## Thursday, May 6, 2010

### Van Inwagen, Pruss, and the PSR

Alexander Pruss has just posted an interesting (albeit concise) reply to Peter van Inwagen's objection to the PSR. Van Inwagen relies on the premise that:

1. No contingent fact can be explained by a necessary fact.

(1), however, seems implausible. Consider the following proposition: "George couldn't divide the fourteen peanuts among the three party-goers because 14 is not divisible by 3."

Technically, 14 is divisible by 3, but I think what Pruss means is that 14 divided by 3 does not give us a number without a fraction (14 divided by 3 equals 4 2/3). What we have, then, is a necessary fact - 14 cannot be divided into 3 equal shares without fractions - that explains a contingent fact - namely, that George wishes to divide the peanuts equally among himself and his guests.

Now, it might be said that there additional, contingent facts about this instance. George and his friends do not go to the party by any necessity, nor do they exists by necessity, nor are there 14 peanuts by necessity. Each of these facts is contingent. However, what Pruss' illustration does show is that a necessary fact can at least partially explain a contingent fact. I'm not sure if anyone doubts this, though, or if it really ends up as a defense of the strong version of the PSR at all. There are many weaker versions of the PSR (I myself have defended a number of them), so we might just add another to the list in which all contingent facts have at least a partial explanation.

1. You said:

"What we have, then, is a necessary fact - 14 cannot be divided into 3 equal shares without fractions - that explains a contingent fact - namely, that George wishes to divide the peanuts equally among himself and his guests."

How does this mathematical truth explain George's wish as mentioned above?

2. I take Pruss to be thinking of a necessary mathematical axiom as "explaining" some contingent fact insofar as it serves as a necessary precondition for that fact's instantiation.

If X, then Y.

But, if ~X, does Y obtain? If not, then the reality of X appears to serve as a (at least partial) explanation for Y.

3. George's wish is itself an additional contingent fact, but I don't think Pruss is suggesting that the mathematical truth in question explains that.