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An Irrefutable Ontological Argument?

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:

Goodness
Power
Knowledge
Being concrete (as opposed to being abstract)
Necessary existence

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:

Goodness
Power
Knowledge
Being Concrete

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).

Comments

AIGBusted said…
A combination of such properties could be compatible with necessary existence (for all I know!), but I think theists need to provide some proof that it is.

I also see no reason that evil, unconcern, stupidity, etc. could be compatible with necessary existence. That does not disprove this ontological argument, I am simply making the point that a necessary being might not be anything like what human beings think of as "God".

Here's another point to contemplate: Far more possible objects are non-intelligent and are not agents than are. Therefore, if there is a necessary thing (or small collection of necessary things) they are likely not conscious and not intelligent.

What do you think EA?
TKD said…
Hey EA,

I enjoy your blog, though this is my first time commenting, lol. I agree with your analysis of the situation here, but I would like to ask you what you think of Almeida's treatment of epistemic possibility in one of his previous entries. He stated here that this is the angle that he's taking in this new ontological argument.

Thanks!
TKD
exapologist said…
Hey TKD,

Thanks for commenting!

As it happens, this issue is one of the main topics of my dissertation. I'd like to keep my reasons for rejecting accounts of that sort under wraps until I hear back from some journals, if you don't mind. For now, I'd like to just register my disagreement with such accounts.

In the meantime, if you haven't already, I'd read: Stephen Yablo's, "Textbook Kripkeanism and the Open Texture of Concepts", (Pacific Philosophical Quarterly 81 (2000), pp. 98-122); Alexander Bird's "Necessarily, Salt Dissolves in Water" (Analysis 61:4 (2001), pp. 267–274); Peter van Inwagen's "Modal Epistemology" (Philosophical Studies 92 (1998), pp. 67-84); and George Seddon's classic paper, Logical Possibility" (Mind 81 (1974), pp.481-494). Yablo's paper raises worries for epistemic possibility accounts of the sort Almeida seems to accept; the other papers raise worries for the more general claim that we have extensive knowledge of far-out possibilities.

Best,

EA
exapologist said…
Hey AIG,

A combination of such properties could be compatible with necessary existence (for all I know!), but I think theists need to provide some proof that it is.I think he does offer reasons, though. First, (as TKD pointed out) in the past he's appealed to a Chalmers'-style account of modal epistemology as his basis for the conceivability-possibility connection. Second, as I mentioned in the post, he's offering a probability argument for the relevant possibility, based on the likelihood that at least one combination of the degrees of properties at issue are compossible. However, my sympathies are with you that neither of these reasons are sufficient.

I also see no reason that evil, unconcern, stupidity, etc. could be compatible with necessary existence. That does not disprove this ontological argument, I am simply making the point that a necessary being might not be anything like what human beings think of as "God".Someone raised a point similar to your first sentence here. I'm still thinking about that one, but I think you have a point. Mike agrees with you about your last sentence here. His aim is more modest than the one in other ontological arguments. He's content to show that some being or other has the properties he lists. He thinks that it's a significant conclusion nonetheless, even if it doesn't get him a home run argument for theism.

Best,

EA
AIGBusted said…
Thanks EA. The argument is interesting, I suppose, but its not strong enough to move me from my position of atheism.

:-)
Rayndeon said…
Hi exapologist,

I don't think that I accept that any combination of properties of goodness, power, and knowledge are compossible with necessary existence. It seems to me that to accept such a claim, I would have to find inconceivable the nonexistence of a concrete object. But, if one believes that worlds containing "nothing" (as in no concrete entities) are possible, then surely one must find (1) of Professor Almeida's argument unacceptable? I also very much like Professor Nagasawa's objection, since Professor Almeida's argument seems quite a bit more vulnerable to parody objections than most other ontological arguments.

Cheers,

A.Y.

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