Originally posted by SwissGambit
def. [b]God: a being which is "maximally excellent" in every possible world. Maximal Excellence includes such properties as omniscience, omnipotence, and moral perfection. A being which has maximal excellence in every possible world would have "maximal greatness."
Premises:
1. It is possible that a maximally great being exists.
2. If it is pos accept the argument entirely. For my atheist brethren: which premise(s) would you reject?[/b]
If we hold to S5 modal logic, then I think Premise 3 just follows trivially from P's own definitions of his world-indexed properties and thus cannot be reasonably rejected. For instance, P states "The property
has maximal greatness entails the property
has maximal excellence in every possible world". Based on P's formulation, I think it should follow that 'maximal greatness' is a property that is either instantiated in every possible world or not instantiated at all. So, I would not reject Premise 3 (though, I think it could be rejected on the grounds that S5 is not the right system here, in virtue of P's use of world-indexed properties).
Premise 1, though, needs to be rejected. The problem again goes back to P's use of world-indexed properties. Premise 1 seems innocuous enough because it is very natural for us to infer from non-contradiction to mere possibility and thus to possible worlds. For instance, if a property does not itself entail contradiction, then it is ordinary to conclude that there is some possibility that this property is instantiated; and to the extent that 'maximal greatness' does not itself entail contradiction, it is natural to infer that there is some possibility that maximal greatness is instantiated (and it is this which is supposed to constitute the justification for Premise 1). This pattern of inference from internal consistency to an associated possibility or a possible world is fine, if the possible worlds are independent of each other. However, within P's system of world-indexing here, the possible worlds are not independent of each other because, for example, properties in some possible world entails properties in others. The upshot is that the pattern of inference from non-contradiction to possibility or a possible world is no longer innocuous, since the possible world associated with some non-contradiction may in fact be inconsistent with the possible world associated with some different non-contradiction. We have no good reason here to accept Premise 1.
At the very least, we can say this: if the only proposed justification for accepting Premise 1 is that we ought to infer from non-contradiction of a property to the possibility that the property is instantiated; then that is wholly inadequate in this particular case. We can see that it is inadequate by considering another term defined by P as 'no-maximality', which is basically the counter-concept of maximal greatness (the one is exemplified where the other is not and vice versa). We could then construct a similar argument as follows:
1*. It is possible that no maximally great being exists.
2*. If it is possible that no maximally great being exists, then no-maximality is exemplified in some possible world.
3*. If no-maximality is exemplified in some possible world, then it is exemplified in every possible world.
4*. If no-maximality is exemplified in every possible world, then it is exemplified in the actual world.
5*. Therefore, it is not the case that a maximally great being exists.
Now, if the justification that it is natural to infer from non-contradiction to possibility were good enough for Premise 1, it should also be good enough for Premise 1*. But, this leads one to taking on possible worlds that are, in fact, incompatible with each other. The sensible conclusion here is that there is clearly something wrong with this pattern of inference for this case that features world-indexed properties (at least when conjoined with the S5 system).
If you want a short, but good in my opinion, refutation of P's ontological argument, you can check out the section in Mackie's
The Miracle of Theism that deals specifically with P's argument. Mackie thrashes P's argument.