November 19, 2011

Counterpossible Reasoning in Philosophy of Religion (and Elsewhere)

The latest (July 2011) Faith and Philosophy contains an excellent article by Jeff Speaks on some difficulties related to establishing the consistency of certain claims (he uses as examples the existence of human freedom and the existence of evil) with the existence of an Anselmian God. The basic idea is this: since an Anselmian God is, by definition, a necessary being, establishing the possibility of an Anselmian God is tantamount to establishing the necessary, and therefore actual, existence of an Anselmian God. But these compatibility arguments typically, in one way or another, assume the possibility, and so the actuality, of an Anselmian God. If we were allowed to assume this premise, our task would be extremely easy! We could argue as follows:

  1. God (actually) exists

  2. Evil (actually) exists

  3. Therefore,
  4. The existence of God is consistent with the existence of evil.

Piece of cake! Now I, of course, take this argument to be sound. In fact, I even think that some people (depending on their background beliefs) might be rational in allowing this argument to increase their confidence in the truth of (3). But clearly this argument cannot be used to respond to atheist arguments from evil against the existence of God. It is dialectically inadmissible in that context.

In his paper, Speaks argues that Warfield's argument for the compatibility of necessary omniscience with human freedom and Plantinga's free will defense are both a lot like this. That is, they both assume that, possibly, an Anselmian God exists. But if that assumption is admissible, then we could just use this simpler argument. But obviously we can't use this simpler argument, so the premise must be inadmissible. (This isn't exactly the way Speaks puts his points together; it's my interpretation of what his arguments actually show.)

Speaks states the "principal conclusion" of his paper as follows:

any argument for the compatibility of two propositions must also be an argument for the possibility of each of those propositions. Hence it is impossible to argue for the compatibility of two propositions, one of which is necessary if possible, without arguing for the truth of that proposition. (p. 291)

In this post, I'm going to push back. Specifically, I believe that the standard (Lewis-Stalnaker) semantics for subjunctive conditionals is flawed in its treatment of impossible antecedents, and that once we recognize this flaw for what it is, we can save these compatibility arguments (though, for reasons which will emerge, it might be better to call the modified arguments 'might' arguments, or some such). I should note that my suggestion is in some ways similar to a suggestion Speaks makes at the end of his paper, namely, that if we had a notion of some sort of asymmetric 'dependence' relation which could obtain between necessary truths, we might show that God's existence and human freedom are, in this sense, independent. But my solution will require only subjunctive conditionals, and not these additional dependence relations.

I'm going to use Plantinga's Free Will Defense as my example since it's more familiar to me, and probably to most readers, than Warfield's argument. I'll use the following symbols:





□→The 'would' subjunctive, as in 'If I were to flip this coin, it would land either heads or tails.'
◊→The 'might' subjunctive, as in 'If I were to flip this coin, it might land heads.'
GThe proposition that necessarily, an omnipotent, omniscient, and morally perfect being exists.
EThe proposition that evil exists
TWDThe proposition that every creaturely essence suffers trans-world depravity (if you don't know what that means, you should read Plantinga's The Nature of Necessity, but I think you'll be able to understand most of what I say without it).

Now, we can think of the argument from evil as going like this:

  1. G □→ ~E

  2. E

  3. Therefore,
  4. ~G

This is clearly valid (subjunctive conditionals support modus tollens). Plantinga's free will defense is meant to be an argument for the negation of premise (1). Now, if the conditional is truly a 'would' conditional (rather than a 'would probably' conditional or some such), then (1) is inconsistent with the following claim:
(FWD) G ◊→ E

That is, if it's really true that if God existed there (definitely) wouldn't be evil, then it must not be true that if God existed there might be evil. Plantinga's free will defense can be construed as an argument for this proposition (which is why I've labeled the proposition 'FWD').

Now, slightly modifying Plantinga, we can run the argument as follows

  1. G ◊→ TWD ("[even] if God existed, all creaturely natures might [still] suffer trans-world depravity")

  2. (G & TWD) ◊→ E ("if God existed and all creaturely natures suffered transworld depravity, then there might be evil in the world")

  3. Therefore,
  4. G ◊→ E ("[even] if there was a God, there might [still] be evil in the world")

Here's where Speaks' problem comes up: on the standard semantics p ◊→ q is equivalent to ◊(p & q) which, of course, entails both ◊p and ◊q. So if G is impossible, the argument is unsound. But if G is possible, then G, and we can take the easy way out, as above.

This implication of the standard semantics is, I submit, incorrect. I think the following conditional is true:

If some humans were able to draw round squares, I might be able to draw round squares.

Furthermore, I think that mereological universalism is necessarily false, but I think the following conditional is true:
If mereological universalism were true, then my body might be part of an object which also had an alien space ship as a part.

In fact, as Trenton Merricks points out near the beginning of his Objects and Persons, pointing out the truth of conditionals like this is an important strategy in metaphysical argument; the fact that this conditional is true is one of my reasons for believing that mereological universalism is necessarily false. But if these sorts of 'might' conditionals can be true, then it seems that premise (1) in my rendition of Plantinga's free will defense might very well be accepted (consistently) by an atheist after all.

(cross-posted at The Prosblogion)

Posted by Kenny at November 19, 2011 12:51 PM
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