The Paradox of the Stone

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Brian Bosse

"The Brain"
Part I

Hello Everyone,

Caleb sent me an article written by C. Wade Savage titled “The Paradox of the Stone.” It was published in The Philosophical Review, Vol. 76, No. 1. (Jan., 1967), pp. 74-79. This will be part 1 of a critical analysis of the article. All quotes are taken from this article.

Argument

(1) Either God can create a stone which He cannot lift, or He cannot create a stone which He cannot lift.
(2) If God can create a stone which He cannot lift, then He is not omnipotent (since He cannot lift the stone in question).
(3) If God cannot create a stone which He cannot lift, then He is not omnipotent (since He cannot create the stone in question).
(4) Therefore, God is not omnipotent.

According to the article, George I. Mavrodes argues that (3) is false because the task of an omnipotent being creating a stone which he cannot lift is self-contradictory, and the inability to perform the self-contradictory does not limit the agent. Regarding this Wade says…

…“a stone which God cannot lift” is self-contradictory…only if “God is omnipotent” is necessarily true…if “God is omnipotent” is necessarily true…then his assumption that God exists begs the question of the paradoxical argument. For what the argument really tries to establish is that the existence of an omnipotent being is logically impossible… the claim that inability to perform a self-contradictory task is no limitation on the agent is not entirely uncontroversial.

Wade argues against Mavrodes in two ways: (A) the idea that the inability to do a self-contradictory act is not limiting “is not entirely uncontroversial,” and (B) the argument that “God creating a stone too heavy to lift” is self-contradictory begs the question. Concerning (A), to simply say the idea is “not uncontroversial” is not much of an argument. Now, it may be that Mavrodes has not adequately argued for his position, but his position seems reasonable to me. If God cannot create a square circle, does this limit God? If it does, then it does not do so in any meaningful (rational) way. One can simply define ‘omnipotence’ in such a manner that self-contradictory actions are not disqualifiers for omnipotence.

Concerning (B), this is somewhat more complicated. For the moment, pretend that the above argument has not been presented and that Mavrodes presents to the skeptic the following argument…

Prove ~A: God cannot create a stone which He cannot lift.
Assume A: God can create a stone which He cannot lift.
Step 1 (A --> ~B): If God can create a stone which He cannot lift, then God is not omnipotent.
Step 2 (B): God is omnipotent.
Step 3 (~A): God cannot create a stone which He cannot lift. (Modus Tollens)
Q.E.D.

The skeptic accepts step 1 as true because he uses it as his (2) above. So, the skeptic denies step 2. (Note: everything else follows by force of logic.) To defend this denial he presents the initial proof in this post. Mavrodes accepts (1) and (2), and therefore denies (3). He proceeds to argue as follows:

The proof is unsound because (3) is false. (3) is false because “God creating a stone too heavy to lift” is self-contradictory. The action of “God creating a stone too heavy to lift” is self-contradictory because “God can lift all created stones.” “God can lift all created stones” because God is omnipotent. Mavrodes has just begged the question with this argument. He has assumed that which is the very thing under question. It seems that trying to overcome the skeptic’s argument using the idea of “self-contradiction” does beg the question. There may be another way that Mavrodes could argue for "self-contradiction" that does not beg the question, but I am unaware of it. Perhaps, Anthony or others who have argued this way can present their ideas?

Conclusion

Wade’s argument (A) against Mavrodes is very weak, but his argument (B) is stronger. The problem with (B) is that Wade did not explicitly lay out Mavrodes’ argument for self-contradiction. We were left to try and guess what it was. It could be that Mavrodes’ argument in the end does not beg the question. But, my reconstruction of the argument does beg the question. So, if my reconstruction is correct, then Wade’s criticism is good. If Mavrodes’ argument is different, then the issue is still not settled. With that said, there are better ways to overcome the skeptic’s argument. I will address this latter. In the meantime, I will await comments before going to part II.

Sincerely,

Brian
 

Cheshire Cat

Puritan Board Sophomore
I should add that I recieved the Savage article from Brian Lanier. He also sent the Mavrodes article, so if you wish he can send you that or I can if you like.
 

BrianLanier

Puritan Board Freshman
Wade’s argument (A) against Mavrodes is very weak, but his argument (B) is stronger. The problem with (B) is that Wade did not explicitly lay out Mavrodes’ argument for self-contradiction. We were left to try and guess what it was. It could be that Mavrodes’ argument in the end does not beg the question. But, my reconstruction of the argument does beg the question. So, if my reconstruction is correct, then Wade’s criticism is good. If Mavrodes’ argument is different, then the issue is still not settled. With that said, there are better ways to overcome the skeptic’s argument. I will address this latter. In the meantime, I will await comments before going to part II.

Hi Brian,

Glad you enjoyed the article.

Mavrodes did not explicity lay out his argument in premise form. But Wade *does* give his reconstruction of Mavrodes' arguement (which you gave above in four premises) but not in reductio form but in a dilemma.

And regarding his argument A (using your numeration), he relies on Harry Frankfurt's article on "The Logic of Omnipotence" to make his point (See Frankfurt, Harry G. "The Logic of Omnipotence". The Philosophical Review. 73 (1964).) So it is argued for (though not by him) - and I think it is more of a side point than anything.
 
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