Craig, conventionalism, and voluntarism

At his personal Facebook page and also at the Reasonable Faith Facebook page, William Lane Craig briefly comments on my First Things review of his book God Over All.  Bill says:

For our philosophically inclined readers who are interested in divine aseity and Platonism, here's a great little philosophical exercise: Where does this review by Ed Feser go wrong? (Hint: do I hold that mathematical truth is conventional? Why think I should?)

End quote.  Bill evidently thinks I have misunderstood him.  However, it seems he has misunderstood me.  I neither said nor implied in my review that Bill is a conventionalist about mathematics.  What I did say – and I put great emphasis on the point and developed it at some length – is that his position is in danger of collapsing into a kind of divine voluntarism about mathematics.  It isn’t human convention, but divine arbitrary stipulation, that seems in his view to be the foundation of mathematical truth.

Mind you, I also made it clear that I don’t think Bill wants to end up with such a voluntarist position either.  But I think his view inadvertently opens the door to voluntarism, for reasons I spell out in the review.  I also explain why I think this is a problem.

As near as I can tell, Bill’s misunderstanding is based on a line in the review where I say: “For the Aristotelian, the Platonist is correct to regard mathematics as a description of objective reality rather than as mere linguistic convention.”

But it would be a mistake to infer from that line that I think that Bill takes a conventionalist view about mathematics.  Again, I didn’t think that and I wasn’t saying that.  First, the context in which that remark occurs is a general explanation of what an Aristotelian approach to mathematics involves and how it contrasts with the best-known alternative positions.  The line in question wasn’t meant to contrast the Aristotelian position with Bill’s views, specifically, but rather to contrast it with the best-known versions of anti-realism.

Second, I now see that what I originally wrote had been slightly altered by the copy editor in a way that, unfortunately, I overlooked when I went over the proofs.  In my original draft, the sentence in question ended: “…a description of objective reality rather than mere linguistic convention or the like.”  Those last three words were intended to indicate that convention is not the only thing an anti-realist might regard as the ground of mathematical truth.  (And I had already made it clear earlier in the review that anti-realism comes in many versions.)

Unfortunately, the copy editor apparently thought those three words otiose and removed them, and, again, I failed to notice the change when reviewing the proofs.  (I’m not blaming the copy editor, but myself.  These things happen, and copy editors have saved me from many infelicities over the years!)  

Anyway, as I say, the rest of the review makes it clear that it is the threat of voluntarism that is the problem.  I also point out that there are two serious lacunae in Bill’s discussion: first, too superficial a treatment of the Aristotelian realist approach to mathematics; and, second, a failure to consider how absolutely central the doctrine of divine simplicity is to the way the classical theist tradition understands both divine aseity and divine conceptualism.

These three issues – voluntarism, Aristotelian realism, and divine simplicity – are the ones my critique of Bill’s position hinges on.  It has nothing to do with conventionalism. 

By the way, as I hope my review also made clear, none of this should keep anyone from reading Bill’s book.  On the contrary, anyone interested in these issues ought to read it.  You will always profit from reading and engaging with Bill’s work, even when you end up disagreeing with him.