Friday, May 20, 2011

The Weak Weak Principle of Sufficient Reason

Richard Gale and I have shown that once you grant:

  • WPSR: for all contingent truths p, it is possible that p has an explanation,
the existence of a necessary and causally efficacious being necessarily follows (given some plausible necessary truths as premises). WPSR is the weak PSR. The strong PSR claims that every contingent truth has an explanation. The WPSR merely claims that every contingent truth can be explained, i.e., that there is some possible world where it is explained, though it prima facie leaves open the possibility that some contingent truth actually lacks an explanation, though it could have had one. One might worry about the WPSR because one might think that our world contains some in principle inexplicable processes. If that is one's worry, one might be attracted to:
  • WWPSR: possibly WPSR is true.
WWPSR says that WPSR, while perhaps not true at the actual world, is true at some world. But here is something that occurred to me after talking with Richard Gale, because he mentioned that a strength of our argument is that it works in every world: WWPSR is enough to show the existence of a necessary being that is necessarily explanatorily efficacious over at least one contingent proposition. For we can just run our argument in the world, w1, in which WPSR holds. And then we get that in that world there is a necessary being that explains all contingent truths there. Call that being Nec. By S5, that being exists in all worlds. So far the argument is pretty rigorous. The rest will be a bit handwavy.

Nec explains at least one contingent truth in every world. For Nec explains at least one contingent truth at w1 (as it explains them all there). So suppose for a reductio that it is a contingent proposition that Nec explains at least one contingent truth. Call that proposition e. Since it is contingent, and it is true at w1, Nec must explain e at w1. But arguably it would be circular for an exercise of explanatory efficacy to explain why there is at least one piece of explanatory efficacy.

Moreover, since Nec exists in every world, what could prevent his activity from having explanatory efficacy in some world w2? Whatever that is, it is something that he must have squelched in w1. So in w2, presumably he did not squelch that thing or event, and that seems to be a contingent truth at w2 that he had explanatory efficacy over.


Drew said...

Are there any articles I can read that give a defense of S5. I have been hearing a lot about how it is incompatible with actualism, and I would like to hear your take on it.

Alexander R Pruss said...

See my possible worlds book, especially the section near the beginning on S5, and the sections near the end on identity.

ryanb said...


There was a similar question to the one you take up here that I had to think about a while back when I was thinking about kalam arguments run on other possible worlds. The question I had to think about was how to argue from the existence of a necessary being which is causally responsible for some if not all facts in some other possible world to a necessary being with similar features in the actual world. I'm wondering if the solutions to these questions might be parallel.

David Parker said...
This comment has been removed by the author.
David Parker said...

Let me see if I am getting this right:

If one says that WPSR is false in the actual world...then they claim the actual BCCF has some p that has no explaining q in any possible world.

But there are possible worlds where the BCCF doesn't include that p. So the WWPSR just says that there is some BCCF out there without any lonely p. Correct?

Alexander R Pruss said...



Alexander R Pruss said...

My link should work now.