Does it show that a modally necessary God exists? Is ◊◻∃xGx true and does ◊◻∃xGx entail ◻∃xGx? — Michael
Nevertheless, it might be the case that the underlying metaphysics that facilitates the argument is the correct one. It just still would have relatively little to do with a god. Or, as with other ontological arguments, you can perform the same conjuring trick where you posit an entity with G and then it suddenly exists. Like the aether example. — fdrake
Second quibble: possibly there exists x such that Gx is unsupported. Modal logics do lots of different things. You can say that 1 is possible for 2 under the accessibility relation "less than or equal to" in the integers. Whether the relevant sense of modality in the logic models an appropriate notion of metaphysical necessity is still something that you can quibble with. Why would you need something like an equivalence accessibility relation between worlds? — fdrake
So if anything it's a reductio ad absurdum against the assumption that ◇∃x□Fx is true for every logically consistent Fx. — Michael
The argument does depend on S5 where the accessibility relation is universal. From my reading there are good reasons to accept S5 so it would be shortsighted to deny it simply to dismiss the modal ontological argument, and special pleading to deny it only for the modal ontological argument. — Michael
In that regard, either we'd have to rejected that the luminiferous aether isn't possibly physically necessary, or the law of logic which leads to the inference. I'm inclined to reject the latter, since I intuit that things like physical laws are "physically necessary" (whatever that means). — fdrake
But explaining clearly what is added to an apple by existing...? — Banno
It's not difficult to understand an apple that is not sweet, or an apple that is not red - but an apple that does not exist? What is it? — Banno
Existence IS God. — EnPassant
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