Here's an old chestnut I haven't thought about in awhile but had reason to re-visit tonight.
It's an argument for the incompatibility of omnipotence and omniscience by Richard LaCroix (Analysis 33:5, April 1973).
Consider a being B which has the following properties:
(1) B is finite
(2) B does act A.
(3) B is the only being in existence who knows that (2) is true.
He says that if "x is omnipotent" entails the following
(4) x can create any finite being y, provided that (i) y has properties such that the statement that y has those properties is neither self-contradictory nor entails a contradiction and (ii) there is no being z such that the statement that z and y exist is either self-contradictory or entails a contradiction.
then an omnipotent being can create a being with (1)-(3).
Since "x is omniscient" entails
(5) For any finite being B and act A, if B does A then x knows that B does A.
it follows that omnipotence so conceived is inconsistent with omniscience.
I'll put my response below the fold to see if we come to the same conclusion.
I think it's pretty clear that omnipotence does not entail (4). The problem with (4) is that it adverts to *strict* logical impossibility rather than *broad* logical impossibility. It's a simple solution not requiring much creativity...not *after* the advent of wide-spread understanding of broadly logical possibility for which the semantics was given by Kripke (and independently by Hintikka I understand) but which was popularized by Alvin Plantinga just a few years after the LaCroix piece (Lewis's original account of modal logic was in terms of consistency by the way).
What interests me most here is the sociological aspect. It would have been pretty easy to be taken in by this kind of argument at the time (though perhaps it will turn out to have the same structure as the paradox of the stone, I haven't spent the time to consider that). I'm honestly not sure what the moral of the story is: whether it's "Don't accept the conclusions of arguments who's premises seem suspicious but you can't say why" or "How sad it is that rational believers could be mislead by being born six years too early." There's some kind of irony or misfortune here, but I can't quite put my finger on it.
I must be missing something. Suppose, for reductio, there is an x that is omnipotent and omniscient. We infer,
1. (Ex)(x is omniscient & omnipotent)
We assume (following Lacroix) that (4) holds for omnipotent beings such as x,
4. x can create any finite being y, provided that . . . (ii) there is no being z such that the statement that z and y exist is either self-contradictory or entails a contradiction.
We are moved to conclude, contrary to Lacroix, that x cannot create B, since B has the property in (3),
3. B is the only being in existence who knows that (2) is true.
Why? Because (1) above entails, contrary to (3), that there exists some other being z such that z = x and ~(z = B) and,
1'. z knows (2) is true.
Recall that x (= z) is omniscient and so knows that (2) is true. So, it seems possible that x is omnipotent and omniscient and cannot create B. The creation of B would violate condition (ii) of (4) on omnipotent beings. We should conclude instead that being omniscient is not incompatible with being omnipotent.
If I understand your point correctly Mike it's that LaCrox's argument must be a reductio, but once you assume the thing to be reduced to absurdity you get something that entails the negation of one of the further necessary premises. Is that right?
If I've got that right, then, if it's true that LaCroix's argument must be formulated as a reductio, then that's not as clear to me as I'd like.
It seems to me that the form of the argument is like this:
(6) Consider property P1: it entails property P2.
(7) Now consider property P3: it precludes property P2.
(8) Nothing can exemplify two properties one of which includes and the other of which precludes a third property.
(9) Thus, nothing can exemplify both P1 and P3.
Also, I'm unclear whether you agree with me that omnipotence does not entail (4).
Happy thanksgiving!
Lacroix claims that omnipotence and omniscience are incompatible. If that's true, then there could be no being that is both. Let's test that. Assume there is a being that is both. Can we derive an inconsistency? No, we can't. All we can derive from that assumption is that (3) is false. No inconsistency is derivable from his assumptions. So, it is perfectly possible that there is an omniscient and omnipotent being.
I do agree that (4) is likely false in any case or (maybe) too weak.
Good points, Trent, and quite interesting. The same thing can be said about the simpler chestnut: Nobody can can create an uncreated being. :-)
On the sociological aspect, it's also worth noting that the philosophical tradition, before Kripke, will include philosophers whose accounts of modality include resources sufficient to escape the argument. It is true that the argument was given in a context where the audience was ignorant of these resources. But the resources were there.
I would say that, classically, omniscience is an aspect of omnipotence (power to know). So an omnipotent being cannot create something he can't know for the same reason he can't create something he can't (fill in your favorite power here).
Heath:
I think Swinburne distinguishes being able to know everything, which does follow from omnipotence, from actually knowing everything.