The Big Rock Paradox: Stephen Hawking's Thought-Experiment

[Karl G.]

I was first introduced to this thought-experiment upon reading Stephen Hawking's A Brief History of Time . Suppose an omnipotent being exists. If it does, it would be able to do anything (by definition!). Therefore, it would be able to produce a rock it couldn't lift. Therefore, it wouldn't be able to do anything it wants, therefore it wouldn't be omnipotent. What do you think?
Please nothe that I have phrased this thread to avoid it being locked. Please keep that in mind if you comment.

 

[JoeDawg]

I was first introduced to this thought-experiment upon reading Stephen Hawking's A Brief History of Time . Suppose an omnipotent being exists. If it does, it would be able to do anything (by definition!). Therefore, it would be able to produce a rock it couldn't lift. Therefore, it wouldn't be able to do anything it wants, therefore it wouldn't be omnipotent. What do you think?
Please nothe that I have phrased this thread to avoid it being locked. Please keep that in mind if you comment.

An all powerful being, would be capable of making itself as 'physically strong', at any given moment, as it wanted to. So it makes itself physically capable of lifting a certain amount. Then it makes a rock that weighs more. Now it can't lift it. Then it decides it really wants to, so it makes itself physically stronger. Voila.

 

[Karl G.]

Hmmm... your argument is invalid due to the definition of omnipotence. An omnipotent being can't make itself stronger to lift a rock ... its omnipotence already ensures it can do that.

 

[Ivan Seeking]

I prefer the other version of this question: Could God make a salsa so hot that he can't eat it?

 

[JoeDawg]

Hmmm... your argument is invalid due to the definition of omnipotence. An omnipotent being can't make itself stronger to lift a rock ... its omnipotence already ensures it can do that.

It ensures that it 'can', not that it 'must' in any particular instance.

 

[DaveC426913]

To me, this has little to do with a thought-experiment and much more to do with the semantics of "omnipotent".

i.e. so there's a word in the English language wherein you can form sentences that are seemingly paradoxical. So what?

 

[Karl G.]

To me, this has little to do with a thought-experiment and much more to do with the semantics of "omnipotent".

i.e. so there's a word in the English language wherein you can form sentences that are seemingly paradoxical. So what?

The fact that 'omnipotent' is paradoxical means it can't exist.

 

[Karl G.]

It ensures that it 'can', not that it 'must' in any particular instance.

But since it CAN'T, it isn't omnipotent.

 

[JoeDawg]

But since it CAN'T, it isn't omnipotent.

It can when it wants to. And yes, its a word game.

But just because our understanding of something seems paradoxical, doesn't mean that something doesn't exist.

 

[DaveC426913]

Alternately:

It can when it wants to. And yes, its a word game.

But just because our understanding of something seems paradoxical, doesn't mean that something does exist.

 

[JoeDawg]

Alternately:

All hail the Big Rock.

 

[confinement]

The fact that 'omnipotent' is paradoxical means it can't exist.

Liars are paradoxical, as I am sure you know, but they do exist.

 

[JoeDawg]

Liars are paradoxical, as I am sure you know, but they do exist.

Maybe its Schroedinger's rock.

 

[Karl G.]

Liars are paradoxical, as I am sure you know, but they do exist.

Liars aren't paradoxical. People who admit that they are liars are paradoxical.

 

[TVP45]

Suppose a right-wing radio commentator were to say, "I always tell the truth." That's not paradoxical; it's merely that we ordinary mortals are incapable of understanding the meanings of superior beings. So might it be with gods.

 

[jambaugh]

This is actually a form of Russell's paradox. (Define the set of all sets which do not contain themselves as elements and ask if that set contains itself.) You can form this when you allow both open ended definitions and circular or self reference.

This is the problem with open ended definitions e.g. omnipotence. To solve this one you just have to acknowledge that "a rock that God couldn't lift" is an ill defined concept as given any rock that could exist this God could both create and lift a larger one. Omnipotence only covers the ability to effect well defined states of reality.

 

[alxm]

It's called the http://en.wikipedia.org/wiki/Omnipotence_paradox" .

As far as Christianity is concerned, a fairly authoritative answer was given by http://www.ccel.org/ccel/aquinas/summa.FP_Q25_A3.html" in Summa Theologica's first book.

Not really an interesting question IMHO.

 

[DaveC426913]

This is actually a form of Russell's paradox. (Define the set of all sets which do not contain themselves as elements and ask if that set contains itself.)

Which is actually a subset of http://xkcd.com/468/" .

 

[confinement]

Liars aren't paradoxical. People who admit that they are liars are paradoxical.

Omnipotent beings are then not impossible in general, only those omnipotent beings that make rocks so heavy that they cannot lift them are paradoxical. In other words, any liar and any omnipotent being has the potential to be paradoxical.

 

[Helios]

What if the god moved the universe so the rock will have, in effect, been moved?

 

[Jacob Perry]

Actually if omnipotence means to be able to do anything, that means an omnipotent being could be something and not be something at the same exact time. It could do everything it couldn't do and it could be paradoxical and perfectly fit within human logic and reason. It could have no beginning and no end while having both and could and couldn't be grasped. So really, this 'paradox' proves the oneness of everything and nothing.

 

[TheStatutoryApe]

Doesn't the question rather unnecessarily anthropomorphize the omnipotent being? It seems rather pointless. Compared to a guppy I'm a rather powerful being though it may wonder what is so special about a being unable to breathe water.

 

[Count Iblis]

Suppose I have a computer powerful enough to simulate a planet like the Earth complete with people living on it down the the molecular scale. Then, I could play God in that world by modifying the simulation. I put on my virtual reality helmet, and the simulation simulates me (God) in that world.

Then, since I'm not bound by any laws of physics that operate in the virtual world, I cannot make a rock that I can't lift. But it could be that there are some actions that would cause the computer to crash when performed by me.

 

[humanino]

Doesn't the question rather unnecessarily anthropomorphize the omnipotent being? It seems rather pointless. Compared to a guppy I'm a rather powerful being though it may wonder what is so special about a being unable to breathe water.

Thank you for this comment. These is another aspect that I especially dislike in this paradox. It is restricted to an omnipotent being undergoing time (creating an object and then facing a paradox). Now consider a Leibnizian conception of omnipotent being, say for definiteness "a theory of everything" (I'm simplifying of course, but hopefully not oversimplifying). Then I hope you can see how such a conception does not undergo time. I am not defending any conception over another, neither do I think that would be interesting, I am merely trying to point out a specific example, which I think respects the general criterion provided by

Omnipotence only covers the ability to effect well defined states of reality.

By the way,

Which is actually a subset of http://xkcd.com/468/" .

was quite funny :

 

[Russell Berty]

Let Z be an omnipotent being.

Z has a rock fetish. Z thought about the large rock idea. (We are not certain if it ever happened.) Z then decided to make a rock, to be called "little mu", that was so incredibly difficult to detect that even the all-powerful Z could not detect it. Can Z ever be sure that little mu has been created?

Some people in this discussion have come close to my stance on these "paradoxes". We are arguing using our human logic. But, how can we be sure that such logic applies to the realities and lives of the all-powerful, all-knowing? What we see as a paradox might not be in some ultra-nonhuman-impossible for us to follow-hyperlogic.

Here is another lil' diddy ---
Anyone who has seen the Incompleteness Theorem may have run across this "paradox": Can Z know all the true statements of Number Theory? (If Number Theory is consistent then there is a contradiction for Z would be a truth predicate.)

My response is this... Yes because Number Theory is inconsistent, so every statement is provably true (and at the same time false.) But Z does not want us to be afraid, and if 1+1=2 leads to a contradiction we would be. So, Z makes sure that any inconsistency is out of reach. Whenever we get close to a proof of a contradiction, Z simply redoes the (faulty) Model of Number Theory so that the contradiction is further away.

 

[Hurkyl]

Here is another lil' diddy ---
Anyone who has seen the Incompleteness Theorem may have run across this "paradox": Can Z know all the true statements of Number Theory? (If Number Theory is consistent then there is a contradiction for Z would be a truth predicate.)

Gödel's incompleteness theorem doesn't say that there are no complete sets of axioms for number theory -- it merely says that such things cannot be recursively enumerable. Your "truth predicate" cannot be computed via Turing machine, and therefore there is no contradiction.

It's an easy exercise to use the axiom of choice to prove that there exist a complete sets of axioms for number theory, one doesn't need to invoke any hypothetical omnipotent/omniescient beings at all.

 

[Dadface]

Let Z be an omnipotent being.


Some people in this discussion have come close to my stance on these "paradoxes". We are arguing using our human logic. But, how can we be sure that such logic applies to the realities and lives of the all-powerful, all-knowing? What we see as a paradox might not be in some ultra-nonhuman-impossible for us to follow-hyperlogic.

.

Agreed.An omnipotent being does not have to conform to our logic and understanding.It is the definition of the word itself that raises the apparent paradox.

 

[Russell Berty]

Gödel's incompleteness theorem doesn't say that there are no complete sets of axioms for number theory -- it merely says that such things cannot be recursively enumerable. Your "truth predicate" cannot be computed via Turing machine, and therefore there is no contradiction.

It's an easy exercise to use the axiom of choice to prove that there exist a complete sets of axioms for number theory, one doesn't need to invoke any hypothetical omnipotent/omniescient beings at all.

I agree. Perhaps I was a bit sparse on my description. The real "paradox" comes in when we ask "Can Z construct a formula in arithmetic that is a truth predicate?" For, surely, Z can know all true statements, and being all-powerful, Z can make arithmetic statements that say define whatever subsets of N Z desires.

 

[Moridin]

Yes, the concept of omnipotence as defined in the opening post leads to absurd contradictions, and therefore, cannot stand.


Russell Berty,

Some people in this discussion have come close to my stance on these "paradoxes". We are arguing using our human logic. But, how can we be sure that such logic applies to the realities and lives of the all-powerful, all-knowing? What we see as a paradox might not be in some ultra-nonhuman-impossible for us to follow-hyperlogic.

There is no "human" logic. There is only logic. Horses do not have any different, equally valid, method of coherent argumentation. To say that an entity is "above" logic makes the argument fall apart at once -- if it is above logic, then it can change logic arbitrarily and make it invalid.

 

[DaveC426913]

There is no "human" logic. There is only logic. Horses do not have any different, equally valid, method of coherent argumentation. To say that an entity is "above" logic makes the argument fall apart at once -- if it is above logic, then it can change logic arbitrarily and make it invalid.

Yeah, I think his "human logic" versus "hyperlogic" is really better defined as "human-conceivable premises" versus "omniscient-cognizant premises".

If we humans had access to the knowledge (premises) of the omniscient-dude, our logic would more closely fall in line. But our premises are flawed.

 

[Hurkyl]

My response is this... Yes because Number Theory is inconsistent, so every statement is provably true (and at the same time false.) But Z does not want us to be afraid, and if 1+1=2 leads to a contradiction we would be. So, Z makes sure that any inconsistency is out of reach. Whenever we get close to a proof of a contradiction, Z simply redoes the (faulty) Model of Number Theory so that the contradiction is further away.

Incidentally, it strikes me that what you are describing sounds very much like the things you can do with plain, ordinary "human logic".

 

[Russell Berty]

Incidentally, it strikes me that what you are describing sounds very much like the things you can do with plain, ordinary "human logic".

Humans have at times had to rethink their definitions when contradictions arose. But, what we can not do is restructure the actual truths or laws of reality (if there are any.) We assume that a structure we call Number Theory exists (the one that would satisfy 2nd order arithmetic) but we cannot prove it exists. It is a supposed structure of reality that we try to analyze using our "human logic". What I was trying to say is that Z can do what we cannot do. That is, Z can restructure this innate property of reality called Number Theory so that we will not run into a contradiction in are pursuits.

 

[Focus]

Humans have at times had to rethink their definitions when contradictions arose. But, what we can not do is restructure the actual truths or laws of reality (if there are any.) We assume that a structure we call Number Theory exists (the one that would satisfy 2nd order arithmetic) but we cannot prove it exists...

We cannot prove that anything exists other than yourself, what is your point?

There are no laws of reality. There is no way that we can claim 100% that reality follows X or Y. The whole of science is built on the assumption of history repeating it self.

Some people in this discussion have come close to my stance on these "paradoxes". We are arguing using our human logic. But, how can we be sure that such logic applies to the realities and lives of the all-powerful, all-knowing? What we see as a paradox might not be in some ultra-nonhuman-impossible for us to follow-hyperlogic.

This is pretty weak claim. You can argue this way with everything. Do you claim that laws of nature do not apply to a being (or maybe more)? If your answer was yes, then you need to prove that God exists. Otherwise I can make the same statement you made to claim that trees are both trees and not trees (they have tree logic).

 

[Russell Berty]

I am not sure what you are getting at in your reply.

You can prove that you exist? Then you are more clever than I, for I cannot prove that I exist.

There are no laws of reality? You can prove this?

For me, I assume that:
1) I exist.
2) Reality exists and has order; it is predictable. i.e. there are laws.

From these assumptions I deduce my theories about reality.

As far as whether or not gods exist, I cannot say. What I am trying to say is that my arguments (or human arguments) are not valid in the realm of the "all-powerful" beings (if there are any.) To argue for or against the existence of such beings is futile. For example, if the all powerful Z decides to make modus ponens invalid then where does that leave us?

 

[JoeDawg]

You can prove that you exist? Then you are more clever than I, for I cannot prove that I exist.

Don't worry, Descartes, a very clever man, already did that: I think therefore I am.