After leaving the polling place this morning, I headed out on a sunrise hike over the local hills whereupon the muse of philosophy bestowed upon me some good thoughts. Suppose we compare a modal ontological argument with an argument from evil in respect of the question of evidential support for the key premise in each. This post continues our ruminations on the topic of contingent support for noncontingent propositions.
A Modal Ontological Argument
'GCB' will abbreviate 'greatest conceivable being,' which is a rendering of Anselm of Canterbury's "that than which no greater can be conceived." 'World' abbreviates 'broadly logically possible world.'
1. The concept of the GCB is either instantiated in every world or it is instantiated in no world.
2. The concept of the GCB is instantiated in some world. Therefore:
3. The concept of the GCB is instantiated.
This is a valid argument: it is correct in point of logical form. Nor does it commit any informal fallacy such as petitio principii, as I argue in Religious Studies 29 (1993), pp. 97-110. Note also that this version of the OA does not require the controversial assumption that existence is a first-level property, an assumption that Frege famously rejects and that many read back (with some justification) into Kant. (Frege held that the OA falls with that assumption; he was wrong: the above version is immune to the Kant-Frege objection.)
(1) expresses what I will call Anselm's Insight. He appreciated, presumably for the first time in the history of thought, that a divine being, one worthy of worship, must be noncontingent, i.e., either necessary or impossible. I consider (1) nonnegotiable. If your god is contingent, then your god is not God. There is no god but God. End of discussion. It is premise (2) -- the key premise -- that ought to raise eyebrows. What it says -- translating out of the patois of possible worlds -- is that it it possible that the GCB exists.
Whereas conceptual analysis of 'greatest conceivable being' suffices in support of (1), how do we support (2)? Why should we accept it? Some will say that the conceivability of the GCB entails its possibility. But I deny that conceivability entails possibility. I won't argue that now, though I do say something about conceivability here. Suppose you grant me that conceivability does not entail BL-possibility. You might retreat to this claim: It may not entail it, but it is evidence for it: the fact that we can conceive of a state of affairs S is defeasible evidence of S's possibility.
Please note that Possibly the GCB exists -- which is logically equivalent to (2) -- is necessarily true if true. This is a consequence of the characteristic S5 axiom of modal propositional logic: Poss p --> Nec Poss p. ('Characteristic' in the sense that it is what distinguishes S5 from S4 which is included in S5.) So if the only support for (2) is probabilistic or evidential, then we have the puzzle we encountered earlier: how can there be probabilistic support for a noncontingent proposition? But now the same problem arises on the atheist side.
An Argument From Evil
4. If the concept of the GCB is instantiated, then there are no gratuitous evils.
5. There are some gratuitous evils. Therefore:
6. The concept of the GCB is not instantiated.
This too is a deductive argument, and it is valid. It falls afoul of no informal fallacy. (4), like (1), is nonnegotiable. Deny it, and I show you the door. The key premise, then, the one on which the soundness of the argument rides, is (5). (5) is not obviously true. Even if it is obviously true that there are evils, it is not obviously true that there are gratuitous evils.
In fact, one might argue that the argument begs the question against the theist at line (5). For if there are any gratuitous evils, then by definition of 'gratuitous' God cannot exist. But I won't push this in light of the fact that in print I have resisted the claim that the modal OA begs the question at its key premise, (2) above.
So how do we know that (5) is true? Not by conceptual analysis. If we assume, uncontroversially, that there are some evils, then the following logical equivalence holds:
7. Necessarily, there are some gratuitous evils iff the GCB does not exist.
Left-to-right is obvious: if there are gratuitous evils, ones for which there is no justification, then a being having the standard omni-attributes cannot exist. Right-to-left: if there is no GCB and there are some evils, then there are some gratuitous evils. (On second thought, R-to-L may not hold, but I don't need it anyway.)
Now the RHS, if true, is necessarily true, which implies that the LHS -- There are some gratuitious evils -- is necessarily true if true.
Can we argue for the LHS =(5)? Perhaps one could argue like this (as one commenter suggested in an earlier thread): If the evils are nongratuitous, then probably we would have conceived of justifying reasons for them. But we cannot conceive of justifying reasons. Therefore, probably there are gratuitous evils.
But now we face our old puzzle: How can the probability of there being gratuitous evils show that there are gratuitous evils given that There are gratuitous evils, if true, is necessarily true?
We face the same problem with both arguments, the modal OA for the existence of the GCB, and the argument from evil for the nonexistence of the GCB. The key premises in both arguments -- (2) and (5) -- are necessarily true if true. The only support for them is evidential from contingent facts. But then we are back with our old puzzle: How can contingent evidence support noncontingent propositions?
Neither argument is probative and they appear to cancel each other out. Sextus Empiricus would be proud of me.