Richard Gale and Alexander Pruss have advanced an
interesting update on the traditional Cosmological Argument for the existence
of God.[i]
This argument begins with some definitions.
A possible world
is a “maximal, compossible conjunction of abstract propositions. It is maximal
in that, for every proposition p, either p is a conjunct in this conjunction or
its negation, not-p, is, and it is compossible in that it is conceptually or
logically possible that all of the conjuncts be true.”[ii]
The Big Conjunctive
Fact for a possible world consists of the conjunction of all of the
propositions that would be true if that world were the actual world. Some of these are necessarily true. But the
Big Conjunctive Fact of each possible world also contains propositions that are
contingently true- true in some possible worlds and not in others. Each
possible world contains a unique conjunction of contingent propositions. Gale-Pruss
refer to this as the Big Conjunctive Contingent
Fact, or BCCF. It is the BCCF of a world that individuates that world,
distinguishing it from all other possible worlds. Let p be the BCCF of the actual world.
Is there an explanation for p- an explanation for why this particular set of contingent facts
is the case, rather than not?
At this point the defender of a traditional Cosmological
Argument would introduce the Principle of Sufficient Reason:
For every proposition, p, if p is
true, then there is a proposition, q, that explains p.
But it may not be reasonable to expect the skeptic to accept
this principle. In its stead, Gale-Pruss offer a weaker form of the Principle
of Sufficient Reason:
For any proposition, p, if p is
true, then it is possible that there
exists a proposition, q, such that q explains p.
Unlike traditional cosmological arguments, Gale-Pruss’
argument does not require us to assume that there actually is an explanation for p. It only needs to be possible that there is such an explanation. Gale-Pruss assert that
it is: There is some possible world, W1, in which p is true, and in W1, some proposition q is true,
and q explains p.
Now, are W1 and the actual world the same world? Gale-Pruss
insist that they are. For p is the Big Conjunctive Contingent Fact of the actual
world; p is true in W1, and the BCCF of a given world is what individuates it. Therefore,
there is some proposition q that is true in the actual world and explains p,
the BCCF of the actual world. Now, what sort of explanation is it?
According to Gale-Pruss there are only two kinds of
explanation: Scientific, and personal. Personal explanations are explanations
in terms of the intentions of some person. But q cannot be a scientific explanation.
A scientific explanation “must contain some law-like proposition, as well as a
proposition reporting a state of affairs at some time.”[iii]
But these are contingent propositions, and therefore members of p. Yet they
purport to explain p, as well as each proposition contained within p, which
means they would explain themselves, and this is impossible.
Therefore q must be a personal explanation. Now what sort of
person does q invoke? It cannot be a contingently existing being, since a
proposition asserting the existence of a contingently existing being would be
part of p and once again, q would explain itself. So q explains p, the Big Conjunctive
Contingent Fact of the actual world, by reference to the intentional action of
a necessary being. The proposition q, then, asserts something like this:
“There
exists a necessary being who intentionally creates the world.” [iv]
Analysis
Gale-Pruss treat q as though it is not one of the
member-conjuncts of p. This is well motivated. For one thing, if q were
contained within p, the Big Conjunctive Contingent Fact of the actual world,
then q would be part of the very state of affairs that it hopes to explain. But
worse than this, to define p as the BCCF of the actual world, and then to presume
that q is contained within p, is to presume at the outset that the actual world
is explained by the intentions of a necessary being, and this is what the
argument seeks to prove.
And yet, as Gale-Pruss acknowledge, q is a contingent
proposition,[v]
and so prima facie, one would think
that for any possible world, either it, or its negation, is a member-conjunct
of that world’s Big Conjunctive Contingent Fact.[vi]
But let us set this observation aside and follow Gale-Pruss in treating q as
though it is not contained within p.
Since q is a contingent proposition, there are possible
worlds in which it is not true. That means that in addition to W1, which
contains p and in which p is explained by q, there is another possible world,
W2, which contains p, and in which p is not
explained by q, because it is not true in W2 that there is a necessary being
who intentionally creates that world. As it turns out, if a Big Conjunctive
Contingent Fact does not contain either q, or its negation, then pace Gale and Pruss, it does not
individuate a possible world.
This means that a world’s containing p does not imply that
it is identical with the actual world. Gale and Pruss are not entitled to infer,
from the fact that p is true in W1, that W1 is identical with the actual world,
since p is true in W2 as well.
The actual world is identical with one of these worlds, W1 or
W2, but the Gale-Pruss argument leaves us with no reason to prefer one over the
other. Since they hoped to prove that the existence of the actual world is
explained by the intentions of a necessary being, and they can do this only if
they can show that the actual world is identical with W1 rather than W2, Gale
and Pruss’ argument fails.
Department of Philosophy
Sacramento State
[i] “A
New Cosmological Argument,” Richard M. Gale and Alexander R. Pruss; Religious
Studies, vol 35, Number 4 (Dec 1999), pp. 461-476
[ii] “A
New Cosmological Argument,” p. 461. For a more detailed explanation of the
notion of a possible world, see https://plato.stanford.edu/entries/possible-worlds/.
[iii]
Ibid. p 465
[iv]
Gale-Pruss realize that they have not proven the existence of the God of
Western theism, since they have not proven that this being is omniscient,
omnipotent, and benevolent. They require only that God be powerful enough to
create the actual world. But they think- and I agree- that their more limited
conclusion is still an interesting one.
[v] In
fact they argue for this claim on p. 466ff
[vi] It
seems likely that Gale-Pruss are thinking of q as having some kind of special
status that sets it apart from ordinary contingent facts. Perhaps they wish to
say that it is a supernatural fact,
because it reports the intentions of a necessary being. (On p. 468 they claim
that a necessary being is a supernatural one.) In this case p is really the Big
Conjunctive Contingent Natural Fact.
I do not have space to pursue this suggestion here, which does not, in any
case, seem to affect my analysis.
Hello David,
ReplyDeleteI think some objections to your argument might be:
1. Even if p and q are contingent, it doesn't follow that there is a world where q is false but p is true.
I don't think this is a strong objection, since you can modify the argument to address that issue.
2. The proposition Q in the actual world A is something like:
Q(A): There is a necessary personal being who freely creates a world with such-and-such properties.
The properties depend on A, or generally on the world, so for each world W, there would be a Q(W), and sometimes Q(W)=/=Q(W') (they might be the same if some other free agent makes the worlds different).
So, if there is a world W2 at which p is true but Q(A) is false, then p would be explained in W2 by Q(W2). And the BCCF* (more below) doesn't contain either Q(A) or its negation, but it implies ¬Q(A).
This objection looks stronger, given a theistic take on personal explanations.
With regard to the BCCF*, I argued on my blog that the BCCF is incoherent (ht tps://angramainyusblog.blogspot.com/2012/08/downloadin.html#BCCF ), but Alexander Pruss gave an alternative to the BCCF in a more recent version of the cosmological argument namely the the BCCF* (see ht tps://bearspace.baylor.edu/Alexander_Pruss/www/papers/LCA.html ).
I don't know whether the BCCF* is coherent. I argued (same link) for suspending judgment on whether it's coherent, and in any case, I reject the cosmological argument on other, independent grounds, but assuming your argument can get around the objections 1. and 2. above, do you think a modified version could also work against the BCCF*?
Hello Angra. Thank you for your very thoughtful comments. Here are my responses. (It seems I must use more than one field to post them.)
ReplyDelete"1. Even if p and q are contingent, it doesn't follow that there is a world where q is false but p is true."
My assumption was that the disjunction (q or not-q) is true of every possible world, which means it is true in the actual world. Obviously Gale-Pruss think it is possible that there is an explanation for the existence of the natural world- hence W1, in which the actual world’s BCCF (p) is true, and q is true as well, where q explains the truth of p by reference to the intentions of a necessary being.
But they are not allowed to assume that q, rather than not-q, is true in the actual world without begging the question. They must leave open the possibility that q is false in the actual world, which means allowing for a possible world W2 in which p is true and q is false. If there is no such possible world, they owe us an argument to that effect.
"2. The proposition Q in the actual world A is something like:
Q(A): There is a necessary personal being who freely creates a world with such-and-such properties."
Well, perhaps we should not say “a” world, i.e. some world or another, but the actual world in particular. But yes, for any possible world Wn, if *that* world is explained by the intentions of a necessary being, then Q(Wn) will be true. (I’m assuming that by an expression such as “Q(Wn)” you mean something substantially equivalent to “An explanation for the creation of Wn by reference to the intentions of a necessary being.”)
Let’s recall that a possible world is individuated by the BCCF that is true at that world, and that the BCCF that is true at the actual world is p. So the properties in question would seem to be enumerated by p. It seems to me, then, that your “Q(A)” is equivalent to “Q(p).” So an explanation for the creation of the actual world is an explanation for why p is the case. Do you agree?
Since Gale-Pruss stipulate that W1 is a possible world at which p is true, then using your symbolism, we could say that they stipulate the truth of Q(W1). And of course Gale-Pruss assert the identity of W1 with the actual world; if they are right to do this, then Q(A), as you put it, would also be true.
"The properties depend on A, or generally on the world, so for each world W, there would be a Q(W), and sometimes Q(W)=/=Q(W') (they might be the same if some other free agent makes the worlds different)."
The idea that the BCCF of a possible world is not entirely explained by the intentions of a necessary being, given the possibility that it also reflects the intentions of created beings, is interesting, but I thought mention of this possibility would introduce an unnecessary complication to my post.
But yes I agree, for any possible world (Wn), *if* the creation of that world is explained by the intentions of a necessary being, then Q(Wn) would be true. Wn would be individuated by its own BCCF. If Wn is not identical with the actual world, then Q(Wn) would not be identical to Q(p), since Wn would be individuated by some BCCF other than p.
Continued...
My response to Angra continued:
ReplyDelete"So, if there is a world W2 at which p is true but Q(A) is false, then p would be explained in W2 by Q(W2). And the BCCF* (more below) doesn't contain either Q(A) or its negation, but it implies ¬Q(A)."
I have a couple of responses.
(A) It cannot be the case at W2 that Q(A) is false but that p is explained by Q(W2), because if Q(A) is false, then Q(W2) would be false as well. Any explanation for the existence of W2- your Q(W2)- would also be an explanation for the existence of the actual world, Q(A).
If I understand your symbolism, Q(A) is the explanation for the creation of the actual world by reference to the intentions of a necessary being. But A, the actual world, is individuated by p, which is the BCCF of the actual world. So any explanation for the existence of A would be an explanation for the truth of p. Am I right so far?
Now according to the stipulation I made in my post, p is also the BCCF of W2. So any explanation for the existence of W2 would be an explanation for the truth of p. But then, an explanation for the existence of W2 would also explain the existence of the actual world. It cannot be the case that W2 is explained by the intentions of a necessary being without the actual world being similarly explicable; that is, to use your symbolism in the hope I understand it correctly, if Q(W2) is true then so is Q(A). Again, this is because the BCCFs of both worlds are identical.
(B) It was my stipulation that there is a possible world W2 at which p is true but q is false. This is the stipulation that the creation of W2 is not explained by the intentions of a necessary being. So in suggesting that Q(W2) is true, and thus that W2 is explained by the intentions of a necessary being, you appear to be denying me my stipulation. But I don’t see how you can be warranted in doing that without giving some grounds for asserting that there is, so to speak, a q for every possible world.
Now perhaps there is no possible world, the existence of which cannot be attributed to the intentions of a necessary being. (I personally think this is the case, though I very much wish to deny that attributing the existence of a world to the agency of a necessary being means giving an explanation for it.) In this case my stipulation of W2 would be vulnerable to criticism. But if there is no possible world W2 in which p is true and q false, then Gale-Pruss owe us an argument to that effect.
"I don't know whether the BCCF* is coherent. I argued (same link) for suspending judgment on whether it's coherent, and in any case, I reject the cosmological argument on other, independent grounds, but assuming your argument can get around the objections 1. and 2. above, do you think a modified version could also work against the BCCF*?"
I’m aware of objections to the notion of a BCCF; to the degree that I am familiar with the literature on this argument, that seems to be the main objection. My intuition is that the BCCF is in fact coherent, but I have no argument for this and I would not be bothered overly to find out that my intuition is incorrect. The argument I gave in my post hopefully succeeds even if the objections to the BCCF fail.
I was hoping to steer my discussion into the issue of whether there can be an explanation for the existence of the BCCF (there can’t be), and even better, into the issue of whether the story of divine creation gives an explanation for the BCCF (it doesn’t). But I didn’t get there.
In any case, I don’t think any modifications to the BCCF will affect my argument.
I will be interested to hear further responses from you (and others), but I have some other projects to finish before I can reply, so please don’t think I am ignoring you.
Here's the rest of my response:
Delete"It cannot be the case that W2 is explained by the intentions of a necessary being without the actual world being similarly explicable; that is, to use your symbolism in the hope I understand it correctly, if Q(W2) is true then so is Q(A). Again, this is because the BCCFs of both worlds are identical."
Let's say that there are two worlds, W1 and W2, in which NB (i.e., the necessary being) decides to engage in certain creation, and we have Q(W1) - which is true in W1 -, and Q(W2), which is true in W2.
Let's further say that Q(W1) is different from Q(W2). Might it be that the BCCF(W1)=BCCF(W2)?
If we exclude Q(W1) from BCCF(W1), and we exclude Q(W2) from BCCF(W2) (and we do), then I'm not sure what other contingent propositions we exclude, so I'm unsure.
For example, if we only exclude from the BCCF of each world a proposition like "A necessary being deliberately creates entities C1,...Cn, for such-and-such reason", but we include propositions like "C1, who was created by a necessary being for such-and-such reasons, fails to engage in X", then we're already implying that the necessary being in question created C1 for such-and-such reason.
On the other hand, if we do not include in the BCCF of a world propositions like "C1, who was created by a necessary being for such-and-such reasons, fails to engage in X", the following might be possible:
In W1, NB creates C1 for purpose X1. In W2, NB creates C1 for purpose X2=/=X1. Yet, it turns out that C1 behaves exactly in the same manner in both worlds, except in one of them C1 is going in line with NB's purpose, and in W2, C1 is doing something else. Would that entail that the BCCF is the same at W1 and W2, or is it different? I don't know.
I've come to think that the exclusion of q from being a conjunt of p might be an insurmountable problem for the argument, as the extent of the exclusion remains too vague.
"But I don’t see how you can be warranted in doing that without giving some grounds for asserting that there is, so to speak, a q for every possible world."
Right, a question is whether your stipulation is justified in this context, or the negation of that stipulation is justified in this context. Perhaps neither one of them is justified in this context.
"But if there is no possible world W2 in which p is true and q false, then Gale-Pruss owe us an argument to that effect."
But if there is a possible world W2 in which p is true and q false, wouldn't you also owe us an explanation?
A potential modification of your argument would be as follows: instead of asserting that "there is another possible world, W2, which contains p, and in which p is not explained by q, because it is not true in W2 that there is a necessary being who intentionally creates that world.", you might assert that perhaps, this is so, and that P-G have not explained why this is not so.
"I will be interested to hear further responses from you (and others), but I have some other projects to finish before I can reply, so please don’t think I am ignoring you."
No problem, and best wishes with your other projects.
David,
ReplyDeleteI'll have to split the posts as well:
"But they are not allowed to assume that q, rather than not-q, is true in the actual world without begging the question.
They must leave open the possibility that q is false in the actual world, which means allowing for a possible world W2 in which p is true and q is false."
They must leave open the epistemic possibility, but they don't need to grant that a metaphysical possibility.
"Well, perhaps we should not say “a” world, i.e. some world or another, but the actual world in particular."
I think if we include an explicit reference to the actual world in Q, that excludes it from being true in other worlds. Rather, what I was getting at is that a theist might hold that Q includes a partial description of the world that God creates. Maybe there are other possible worlds in which God creates the same, but they end up different in the end.
"(I’m assuming that by an expression such as “Q(Wn)” you mean something substantially equivalent to “An explanation for the creation of Wn by reference to the intentions of a necessary being.”"
Yes. Maybe it's more precise to say that it's a world with some of the properties of Wn.
"Let’s recall that a possible world is individuated by the BCCF that is true at that world, and that the BCCF that is true at the actual world is p. So the properties in question would seem to be enumerated by p. It seems to me, then, that your “Q(A)” is equivalent to “Q(p).” So an explanation for the creation of the actual world is an explanation for why p is the case. Do you agree?"
I had misread part of your argument, sorry. My bad.
It seems the later argument I mentioned is more different from the one you're challenging than I thought it was.
Back to your argument, I would say that while p lists those properties, p might also contain further properties of a world, which result not directly from God's action, but from the action of indeterministic creatures.
"If Wn is not identical with the actual world, then Q(Wn) would not be identical to Q(p), since Wn would be individuated by some BCCF other than p."
I don't know why, given possible nondeterminism. I'm not sure you can rule that out as an unnecessary complication.
"(A) It cannot be the case at W2 that Q(A) is false but that p is explained by Q(W2), because if Q(A) is false, then Q(W2) would be false as well. Any explanation for the existence of W2- your Q(W2)- would also be an explanation for the existence of the actual world, Q(A)."
I had misread that. My bad. I address this issue below.
"If I understand your symbolism, Q(A) is the explanation for the creation of the actual world by reference to the intentions of a necessary being. But A, the actual world, is individuated by p, which is the BCCF of the actual world. So any explanation for the existence of A would be an explanation for the truth of p. Am I right so far?"
I think so, but only if we include the condition that the explanation of p might not necessitate p, so there might be a world W4 such that Q(W4)=Q(A), but BCCF(W4)=/=p.
Splitting my response again...
DeleteRegarding the possibility that there may not be any personal explanation for the creation of the actual world, you say: “They must leave open the epistemic possibility, but they don't need to grant that a metaphysical possibility.”
They have the burden of proof. The critic has no obligation to show that this *is* a metaphysical possibility. So in that sense, without further argument, the question of its metaphysical possibility remains open and Gale-Pruss are not justified in ruling it out. And of course, if they can come up with an argument that it is not metaphysically possible for the actual world to exist without its being created through the intentions of a necessary being, then they have no need for the rest of their argument.
“I think if we include an explicit reference to the actual world in Q, that excludes it from being true in other worlds.”
Q is what potentially explains p, where p is the BCCF of the actual world, by Gale-Pruss’ stipulation.
“Rather, what I was getting at is that a theist might hold that Q includes a partial description of the world that God creates. Maybe there are other possible worlds in which God creates the same, but they end up different in the end.”
P was supposed to be a set of true disjuncts from a logically exhaustive list of disjunctions. Since possible worlds are individuated by their BCCF, I can’t see that p could be true of any possible world but the actual world. In fact Gale-Pruss’ argument depends on this assumption.
“Back to your argument, I would say that while p lists those properties, p might also contain further properties of a world, which result not directly from God's action, but from the action of indeterministic creatures.”
Since p is supposed to exhaust all of the logical possibilities, it would be better to say that p may contain some propositions that are determined by contingently existing created beings rather than by God. But it seems clear that Gale-Pruss would not accept this qualification.
Regarding my claim: If Wn is not identical with the actual world, then Q(Wn) would not be identical to Q(p), since Wn would be individuated by some BCCF other than p...
“I don't know why, given possible nondeterminism. I'm not sure you can rule that out as an unnecessary complication.”
Gale-Pruss wish to say that p is fully determined by God’s intentions. Perhaps they are determinists. If they wish to take an indeterministic position, they might say that God can instantiate any possible world, including worlds that have non-deterministic elements. So for example God sees the possibility of a world W in which x is true, though x not determined to be true by antecedent (natural) circumstances, and also a world W’ in which x is false, even though the falsehood of x is not determined by antecedent natural circumstances; God then instantiates W in preference to W’.
Continuing...
DeleteMy remark: So any explanation for the existence of A would be an explanation for the truth of p. Am I right so far?
“I think so, but only if we include the condition that the explanation of p might not necessitate p, so there might be a world W4 such that Q(W4)=Q(A), but BCCF(W4)=/=p.”
I suppose it is possible that the intentions of a necessary being might under-determine a world. Some necessary being might, for example, have the very modest intention of creating at least one frog, so we could say that this explanation is true at any world that contains at least one frog. But don’t forget that a world’s BCCF is a conjunction. So an explanation for p- which, for Gale-Pruss, is a *sufficient reason* for p- must explain the truth of more than one of its conjuncts.
In any case Gale-Pruss do not concede your condition; on p. 467 they say that q entails p, which means that the truth of q guarantees the truth of p. If this is the case, then it is not possible for q to be true and p false.
Since q is sufficient for p, and q (by hypothesis) explains an exhaustive list of disjunctions- one which individuates a possible world and is therefore true in only one possible world- q could not be true in any world other than the actual world. This is consistent with Gale-Pruss’ claim that q satisfies the Principle of Sufficient Reason (PSR).
Keep in mind that their argument seeks first to show that there is a possible world at which there is a sufficient reason, q, for the truth of p. They then attempt to show that this world is identical to the actual world.
Part of the reason I do not accept traditional cosmological arguments is that I do not think the PSR is true. And I suppose one could argue that its truth is inconsistent with the existence of free beings. On the other hand, it is difficult to argue that the PSR is necessarily false; hence the attraction of the weak version that Gale-Pruss use.
“But if there is a possible world W2 in which p is true and q false, wouldn't you also owe us an explanation? “
An explanation for why q is false at W2? I don’t see why. In arguing that Gale-Pruss have not made their case, the critic has no responsibility to make her own positive case for how the BCCF of the actual world could be true without its being created by a personal God.
“A potential modification of your argument would be as follows: instead of asserting that "there is another possible world, W2, which contains p, and in which p is not explained by q, because it is not true in W2 that there is a necessary being who intentionally creates that world.", you might assert that perhaps, this is so, and that P-G have not explained why this is not so.
If I understand you correctly, that is the argument I intended to give.
Nice chatting with you!
Thanks for the reply, David. Here's mine (also split):
ReplyDelete"They have the burden of proof. The critic has no obligation to show that this *is* a metaphysical possibility."
I agree, but critics may not from starters assume that it is a metaphysical possibility in response to their argument, in order to show some difficulty with it. At least, some argument would have to be given in order to support the claim.
Maybe "it should be obvious" would work, but not in the dialectical context of discussing the cosmological argument (then again, I tend to think "it's obvious" might as well work against many other philosophical arguments; but that's not he sort of reply you're advancing in this context).
"Q is what potentially explains p, where p is the BCCF of the actual world, by Gale-Pruss’ stipulation."
The difficulty I see is with Q including a explicit reference to the actual world, as opposed to a reference to some properties of/events in the actual world. For example, when we want to explain something that happened in the actual world - e.g., the extinction of non-avian dinosaurs - we don't normally include a reference to the actual world: instead, we talk about an asteroid, volcanic eruptions, climate change, etc. Still, it's a side issue.
"P was supposed to be a set of true disjuncts from a logically exhaustive list of disjunctions. Since possible worlds are individuated by their BCCF, I can’t see that p could be true of any possible world but the actual world. In fact Gale-Pruss’ argument depends on this assumption."
The part of my argument you're replying to does not hold that P is the same, but rather, that Q is the same. In other words, if A is the actual world and W is any world, then it might be that BCCF(W)=\=BCCF(A), but Q(W)=Q(A).
At least, that's what I thought before I found the argument. Now I agree with you, since they directly state tha q entals p. So, yes, Q(W)=Q(A) if and only if BCCF(W)=BCCF(A).
"Since p is supposed to exhaust all of the logical possibilities, it would be better to say that p may contain some propositions that are determined by contingently existing created beings rather than by God. But it seems clear that Gale-Pruss would not accept this qualification."
I agree now that in the version of the argument you challenge, they do not (I was going by your description of the argument only; sorry I missed that).
"Gale-Pruss wish to say that p is fully determined by God’s intentions. Perhaps they are determinists."
I know Alexander Pruss isn't a determinist, and I reckon neither was Gale.
In the context of the argument you challenge, they are committed in that argument to non-deterministic libertarian freedom, when they say that "a necessary condition for acting freely is being able to do otherwise, this being could have done other than intentionally bring it about that p, thus establishing the contingency of the proposition that it is necessary that G exists and G intentionally brings it about that p. "
The rest of the reply:
ReplyDelete"In any case Gale-Pruss do not concede your condition; on p. 467 they say that q entails p, which means that the truth of q guarantees the truth of p. If this is the case, then it is not possible for q to be true and p false."
Yes, you are correct. After reading that part, I reckon their argument is more directly self-defeating, for the following reason: when they argue that q says that a necessary being freely brings about that p, they argue that if the NB's action were not free, then q would have a possible explanation r which would entail q. But since r entails q, then r is contingent because q is contingent, and so r is also a conjunct of p. Yet, q would explain p, and thus all of the conjunts of p, so there would be a vicious circle because r would explain q which would explain r.
Now, the problem is that the same argumentation can be used that there is vicious circularity in their argument: given that q is contingent, it's a conjunct of p, and since q explains every conjunct of p, then q explains q. At any rate, if r explains q and q explains r is viciously circular, but for some reason q explains q is not viciously circular, their argument still shows that q is a conjunct of p.
"Part of the reason I do not accept traditional cosmological arguments is that I do not think the PSR is true. And I suppose one could argue that its truth is inconsistent with the existence of free beings. On the other hand, it is difficult to argue that the PSR is necessarily false; hence the attraction of the weak version that Gale-Pruss use."
It turns out that the WPSR is equivalent to the PSR (source: in htt ps://alexanderpruss.blogspot.com.ar/2011/05/weak-weak-principle-of-sufficient.html (comments) ).
"An explanation for why q is false at W2?"
No, sorry if that was not clear.
I meant an explanation for why there is a possible world W2 at which q is false but p is true.
But it turns out that q is a conjunct of p (this is established by the the same argumentation they used to show that r would be a conjunct of p, when arguing that q is about a free action), so it follows from their argument that there is no possible world W2 at which p is true but q is false.
"If I understand you correctly, that is the argument I intended to give."
I see. Sorry I got that wrong. At any rate, given the argument above, now I reckon that it follows from their argument that there is no W2 at which p is true but q is false, so that seems to block the main part of your argument, though the first part applies; a reply would have to be on different grounds.
Nice chatting to you as well!