Continuing my project of reading my hitherto unread reading assigned for the medieval comp, I've been reading Anselm's replies to Gaunilo. As it happens, I never read all of it. When I assigned the text for class, I assigned only an abridged version which at one point says "Anselm continues as some length, but much of what he says seems repetitive". Well, maybe it seems that way to the translator, but the full text is really good stuff. I haven't digested it all, but I think there may be more to Anselm's ontological argument than has caught my eye before. It's at least as good as the S5 ontological argument.
That said, here's another ontological argument, inspired, if memory serves, by a humorous remark my wife made to me once.
- (Premise) To be incapable of existing is a great impotence.
- (Premise) Necessarily, anything that is all powerful lacks all impotence.
- (Premise) A being that exists and is all powerful in one world must exist in all other worlds.
- (Premise) God is essentially all powerful.
- God lacks all impotence. (2 and 4)
- Possibly God exists. (1 and 5)
- There is a world at which God exists and is all powerful. (4 and 6)
- God exists in all worlds. (3, 7 and S5)
- God exists and is omnipotent. (4 and 8)
Step 3 gets a subsidiary argument. More than one comes to mind. But here is one:
- (Premise for reductio) Suppose x exists and is all powerful at w but does not exist at w*.
- (Premise) Necessarily, to be unable to be an efficient cause of any sort (remote or immediate, full or contributing, etc.) of a possible but non-necessary state of affairs is an impotence.
- (Premise) Necessarily, nothing is able to be an efficient cause of any sort of its own failure to ever exist.
- x's failure to ever exist is a possible but non-necessary state of affairs. (10)
- It is true at w that x is unable to be an efficient cause of any sort of its failing to ever exist. (12)
- It is true at w that x is not all powerful. (2, 11, 14) Which absurdly contradicts (10).
- So if x exists and is all powerful at w, it must exist at every other world w*.
I don't know how seriously this argument is to be taken. By the way, it reminds me of something I heard attributed to Scotus.