Thomas Metcalf

Richard Gale and Alexander Pruss have recently-ish (Religious Studies 35 (461-476)) offered a cosmological argument that takes advantage of a weak Principle of Sufficient Reason to explain every contingent existential fact about our world. I'm going to paraphrase what I remember of it here because Religious Studies's e-journal Web site is down.

Here's the Strong Principle of Sufficient Reason, or S-PSR. Let p be any contingent fact about the world and the function E(x) be "there is an explanation for x":

For every p, E(p).

This is kind of a strong thesis. Every contingent fact about the world has an explanation, according to S-PSR. But some people might not willingly assent to that principle, because it's so strong. Is it really obvious that every fact about the world has an explanation? To those who say "no", Gale and Pruss offer a different principle, W-PSR or the Weak Principle of Sufficient Reason.

For every p, it is logically possible that E(p).

All this says is that for any contingent fact, it's possible that the fact has an explanation. Gale and Pruss think this principle is more intuitively acceptable than S-PSR.

Now think about every contingent fact about our universe. Let's imagine they're all conjoined together with ampersands into one big, conjunctive contingent fact or BCCF. This long proposition reports every contingent fact about the actual world.

Now according to W-PSR, it is logically possible that there is an explanation for our world's BCCF. But this entails that there is an explanation for our BCCF in the actual world. For suppose that there is some possible world w in which there is an explanation for our BCCF. There can't be an explanation for a fact without the fact itself, though; otherwise, what would the explanation be explaining? Therefore, in this other possible world, the BCCF obtains. But having distinct BCCFs is all that individuates possible worlds, so the world that contains an explanation for our BCCF is in fact the actual world. Therefore, there is an explanation in the actual world for our BCCF.

Gale and Pruss conclude with some (in my opinion rather dubious) reasoning that the explanation for our BCCF is a monotheistic God. I'm not too concerned with those steps yet. (Let's call those Part 2.) Right now I want to develop what follows from our discoveries about how the W-PSR when applied to our BCCF entails the S-PSR (applied to our BCCF).

Here's my suggestion. It seems to me that if W-PSR is intuitively plausible, a related principle W-PIR (Weak Principle of Insufficient Reason) is likewise plausible:

For every p, it is logically possible that ~E(p).

That means that for every fact about the universe, it's possible that the fact is true without an explanation. To deny this is to affirm S-PSR, and I don't think such an affirmation is warranted. Now what follows from W-PIR as applied to our BCCF? As you might be able to guess, an S-PIR as applied to our BCCF follows.

If W-PIR is true, then there is a possible world in which our BCCF obtains but with no explanation. If that's so, then our BCCF in the actual world must have obtained with no explanation, because the only thing that individuates possible worlds is their BCCFs. So our BCCF has no explanation, and this is inconsistent with theism and with Gale and Pruss's argument.

I guess, then, the question is whether W-PSR is significantly more intuitively plausible than W-PIR. I don't think it's clear that it is. It seems like for every fact about the universe, it's possible that it has an explanation and it's possible that it doesn't have an explanation. Unless we get to assert S-PSR, we can't deny W-PIR.

This completes the discussion of Part 1. I need to go back and review a couple of articles because there might be some responses to what I've written above, but I'd be interested to see others' evaluations of Gale and Pruss's reasoning, and of my own.

As for Part 2, maybe I'll get to that later.

Silent Dave

I think that the problem is with W-PSR itself, in that its negation,

Fot at least one p, it is not logically possible that E(p)

is arguably more defendable. On the one hand, it is more difficult to establish a logical impossibility than a logical possibility; but on the other hand, there are a bloody lot of contingent facts out there -- and that number increases exponentially when one takes into account conjunctive contingent facts, as obviously Gale and Pruss must do. It would only take one such fact to necessarily not have an explanation to establish ~W-PSR.


Dave

Jobar

I think that we can relegate both S-PSR and W-PSR to John Bell, for embalming and burial.

The_Ist

Hmmm, interesting. I find W-PSR more intuitively satisfying than W-PIR. If p is defined as a contingent fact, then could not a sufficient E(p) be given for every p, based specifically on what each different p is contigent upon? If A is contingent on B, is not B an explanation for A?

Thomas Metcalf

Originally posted by Silent Dave :

Indeed, the negation of "for every p, it is logically possible that E(p)" is "there is some p such that it is necessary that ~E(p)". Here's a derivation to make it explicit, where (Ex) is the existential quantifier, <> is the possibility operator and [] is the necessity operator, and X is the predicate "has an explanation":

1. ~(p)(<>Xp) (Negation of (p)(<>Xp).)
2. (Ep)~(<>Xp)
3. (Ep)[]~Xp

But I wonder what the conditions are for there to be this necessarily unexplained fact in our world. I think for it to be necessarily unexplained, there'd have to be a contradiction in saying "p and E(p)", and I can't think of any contingent fact p like that. There's the matter of indeterministic events, which do produce contingent facts, but Gale and Pruss would say (and I believe have said) that W-PSR really only applies to facts that are explainable in principle. Then again, that sounds an awful lot like saying it only applies to logically possibly explained facts, which is what it asserts exist in the first place. I think I should do more research; there's probably a more defensible version of W-PSR that doesn't have this strange question-begging character.

Thomas Metcalf

Originally posted by The_Ist :

This is an interesting point. But I think we can legitimately draw a distinction between contingent and dependent facts, and to say that all contingent facts are contingent upon something seems to commit us to S-PSR at the outset. A contingent fact, contrary to the common English usage of "contingent", is simply a fact that obtains in some possible worlds but not in all. So if in some possible world, some fact happened to obtain without an explanation, that fact would still be a contingent fact (if it didn't obtain in every possible world) -- even if it wasn't a dependent fact.

HRG

Note that the set of all contingent facts about the universe need not be finite (e.g. if space is not discrete). In this case BCCF is not well defined - as an infinite conjunction - and infinite regresses of explanations are conceivable.

IMHO, it is certainly not logically required that space is not discrete.

Regards,
HRG.

Thomas Metcalf

I'm not sure my objection concerning W-PIR really works. Here's W-PIR: For every contingent fact p, there is a possible world in which p has no explanation.

When we say that for every contingent fact p, there's a possible world in which p doesn't have an explanation, I don't think that entails that there's a possible world in which our BCCF obtains but doesn't have an explanation. All it entails is that there's a possible world in which our BCCF doesn't have an explanation. But the fact that there's no explanation for our BCCF in another possible world doesn't mean our BCCF obtains nonetheless -- in fact, it suggests that it probably doesn't obtain in that possible world.

I wonder if this principle is intuitively appealing:

W-PIR2: For every contingent fact p, there is a possible world in which p obtains but p has no explanation.

(p)<>(Cp & Op & ~Xp) ... where C is the predicate "contingent", O is the predicate "obtains" and X is the predicate "there is an explanation for", while "p" ranges over facts

Now the denial of this principle,

~(p)<>(Cp & Op & ~Xp)

yields

(Ep)~<>(Cp & Op & ~Xp)

which means that for some contingent fact p, there's no possible world in which p obtains and there's no explanation for p. This, itself, is a strong thesis, that some fact just must have an explanation whenever it obtains, and it's not clear what it would be about the fact itself that requires it to have an explanation in every possible world in which it obtains.

Maybe an example of such a fact would be "this fact has an explanation." But perhaps a case can be made that this fact isn't really a fact at all, or that it couldn't possibly be explained by a contingent fact, or that "p" should only range over non-self-referential facts. Those don't seem to be particularly counter-intuitive considerations. But are there other contingent facts that must have an explanation in every possible world in which they obtain?


Okay, here's another objection to Gale and Pruss. It seems that we're obligated if we accept W-PSR to say that there's a possible world in which the BCCF has an explanation, and that the BCCF therefore obtains in this possible world. Fine. But that doesn't entail that the BCCF reports the only contingent facts in that other world. That is, if the actual world contains the BCCF, another distinct possible world would be our BCCF plus some other fact. A case could be made that one of the conjuncts of our BCCF is "no other facts obtain than the ones already mentioned in this conjunctive fact", but that's another weird self-referential fact, and I'm not sure that's legitimate.

Thomas Metcalf

Originally posted by HRG :

In fact, I think it is inescapable that there be an infinite number of contingent facts about the universe. If fact p obtains, then then fact "p is true" also obtains, as does the fact "'p is true' is true", etc. Although in this case it seems easy for one explanation to explain all those facts simply by explaining p.

Also, if counterfactual conditionals are true and supervene on something about the universe, then we could have an infinite number of conjuncts. "If object 1 were placed in position 2, it would produce effect 3", "If object 2 were placed in position 2, it would produce effect 4", etc.

The_Ist

I see your point. It would seem that if being a contingent fact intrinsically entailed having an explanation, then their argument would beg the question.

I guess I don’t know enough about this argument to comment further. For example, what do they consider a valid explanation of a contingent fact?