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Invisibleshroomydan
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Solution to the Paradox of the Stone
    #6704530 - 03/23/07 11:33 PM (14 years, 9 months ago)

Solution to the Paradox of the Stone
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Can God make a rock so Big he can't pick it up?

A friend confronted me with this dilemma a few weeks ago. In his opinion, the paradox of the stone constituted a logical proof against the existence of God.

If one understands omnipotence to entail being able to accomplish any and all tasks, then the dilemma generated by this question is in fact a proof against the existence of God. It is something akin the barber paradox:

In a certain village, there is a barber who shaves all and only those who do not shave themselves. The only way this could be true is if the barber both does and does not shave himself. Therefore, by reductio absurdum, there can be no such barber.

In order for God to maintain omnipotence as defined, he would have to be able to make the rock so big he could not pick it up, and at the same time be able to pick it up. This of course is a straight up contradiction. If for logical reasons one concludes a barber who shaves all and only those who do not shave themselves cannot exist, then she should likewise conclude the non-existence of a being capable of making and lifting an unliftable rock. So much the worse for God!

Or so much the worse for logic? Within a unified system of belief, a sentence is meaningful only as it relates to all the other sentences held true within the system. When indomitable evidence demands adjustments be made to sentences in a person’s web of belief, changes will be made in accordance with the maxim of minimum mutilation (Quine). If a person’s belief in an omnipotent God is more important to him than his attachment to logic, then he might assert that God exists and that God is omnipotent regardless of what logic has to say about the matter. If logic says that God does not exist, or that God cannot be omnipotent, then the logic must be wrong. If belief in an omnipotent God is central to one’s system of belief, and if conflict arises between this belief and another, then it is the other belief-not the belief in God-that must be reevaluated. Reduction to absurdity might triumph over the barber who shaves all and only those who do not shave themselves, but when it threatens the very foundation of a system of belief, reductio absurdum falters.

Denying the applicability of logic to things divine is a coping method employed by many theists, especially biblical literalist, when faced with evidence contrary to deeply held beliefs. Denying the universal validity of logic is one way to escape the God –rock dilemma, but those among us compelled to cling to both God and logic must find another way.

A brief history of modern mathematics provides a parallel of the theist’s escape from the paradox of the stone.

Around the beginning of the twentieth century, a mathematician and logician by the name of Gottlob Frege was working on a set-theory that he believed provided a solid theoretical foundation for mathematics. But to Frege's consternation, after he finished constructing the system his contemporary Bertrand Russell pointed out a foundation shattering paradox. A linchpin in Frege’s theory was the existence of a set that contains all and only those sets that are not members of themselves. When Russell pointed out that such a set, if it existed, would have to be both a member and not a member of itself, Frege is said to have exclaimed, “Arithmetic totters!”

The only way to save mathematics from Russell’s paradox was to restructure set theory around the paradox. In this process, “set” was redefined and the paradox was avoided. Set theory was saved from the oblivion of Russell’s paradox by a reformulation of its basic axioms, so it seems only natural that omnipotence might be saved from oblivion by reconsidering what it means to be omnipotent.

In order to salvage belief in an omnipotent God it is not necessary to renounce belief in logic. If omnipotence is defined as "being able to accomplish any and all tasks that do not entail un-accomplishable tasks" rather than "‘being able to accomplish any and all tasks", then the damage inflicted by the paradox of the stone is diminished to nil. In the same way set theory was saved by redefining ‘set’, omnipotence theory is saved by redefining ‘omnipotence’. The answer to the question can ‘God make a rock so big he can’t pick it up?’ is no, but vacuously so. The omnipotent being is not able to perform omnipotence defeating tasks, but this ‘lack of ability’ does nothing to diminish the perfection of God. No is the answer to similar questions like ‘Can God as an omnipotent and necessary being destroy himself?’ The answer to these kinds of questions is no, but the questions themselves are vacuous because the superlative attributes of God reside within a single being and are directed by a single will. To pit God’s omnipotence against God’s necessity, or to pit God’s omnipotence against God’s omnipotence, is to deny the unity of God’s will and purpose. The paradox of the stone, and the dilemma it generates, are the result of a naïve conception of omnipotence. When omnipotence is properly understood as the perfect actualization of a perfectly unified will, the question remains, but the paradox falls away. God cannot defeat his own omnipotence, because omnipotence is by nature non-self defeating.


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OfflineMuppet
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Re: Solution to the Paradox of the Stone [Re: shroomydan]
    #6704987 - 03/24/07 02:09 AM (14 years, 9 months ago)

I'm pretty positive my inferior intellect can not possibly begin to live up to the sort of 'standards' you've laid out for this thread already (simply in the vocabulay that you used, and the way you worded things alone...yet alone the ideas themselves behind all of this) ...BUT...I'm going to *attempt* to take a wing at it

it seems to me that there are a LOT of thing in this world that meary 'sound good in theory' but don't necessarily pan out in practice (e.g. they should follow certain 'rules' ..... yet, upon closer inspection, all sorts of little things pop-up that go against it) and I generally chalk this up to living in a world that is based on chaos

no matter how much structure we try to put on this place (and by 'we' I'm referring to the entire spectrum of entities here...physical and spiritual alike) there will ALWAYS be that infamous 2% that exists apparently solely to force us to have to constantly re-evaluate our beliefs

god can, in theory, be 'omnipotent' ..... but only up to a certain extent (like you said)

...only...

it is not so much because 'we' have the wrong ideas of what exactly 'omnipotent' means...but rather - we live in a world where nothing has a strictly enforced 'According to Hoyal' definition (or, at least, from my point of view anyway)





'omnipotent' still means omnipotent
it just can't be 'omnipotent' 100% of the time
(if that makes any sense)


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OfflineMuppet
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Re: Solution to the Paradox of the Stone [Re: Muppet]
    #6704993 - 03/24/07 02:12 AM (14 years, 9 months ago)

oh...and not to get all nit-picky or anything, but the true definition of 'omnipotent' is actually - all knowing (not all powerful)



but that's a minute point really considering you were quite clear about what you intended the term to mean

I'm just giving you a hard time  :wink:


--------------------


:craven:  Ravings of a Madman  :craven:


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InvisibleLakefingers

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Re: Solution to the Paradox of the Stone [Re: Muppet]
    #6705547 - 03/24/07 07:27 AM (14 years, 9 months ago)

Why are Anglo-americans so worried about proofs?


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OfflineWasteland
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Re: Solution to the Paradox of the Stone [Re: Muppet]
    #6705558 - 03/24/07 07:40 AM (14 years, 9 months ago)

Omni=all
Potent=concentrated.

God is orange juice.

My logic is invincible.


--------------------
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InvisibleSilversoul
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Re: Solution to the Paradox of the Stone [Re: Muppet]
    #6705589 - 03/24/07 08:08 AM (14 years, 9 months ago)

Quote:

Muppet said:
oh...and not to get all nit-picky or anything, but the true definition of 'omnipotent' is actually - all knowing (not all powerful)



Nope, that's omniscient. NEXT!


--------------------


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OfflineNewbieS
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Re: Solution to the Paradox of the Stone [Re: Wasteland]
    #6705694 - 03/24/07 10:02 AM (14 years, 9 months ago)

Quote:

Wasteland said:
Omni=all
Potent=concentrated.

God is orange juice.

My logic is invincible.




:lol: I like that one.


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Offlinewoleb
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Re: Solution to the Paradox of the Stone [Re: Silversoul]
    #6705709 - 03/24/07 10:08 AM (14 years, 9 months ago)

I agree with your solution, but the paradox itself is a limited one which doesn't exist to prove the non-existence of God rather as a kind of exercise in understanding omnipotence and logic. I think the point you've made about redefining terms to fit logical consistency is a good one and important in philosophy in general. There's no point in arguing your conclusion because as far as I can see the problems possible retort is one of definition, either of god or omnipotence, and you're not going to redefine god. Or it doesn't seem so anyway.

I am curious of two things:

One: Did you write this or did you get it from somewhere else? I don't care whether you wrote it or not I would just like to know the source

Two: Is this intended as an argument for god or just a rebuking of the stone paradox and a nifty bit of logic?


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Re: Solution to the Paradox of the Stone [Re: shroomydan]
    #6705726 - 03/24/07 10:17 AM (14 years, 9 months ago)

Quote:

Can God make a rock so Big he can't pick it up?




In my opinion this shouldn't even be a debate. Asking "can God make a rock so big he can't pick it up?" is asking a contradictory statement, which, of course, violates the law of noncontradiction.

The question invokes an intrinsic possibility; a concept that is impossible in all times, in all dimensions, and to all agents. The stone question is analogous to asking "can God make a married bachelor?" Well, the concept doesn't even exist, because it can't exist! Omnipotence is the power to do all things except for that which implies contradiction.

Ideas that imply contradiction do not exist past the language barrier. A contradictory concept cannot exist in the world. To ask if "God can make a rock so big that He can't life it" is not even a question-- it is a trick. The question is merely words strewn together that carry no value due to their absolute contradiction.


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Re: Solution to the Paradox of the Stone [Re: Muppet]
    #6705768 - 03/24/07 10:44 AM (14 years, 9 months ago)

no matter how much structure we try to put on this place (and by 'we' I'm referring to the entire spectrum of entities here...physical and spiritual alike) there will ALWAYS be that infamous 2% that exists apparently solely to force us to have to constantly re-evaluate our beliefs

Robert Anton Wilson would have been proud.:thumbup:


--------------------
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" All that lives was born to die"-Anom.

With much wisdom comes much sorrow,
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Re: Solution to the Paradox of the Stone [Re: Silversoul]
    #6705920 - 03/24/07 11:57 AM (14 years, 9 months ago)

Quote:

Silversoul said:
Quote:

Muppet said:
oh...and not to get all nit-picky or anything, but the true definition of 'omnipotent' is actually - all knowing (not all powerful) 



Nope, that's omniscient.  NEXT!



go figure...see what happens when I try an act smert  :lol:


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InvisibleSilversoul
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Re: Solution to the Paradox of the Stone [Re: Muppet]
    #6705922 - 03/24/07 11:59 AM (14 years, 9 months ago)

Don't fuck with my omniscience.


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Invisibleshroomydan
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Re: Solution to the Paradox of the Stone [Re: woleb]
    #6705965 - 03/24/07 12:24 PM (14 years, 9 months ago)

Quote:

am curious of two things:

One: Did you write this or did you get it from somewhere else? I don't care whether you wrote it or not I would just like to know the source

Two: Is this intended as an argument for god or just a rebuking of the stone paradox and a nifty bit of logic?




This is a condensed version of a paper I wrote for my class last quarter on W V Quine. To my knowledge Quine never addressed the God question but he did a lot of work with set theory and paradoxes. I applied some of his theory to the Paradox of the stone to show that it does not constitute a valid proof against the existence of God.

I agree with VigilantMind that the question itself is meaningless, an interesting anomaly of language that demonstrates the ineffability of God. But for those who hold language dearer than God, the surface grammar of the question presents an inescapable dilemma, a fork in the God road leading to two dead ends. For the believer, the question can be dismissed out of hand, and for the atheist it constitutes a proof against the existence of God, but for someone searching for God or running from him, The question can present a real challenge to faith. This paper will be significant for folks in the latter group.


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Re: Solution to the Paradox of the Stone [Re: shroomydan]
    #6708637 - 03/25/07 07:01 AM (14 years, 9 months ago)

I think it's possible for g*d to limit its omnipotence in some separate context, as long as it can reestablish omnipotence again, if it is to. This doen't cancel its whole over-omnipotence.
Why not.


--------------------
Though lovers be lost love shall not  And death shall have no dominion
......................................................
"Our scientific power has outrun our spiritual power. We have guided missiles and misguided men."Martin Luther King, Jr.
'Acceptance is the absolute key - at that moment you gain freedom and you gain power and you gain courage'


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Invisibleshroomydan
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Re: Solution to the Paradox of the Stone [Re: BlueCoyote]
    #6708906 - 03/25/07 10:32 AM (14 years, 9 months ago)

Quote:

BlueCoyote said:
I think it's possible for g*d to limit its omnipotence in some separate context, as long as it can reestablish omnipotence again, if it is to. This doen't cancel its whole over-omnipotence.
Why not.




Gad can do what ever it wants, but this is not about Gad.

Many of the misunderstandings about God arise from considering one of his attributes apart from the totality of his perfection.

Consider gad to be an omnipotent being who is neither necessary nor eternal, neither omniscient nor omni-benevolent. Perhaps gad could let go of some of his omnipotence and then pick it up again at some later time, but God could not because God is eternal. For him there is no later time, there is only now. The eternal God lives the complete fullness of his life in a single moment of infinite duration, an infinite moment simultaneous with all moments of time. If God were to limit his omnipotence there would be no picking it up again, for the simple reason that there is no again for God.

Of course, Christianity throws a wrinkle into the omnipotence/ eternality thing. God limited his omnipotence when he created other rational agents capable of freely acting contrary to the will of God. Even through God loves everybody, he was unable to prevent people from hurting others and themselves, because to do so would violate the freedom he had freely given. Free and rational people who choose against God are rocks so big God can't pick them up. But God found a way. In the fullness of time God incarnated himself as a man, suspending his omnipotence, omniscience, eternality, and immortality, but retaining his omni-benevolence became like us in all things but sin. By stepping into time, dying and resurrecting, God accomplished that which he could not accomplish from eternity, the salvation of free and rational agents who freely choose against the will of God. The details of this salvific process are complex and mysterious, but I think I have sketched an accurate silhouette of the Christian story.

I find it rather striking how the God of Christianity finds ways around the 'limits' placed on the God of philosophy.


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Re: Solution to the Paradox of the Stone [Re: shroomydan]
    #6708988 - 03/25/07 11:06 AM (14 years, 9 months ago)

I think, 'choosing' omnipotence or 'limit it' is part of omnipotence, like the nothing is part of the everything, or nonexistence is part of existence :smile:


--------------------
Though lovers be lost love shall not  And death shall have no dominion
......................................................
"Our scientific power has outrun our spiritual power. We have guided missiles and misguided men."Martin Luther King, Jr.
'Acceptance is the absolute key - at that moment you gain freedom and you gain power and you gain courage'


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Re: Solution to the Paradox of the Stone [Re: BlueCoyote]
    #6724445 - 03/29/07 02:52 PM (14 years, 9 months ago)

actually that paradox is also discussed and answered in buddhism. The paradox is know as a koan. http://en.wikipedia.org/wiki/Koan Just because the mouth can utter the phrase doesnt mean the phrase is reality.


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Re: Solution to the Paradox of the Stone [Re: shroomydan]
    #6724755 - 03/29/07 04:22 PM (14 years, 9 months ago)

If omnipotence is defined as "being able to accomplish any and all tasks that do not entail un-accomplishable tasks" rather than "‘being able to accomplish any and all tasks"...

If omnipotence is defined as "being able to accomplish any and all tasks that do not entail superhuman tasks", then Diploid is omnipotent.

Redefining the terms of a paradox doesn't get around the paradox. What it does is re-context the discussion to something entirely different. The paradox remains.

Just like redefining 'set' to avoid Russell changes the discussion from Set Theory to Other-Than-Set Theory. They are two different things.

Simply replacing the word 'omnipotent' in the original paradox to 'mostly-omnipotent' accomplishes the same thing but does it more concisely, and equally as meaninglessly.


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2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.

4) We need a smaller, less-intrusive government.


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OfflineJackenobi
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Re: Solution to the Paradox of the Stone [Re: shroomydan]
    #6724776 - 03/29/07 04:30 PM (14 years, 9 months ago)

I was thinking about this unanswerable question recently and i realised that answer is yes.

I haven't always thought that but for one reason or another ive decided with as much certainty as man can have that that is your answer.


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Re: Solution to the Paradox of the Stone [Re: vigilant_mind]
    #6725844 - 03/29/07 09:05 PM (14 years, 9 months ago)

Omnipotence is the power to do all things except for that which implies contradiction.

Omnipotence is the power to DEFINE the very nature of contradiction and logic. An omnipotent being can reconstruct logic and make 1 + 1 = 5.

That's the problem with omnipotence. It's a meta-logical construct, and so outside the purview of thought or language.


--------------------
Republican Values:

1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.

4) We need a smaller, less-intrusive government.


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