Mike Almeida has presented an ingenious new probabilistic version of the ontological argument at Prosblogion. As I understand it, the basic idea is this. Consider the following properties:
Being concrete (as opposed to being abstract)
Mike's argument seems to be this. The first three properties admit of an infinite number of degrees. Furthermore, at least very many combinations of these degreed properties are compossible -- perhaps infinitely many. Furthermore, these combinations are compatible with the fourth property of being concrete. So there seem to be an infinite number of compossible combinations of the first four properties:
Therefore, given the infinite number of possible combinations of these properties, it's highly probable that at least one such combination is compatible with the fifth property mentioned earlier, viz., the property of necessary existence. Therefore, since every set of compatible properties is possible, it's highly probable that a necessarily existent concrete individual with some degree of goodness, power, and knowledge is possible. And since (by Axiom S5 of S5 modal logic) whatever is possibly necessary is necessary simpliciter, it's highly probable that a necessary being with some degree of goodness, power, and knowledge exists.
In the comments of the post, Yujin Nagasawa raises the worry that the argument proves too much: if it really is true that at least one combination of the first four properties is compatible with necessary existence, then it also seems highly probable that other combinations of the properties are compatible with necessary existence as well. But if so, then the argument would seem to show that multiple necessary beings of this sort exist.
My own view is that our knowledge of what's metaphysically possible is quite limited, and thus that the probability of the compossibility of the first four properties with necessary existence is inscrutable. The basic idea is that while some properties are intrinsically compatible with other properties (e.g., the property of being a cat is compatible with the property of being white), some are not (e.g., the property of being a prime number is incompatible with the property of being a prime minister, to borrow an example from Plantinga). But if two or more properties are intrinsically incompatible with one another, then the fact that such properties come in degrees -- even infinitely many degrees -- is irrelevant to whether they can fit together coherently: if the properties involved are intrinsically incompatible, then not one of those combinations is possible. And the problem is that we don't know whether the properties involved in the argument are compatible (i.e., we don't know whether they are more like those involved in being a cat and being white, or more like those involved in being a prime number and being a prime minister).
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