Argument A:
(A1) For
any x, if x is capable of creating a stone that x cannot lift, then x is not
omnipotent (because it is incapable of lifting such a stone).
(A2) For
any x, if x is incapable of creating a stone that x cannot lift, then x is not
omnipotent (because there is something that it is incapable of doing).
(A3) For any x, either x is
capable of creating a stone that x cannot lift, or x is incapable of doing so.
(A4) Therefore, an omnipotent
being is logically impossible.
This
is an appealing argument, but (A2) is problematic. Consider the following
argument:
Argument B:
(B1) In any
possible world in which x is omnipotent, there is no stone that x cannot lift.
(B2) Therefore,
there is no possible world in which x is omnipotent and in which there is a
stone that x cannot lift.
(B3) Therefore, “x
is omnipotent and there is a stone that x cannot lift” (S) is impossible.
(B4) For any x, if
x is omnipotent, then what it is for x to create a stone that x cannot lift is
for x to actualize (S).
(B5) Therefore,
for any x, if x is omnipotent, then what it is for x to create a stone that x
cannot lift is for x to actualize something impossible.
(B6) Even if a
being is omnipotent, it is incapable of actualizing the impossible.
(B7) Therefore, for any x, if x is omnipotent, then
it is incapable of creating a stone that x cannot lift.
Let us
symbolize (B7) as “("x)(Ox ®
Ix)”. Premise (A2) can then be symbolized as “("x)(Ix ® ~Ox)”, which is equivalent to “("x)(Ox ® ~Ix)”.
If
argument B is sound, which I think it is, then “("x)(Ox ® Ix)” is proven true. Will argument B then
prove that (A2) (i.e. “("x)(Ox ®
~Ix)”) is false? Not quite, for if there are no omnipotent beings, then both “("x)(Ox ® Ix)” and “("x)(Ox ® ~Ix)” are true.
But that
doesn’t mean (A2) is not problematic as a premise of argument A. Here is how I
see the dialectic: “("x)(Ox ®
Ix)” is true whether there is an omnipotent being, while “("x)(Ox ® ~Ix)” is true only if there are no omnipotent beings. For this reason, (A2) should
not be taken as obviously true and needs to be defended.
A defense
of (A2) may begin with arguing that there are no omnipotent beings. Such an
argument has to be independent of argument A, for otherwise it would be
question-begging. It is, however, not clear how this can be done.
Another way is to argue for (A2) without first arguing
that there are no omnipotent beings. If there are independent grounds for
arguing for (A2), then those can be used, and the argument for (A2) will also
be an argument for the non-existence of omnipotent beings. Argument A will then be used to argue for a stronger conclusion, namely, that an
omnipotent being is logically impossible.
In any case, (A2) can’t just be assumed without argument.
