A Modal Ontological Argument and an Argument from Evil Compared

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?

Conclusion

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.

Comments

[Account Deleted]

Bill,

Excellent post. Need to ponder more. One quick comment. In the conclusion the following sentence appears to contain a misprint: "The key premises in both arguments -- (2) and (4) -- are necessarily true if true."

Did you mean to say premises here 2 and 4 or rather premises 2 and 5?

[Bill Vallicella]

Thanks for catching that mistake, Peter. I have corrected it.

[Allen]

I wonder if you can take the Cantorian idea of there being no "largest infinity" and apply something similar to there being no Greatest Conceivable Being?

There is no greatest conceivable being in the same way that there is no largest infinity.

There may be a limit to what a human can conceive, but surely there are possible worlds where there are "greater conceivers" than us.

In fact, maybe just as there is no greatest conceivable being, there is also no greatest conceiver?

[Steven]

Allen,

The "greatness" of the greatest conceivable being is not a quantified greatness like in the case of numbers; it's a qualitative greatness. I don't see how insights in mathematics have anything to do with whether or not the greatest conceivable being is possible.

[Bill Vallicella]

Allen,

What Steven said in reply is basically right. Also, nothing depends on what we can conceive. To avoid that misinterpretation, I could use 'maximally perfect being.'

[Allen]

Steve and Bill,

So I can say "the largest infinity", but this doesn't refer to anything because there is no largest infinity.

I can say "the maximally perfect being", but why should I think that this refers to anything either?

What does "maximally perfect" even mean? Perfect according to what measure?

In the unbounded space of possibility it seems conceivable to me that (regardless of your measure of perfection) for any being there could always be a "more perfect being" one world further out.

e.g.: "This perfect being has an infinity of cherries on top, but here's another *even more perfect* being with an even larger infinity of cherries!"

Here my measure of perfection is heavily influenced by the number of cherries on top of the being. On what grounds could I be proved wrong?

I'm not certain that you're wrong in saying that mathematical insights don't apply, but I'd like to hear the case made as to why they don't.

[Steven]

Allen,

A maximally perfect being has everything that we think makes a being great to the maximal degree. So for instance, rationality makes a being great -- that is why humans are greater than worms or dirt, or at least one reason -- and so a maximally perfect being would have rationality to the maximal degree. The proponents of such a view would just respond to your question of "Perfect according to what measure?" by saying that there are just objective, non-conventional facts about what makes beings greater or lesser, and it is according to that standard, if it can be called a standard, that the maximally perfect being is maximally perfect.

You say it seems conceivable to you that there be a greater being than any one you could imagine. This doesn't show much, of course, because at best this shows whether or not you are able to find a contradiction in a certain proposition. It doesn't follow from the fact that you can conceive of there being no greatest possible being that therefore there is no greatest possible being.

But I am wondering exactly how you are conceiving of beings being greater than the other. I don't understand your talk of cherries on top of a being.

The fact that there is no greatest number doesn't have any tendency to show that there is no greatest possible being, because "greatest" is equivocal between the two. The greatest number is one that is greatest in terms of quantity; the greatest being is one that is greatest in terms of qualities, and these qualities cannot be quantified, they can't be put into numbers or measured like that.

[Jonny]

A very quick thought on the Argument From Evil, which I'm sure is of no consequence whatsoever: I accept that you don't need the R-to-L reading of 7 in order for the argument to work. But if you were to require it, a formulation of 7 which might work would be:

7'. Necessarily, there can be gratuitous evils iff the GCB does not exist.

(presumably there could be a possible world where no GCB exists but there are no gratuitous evils, just by chance).

7', though, does leave the door open for contingent evidence to make an appearance. For, whilst it is necessary that there can be gratuitous evils iff the GCB does not exist, whether there are or not is an evidentiary matter.

I doubt there's anything of value in that, but I enjoyed the mental workout.