This is a response from Feser to the modal ontological argument, which makes a number of specific errors:
Not everything is a possible world, though. There is no possible world where 2 + 2 = 5 or in which squares are round.
But of course there could well be possible worlds in which ‘distance’ is measured on the Manhattan norm or the Chebyshev norm. However, what we can say is that the logical system of axiomatic Euclidean geometry—not the axioms and postulates of the Elements, which are incomplete, but their modern replacements—proves the same set of theorems in every possible world.
However, when you start talking about Gods or unicorns or whatever you are going beyond logical possibility into metaphysical possibility or even physical possibility, and this is often where problems of ambiguous terms start to creep in.
But the more serious problem with Feser's post is this: he attempts to defend the ontological argument against the reversal of the key premise (as I discussed in the previous post) by analogy (one should always be wary of analogy in logical arguments). He considers the example of comparing the following two premises:
- pU: it is possible that unicorns exist in some possible world
- pNU: it is possible that unicorns exist in no possible world
This pair of premises has a different relationship to each other than do the alternative premises in the God argument. pU and pNU are logical complements: if U is the proposition “unicorns exist”, then pU in modal terms is ⋄U, while pNU is ⋄(◻¬U) which (at least in S5) is ◻¬U which is equal to ¬⋄U.
But for the God argument, if G is the proposition “God exists”, then the pair of premises we are considering is ⋄G and ⋄¬G, which are not complements in modal logic (in fact both ⋄P and ⋄¬P are true for every contingent proposition).
The only way to make the analogy Feser uses precisely equivalent is to beg the question by inserting the necessary-God claim, that G → ◻G, into only one of the two possible premises. If we insert it into neither, or into both, then we see that the argument retains its perfect symmetry and we have no basis to prefer one premise over the other.
To make it explicit, here are various possible pairs of premises that really are symmetrical in the same sense (unlike Feser's example given above):
- it is possible that unicorns exist in some possible world
- it is possible that unicorns do not exist in some possible worldin some possible world unicorns do not exist
- it is possible that God exists in some possible world
- it is possible that God does not exist in some possible worldin some possible world God does not exist
- it is possible that unicorns exist in all possible worlds
- it is possible that unicorns do not exist in all possible worldsany possible world
- it is possible that God exists in all possible worlds
- it is possible that God does not exist in all possible worldsany possible world
A likely theist response at this stage is to point out that God is not contingent and unicorns are, but if we start out with that definition in hand, then the appropriate pair of premises is (4) above, which is still symmetrical between the possible choices and therefore fails.