intelligent persons. But such is a fallacious point of view, since they cannot perceive their own lack of knowledge and what is needed to grant such quality to those leaders.

In the same way, thinking of omnipotence is just a human-subjective conundrum, since we cannot know what omnipotence would mean. There could be literally infinite ways for us to be wrong. For example, perhaps the answer could exceed a "yes/no": in such case, a possible valid answer is this:

Q: Could an omnipotent being create a stone so heavy that even he could not lift it?

A: 1/sqrt(2)|yes>+1/sqrt(2)|no>

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