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Sunday, 5 July 2009

Critically assess Mavrodes’ solution to the paradox of the stone.

Jon Carberry

Mavrodes’ solution to the paradox of the stone is an argument that seeks to invalidate the paradox as a means of undermining the doctrine of omnipotence. Attempts have been made to refute the doctrine of omnipotence by finding examples of things God cannot do, for example drawing a square circle or creating a stone which he cannot lift (or in an episode of “The Simpsons”; “…microwave a burrito so hot that he cannot eat it”). The idea of God being able to draw a square circle is obviously and easily dismissible a priori on the grounds that it is a self contradictory idea. It is not possible for anyone to draw a square circle because such a thing cannot exist. The definition of a circle precludes any possibility of a circle ever being square, in the same way as a square, being defined by its four straight equal sides, joined at corners of precisely 90°, cannot be circular. The paradox of the stone is not so obviously contradictory; however there are contradictions within the paradox and Mavrodes correctly indicates some of these.

The contradiction of asking an all powerful being to create a situation which requires a limit of their power (namely, to create a stone that exceeds their (omnipotent) power to lift) is every bit as contradictory as the square circle. What is essentially being asked of God is that he not only creates the stone but surrenders his omnipotent power so as to render himself unable to lift it (omnipotence, implying that he can lift anything, and is unable to lift no thing) assuming he intends to create a stone which he cannot lift. Certainly for God to create a stone which he cannot lift goes no way towards proving his omnipotence because it would cost him his omnipotence in order to satisfy the demands of the argument.

What Mavrodes suggests, is that to say “God cannot create a stone so heavy that he is unable to lift it” does no damage to the doctrine of omnipotence. He seeks to demonstrate this by firstly setting down parameters; either God is omnipotent, or he is not.

Mavrodes assumes in the first instance that God is not omnipotent and on this basis, points out that “a stone too heavy for God to lift” is not necessarily self contradictory. My power to lift is limited as I am not omnipotent, so it is well within the realms of possibility that I could create something that is beyond my ability to lift. Therefore for a limited God, the ability to create a stone that is too heavy to be lifted is not contradictory. In fact, the only being that would be unable to make such a stone is a being that is able to lift anything. The paradox sets out a task that only an omnipotent being could fail! One could say it is a unique characteristic of non-omnipotent beings that there are things they are unable to do. This characteristic cannot be shared by omnipotent beings precisely because the one thing they lack is a limit to their abilities (other than the limit of what is actually possible and not self contradictory) by definition. As Mavrodes correctly indicates, if we start with the assumption that God is not omnipotent then whether he is able (to create the stone but unable to lift it) or unable to create such a stone, all that is proved is that he is not omnipotent which is the assumption that we started with. The argument is circular in the instance of a non-omnipotent god.

In the second instance, Mavrodes presupposes that God is omnipotent. He states;
“On the assumption that God is omnipotent, the phrase ‘a stone too heavy for God to lift’ becomes self contradictory. For it becomes ‘a stone which cannot be lifted by him whose power is sufficient for lifting anything’…” (Mavrodes, 1963)
demonstrating that for an omnipotent being there is no such thing as a stone they cannot lift, nor could there ever be. Although for a limited being, the idea of something too massive to lift is an everyday reality, this is not the case for those whose power is in no way limited. Because there is no thing that an omnipotent cannot lift, for an omnipotent, such a stone is contradictory and so under St. Thomas Aquinas’ solution to the issue of the square circle, the paradox vanishes in an instant because the doctrine of omnipotence makes no claim about God’s ability to perform self contradictory tasks. It should also be noted at this point that this argument also appears to be circular (a point Mavrodes seemingly misses);
(A) 1. God is omnipotent.
2. Omnipotent beings are capable of performing any task (other than that which is self contradictory).
3. For an omnipotent being an unliftable stone is self contradictory.
4. Therefore God cannot create a stone that God cannot lift because he cannot perform any self contradictory task.
5. Therefore God is omnipotent.
because points 1 and 5 are identical the conclusion that God is omnipotent depends upon the assumption that he is omnipotent!

One point of Mavrodes article that makes for entertaining reading is the objection that he pre-empts in paragraph 8. He supposes that an objector refuses to accept that the existence of a stone that an omnipotent cannot lift is self contradictory. In such a case the objection collapses under its own weight because if the notion of a stone that an omnipotent cannot lift is not self contradictory, then it is compatible with the existence of an omnipotent being and therefore, for God to create such a stone and be unable to lift it would pose no threat to the notion of his omnipotence because there exists the possibility of a stone that no omnipotent being could lift! Thus allowing God to be unable to lift the stone but remain omnipotent. This only further proves how contradictory the notion of the required stone is, rather than demonstrating anything contradictory about the nature of omnipotence itself.

As delightful in its simplicity as Mavrodes solution appears, a critique of it penned by C. Wade Savage four years later raises further interesting objections to Mavrodes. Although in principle Wade Savage seems to agree with Mavrodes it seems he finds his [Mavrodes] solution to be insufficient. Wade Savage argues that in proving the notion [of a stone that an omnipotent cannot lift] to be self contradictory, Mavrodes has side-stepped an important issue of whether or not the inability to create such a stone (self contradictory or not) implies a limitation on Gods power. Wade Savage restates the paradox in much clearer terms that make no allowance for the get-out clause offered by the idea of an omnipotent being unable to perform self contradictory tasks in (A2). He then offers his own solution to the paradox, best summarised as follows;
“Whether x=y or x≠y, x’s inability to create a stone which y cannot lift constitutes a limitation on x’s power only if (i) x is unable to create stones of any poundage, or (ii) y is unable to lift stones of any poundage. And since either (i) or (ii) may be false, ‘x cannot create a stone which y cannot lift’ does not entail ‘x is limited in power’…” (Wade Savage, 1967)
the interesting thing about this solution is that in the case of x and y being omnipotent (where x=y or x≠y) both (i) and (ii) are false and therefore Gods inability to create a stone that God cannot lift implies no limitation to his powers regardless of whether or not the task is self contradictory.

In his concluding paragraph Mavrodes is keen to point out that his solution makes no judgement on whether or not God is omnipotent or not. “All that I intend to show is that certain arguments intended to prove that he is not omnipotent fail.” (Mavrodes 1963) The paradox in its original form attempts to show that the notion of omnipotence is self contradictory, by unwittingly making a self contradictory demand of omnipotence. Mavrodes’ article makes a useful contribution insofar as it shows the task required in the paradox, to be self contradictory and thereby removes the threat to the doctrine of omnipotence posed by the paradox. I do however share the view of C. Wade Savage that Mavrodes solution does not go far enough to solve all forms of the paradox; however since Mavrodes stated intent was merely to “show that certain forms of argument…fail” he manages to do so adequately within the confines of his own stated version of the paradox.


Mavrodes, George I. “Some Puzzles Concerning Omnipotence”, Philosophical Review 72 (1963) pp. 221-23.

Vitti, J. “Weekend at Burnsie’s” The Simpsons, (2002) Season 13 Episode 11

Wade Savage, C. “The Paradox of the Stone”, Philosophical Review 76 (1967) pp. 74-79.

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