Solution to the Paradox of the Stone - Philosophy, Sociology & Psychology

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shroomydan
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Registered: 07/04/04
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Solution to the Paradox of the Stone

#6704530 - 03/23/07 09:33 PM (17 years, 6 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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