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...
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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.

Unknown said...
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Unknown said...

I have an objection to your statement:

“Whereas the atheistic opponents could have been justified in not granting PSR to traditional cosmological arguers, it would seem unreasonable for them not to grant us W-PSR.”

Which appears here:

Objection: WPSR implies the PSR
Consider proposition A: (Possibly x) & (x does not exist)
What reason can possibly be cited for proposition A being true? The only answer I can imagine is:
Proposition B: In a world in which A is true, none of the possible reasons for x obtain.

However, B is only true if the PSR is true and at the point one is considering the WPSR, one should be open to the truth or falsehood of the PSR. If the PSR is false, then brute contingent facts possibly exist. If x is a brute contingent fact in any possible world, than proposition A necessarily has no reason, and the WPSR is false.

If you don't mind, I'd also like your reaction to my objection to an intuitive argument for the PSR.

Objection: All causes are reasons, but not all reasons are causes.

My contention: acceptance of the PSR based on intuition is grounded in causation.

Everything in the world of experience has a cause, and the cause of x can be considered the reason for x (i.e. all causes are reasons). However the term “reason” is broader than the term “cause” (i.e. not all reasons are causes), but there is no basis for assuming the broader term (there is a reason) is true just because the narrower term (there is a cause) is true.

Conclusion: an argument for the PSR based on intuition should fail (and if it succeeds in convincing someone, they have been tricked with semantics). We are, in fact, only justified in assuming there are reasons for contingent things that have been caused, and are not justified (by this argument, at least) in assuming brute contingent facts necessarily do not exist.

Alexander R Pruss said...

1. Yes, WPSR implies PSR. But maybe that's not an objection to WPSR, but a reason to accept PSR.

2. If our intuitions are driven by thinking about causation, then we have an intuition that every contingent state of affairs has a cause. It follows a fortiori that every contingent state of affairs has a reason.

Unknown said...

Regarding 1: this seems vacuous. All we can conclude is WPSR iff PSR. All I see is a setup to try and trick someone into accepting the PSR by disingenuously suggesting they accept the WPSR.
2. No it doesn't, because we have no experience with uncaused states of affairs, which means we have no justification to assume such things have a reason.

Alexander R Pruss said...

In every valid argument, the conjunction of the premises logically entails the conclusion. That doesn't make every valid argument useless.

It seems we have good reason to think there aren't any uncaused states of affairs, given our lack of experience o them.

Unknown said...

I agree we have good reason to think there are no uncaused states of affairs. But this intuition leads to the conclusion there is an infinite chain of causes. Unless we are willing to accept that, we have to start making assumptions that do not match intuition. One such assumption is that brute contingent facts are metaphysically possible. Alternatively, we may assume the PSR is true. Either assumption leads to a coherent ontology.

Alexander R Pruss said...

We only have good reason to think there are no uncaused *contingent* states of affairs. We know of a lot of states of affairs, such as two plus two being four, that seem to have no cause.

And so no regress is generated.

Unknown said...
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Unknown said...

I'd argue that we should first consider why we have this network of causation in the universe. It seems abundantly clear that the answer is: natural law. So it's not unreasonable to assume causation is contingent upon the natural law of the universe (so we can infer that we have the "uncaused *contingent* states of affairs" you spoke of). Under that assumption, there is no reason to assume that the "cause of causation" needs a cause.

To insist that the intra-universe causation implies the universe is caused would be bordering on a fallacy of composition. Of course, you can assume that causation is a metaphysical necessity, but I don't see what grounds you'd have for doing so.

Johannes said...

Just to share the results of some work on the subject, not to start a conversation.

For visual types, the case can be easily seen using two possible worlds:

W-PSR: For any proposition, p, and any world, w, if p is in w’s Big Conjunctive Fact, then there is some possible world, w1, and proposition, q, such that w1’s Big Conjunctive Fact contains p and q and the proposition that q explains p.

Theist's world Wt (w1):

BCCFt = BCCFr + q1 = pt = p1
BCNFt = BCNFr + N1

q1 = free creative decision by NB, necessary and sufficient, in conjunction with N1, to explain pt.
N1 = Necessary Being (NB) exists.

Atheist's world Wa (w):

BCCFa = BCCFr + ¬q1 = pa
BCNFa = BCNFr + ¬N1

It is evident that pa is not explainable in ANY possible world, defined as a maximal, compossible conjunction of abstract propositions, since, due to the requirement of maximality, it contains ¬q1, which is incompatible with the explanatory proposition q1. Therefore an atheist must deny W-PSR. Now, since an atheist holds pa as a contingent truth, and it is impossible that pa has an explanation, then an atheist must hold that there are contingent truths that cannot possibly have an explanation, and consequently that W-PSR cannot possibly be true. Thus an atheist must deny WW-PSR as well.

BTW, from the above and the beginning of the chain of reasoning at the end of your "Ex Nihilo Nihil Fit" paper, it can be easily seen that an atheist must also deny the weaker version of Brouwer axiom "If p holds contingently, then it is possible for p to be both possible and false." At least, he must deny its applicability to any proposition involving the explanation of a world's BCCF or the negation of that explanation.

"For suppose that the PSR is in fact false. Let p be a contingent proposition, then, which has no explanation. Let q be the proposition that p holds and has no explanation. Since p is contingent, so is q. Thus, there is a possible world w at which q is false. Let us transport ourselves to that world. In that world, the proposition q is false, but it is still going to be possible. (This uses the Brouwer axiom which is weaker than S5."

Relating this passage to Wa above:

p = BCCFr
q = BCCFr AND ¬q1
¬q = ¬BCCFr OR q1

Therefore there are 3 possible worlds at which q is false, i.e. ¬q is true:

¬BCCFr, q1 = WG = God, no universe. Explained by a free divine decision not to create.
In WG q is not possible, since contingent beings can exist only by a free divine decision to create them.

¬BCCFr, ¬q1 = W0 = no God, no universe. Quite self-explanatory.
In W0 q is repugnant to reason, since the universe would arise spontaneously out of true nothing (not quantum void).

BCCFr, q1 = Wt = God, universe. Explained by a free divine decision to create.
In Wt q is not possible for the same reason than in WG.