Thursday, May 6, 2010

Explaining the contingent with the necessary

Van Inwagen's argument against the Principle of Sufficient Reason requires the principle that:

  1. No necessary truth can explain a contingent one.
Note, though, that in ordinary language we feel quite free to violate (1) by saying things like:
  1. George couldn't divide the fourteen peanuts among the three party-goers because 14 is not divisible by 3.
  2. Arrow's Theorem explains why the United States' two-party system works better than Canada's electoral system.
  3. It takes a long time to find an optimal path between cities because the Traveling Salesman Problem is NP-hard.
  4. Patricia when told that she could have as much land as she could enclose with a four-mile-long string was wise to put the string in the shape of a circle because of the isoperimetric inequality.
  5. The distribution of error in the experiment was Gaussian because of the Central Limit Theorem.
Now, in all of these cases Van Inwagen might argue that there are omitted contingent aspects of the explanation. It is true that the explanation offered is in some way not complete. But it is, nonetheless, an explanation, and that seems to be enough to show that (1) as it stands is false.

8 comments:

Marc said...

In some of your work on the PSR, you observed that an adequate response to van Inwagen's objection might need to appeal to a necessarily existent agent (like God). It's interesting that your proposed counterexamples to (1) don't rely on such an appeal.

What about an objection as follows?

With respect to (2), suppose van Inwagen agreed that it's contingent, but argued that it's actually a specific expression of a more general necessary truth in disguise: i.e., "it's impossible to divide 14 by 3" or perhaps "it's not within anyone's power to divide 14 by 3." These two propositions individually explain and entail that, necessarily, any attempt to divide 14 by 3 will fail. So while George's particular case obtained contingently, the precise manner in which it obtained--"George couldn't divide"--is explained and entailed by a more general necessary truth.

I don't find myself convinced by such an objection, however.

Mike Almeida said...

14 isn't divisible by 3?

Dan Johnson said...

None of your examples, as far as I can tell, are examples of causal explanation.

I'm not sure whether or how that bears on your point, but it seems somehow important.

Hassan Abdillah said...

Professor Pruss, is it necessary for you to defend the PSR in order for your (and Gale's) cosmological argument to go through? After all, you only use w-PSR as a premise.

Thanks!
Hassan

ydoaPs said...

This post is actually fairly irrelevant to the point Van Inwagen is making. His entire objection is about the case where *all* of the grounding explanans are necessary fact. You can't derive a contingent truth from *only* necessary truths. That's itself a necessary truth.

The idea of the objection to PSR can be explicated by a branching reasoning structure.

Either the chain of explanation is infinite with every explanans being an explanandum with its own explanans, or the chain has some sort of ending in grounding facts. If the chain of explanation is infinite, then PSR is false.

If the chain has an ending in grounding facts, that set of facts is either composed entirely of necessary facts or is composed of a mixture of necessary facts and contingent facts. If it's a mixture, then there are contingent facts without explanation, so PSR is false.

If it's all necessary is where this blog post is trying to be relevant. If the set of grounding facts is composed entirely of necessary facts, then we have modal collapse.

But, as Pruss points out, all of his examples involve a mixture of contingent and necessary facts to explain the contingent fact. As such, it misses the point.

Alexander R Pruss said...

Mr. Abdilla:

The W-PSR implies the PSR, so yes.

ydoaPs:

Could be.

N McNeely said...

Could you explicate that 'could be' a little bit more? It's not clear to what you're responding. Nor is it clear what it is you mean.

Alexander R Pruss said...

Could be that my examples miss the point.