HRG

True. Also one might classify "p is true" as a metafact etc.

Quote:

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.

Being a simple physicist and not a creative philosopher I've been thinking of

"The expectation value of the center of mass of particle p at time t is to the right of point x_i"

If space is not discrete, there are (at least) countably many points x_i in every interval. They define a countably infinite set of contingent facts.

Regards,
HRG.

Clutch

What's an explanation, to these Cosmo-argument folks?

In general, what counts as an explanation is a partial function of the explanatory context. The whole thing is rather pragmatic.

One influential view, moreover, is that explanation is inherently contrastive: why this instead of that. Which again plays into the pragmatic aspect, since a satisfactory contrast between outcomes A and B may not settle the matter with respect to outcomes A and C.

Eg, why did this atom in the sample decay [instead of turning into a pumpkin]? Explanation provided by basic physical laws, statistical reasoning and knowledge of half-life of substance.

Why did this atom in the sample decay [rather than that one]? No contrastive explanation available.

Thomas Metcalf

Originally posted by HRG :

As a physicist, does it look to you as if space is discrete? I suspect that it is, based on my moderate familiarity with quantum mechanics and on Zeno's kinds of considerations.

Here are some more facts. "There is no book that has been read by someone two times at position x,y,z; there is no book that has been read by someone two times at position x,y,z; ... there is no book that has been read by someone n-1 times at position x,y,z; there is no book that has been read by someone n times at position x,y,z."

At this point I want to make sure, however, that it follows from there being an infinitely long conjunction of facts that this conjunction is somehow not well-formed and therefore doesn't require an explanation, or can explain itself.

Wyrdsmyth

I'm more interested in Part 2. That's where I get lost. It looks to me like the old "and this what we call God" trick.

*

"Aquinas, what would you call that rather ambiguous philosophical abstraction you concluded from your first cause argument?"

"Why, I'd call it God," Thomas Aquinas replied.

Thomas Metcalf

Originally posted by Wyrdsmyth :

To me, too. Here's what Gale and Pruss say in the original article:

And then q is simply the explanation for p, and p is the BCCF. But I would say in response that these are not the only two sorts of explanations possible. There is at least one more, viz., a mindless entity that exists at the beginning of every possible world, that brings the universe into existence immediately and necessarily, and then immediately ceases to exist, itself. The (necessary) action of this entity would be an explanation for the obtainment of our BCCF, but such an explanation would not be a contingent fact.

(It has not escaped my attention that if the universe is all that exists, the initial singularity of the big bang provides a close match to the sort of entity I've sketched.)

SRB

Another way of putting your original objection, Thomas, is that W-PSR entails S-PSR. Pruss and Gale claim that their argument hinges on the fact that S-PSR is something atheists can reasonably be expected to reject, while W-PSR is supposed to be very plausible. But since W-PSR logically entails S-PSR, it can be seen that their project is fundamentally flawed.

Here is an informal proof that W-PSR entails S-PSR:

(1) For every contingent fact, it is possible that it has an explanation [W-PSR].
(2) Therefore, if W-PSR is true then then there is a possible world in which the Big Conjunctive Fact (BCF) of the actual world is true and has an explanation [from (1)].
(3) The only world in which the BCF of the actual world is true is the actual world [from the definitional truth that BCFs individuate possible worlds].
(4) Therefore, if W-PSR is true then the BCF of the actual world is true and has an explanation in the actual world [from (2) and (3)].
(5) If the BCF of the actual world has an explanation, then every conjunct of that BCF has an explanation [premise - see below]
(6) Therefore, if W-PSR is true every contingent fact in the actual world has an explanation [from (4) and (5)].
(7) Therefore, if W-PSR is true then S-PSR is true [from (6)].

The only premise here that might be challenged is (5). That premise asserts that explanation is distributive over conjunction (i.e. if P & Q has an explanation then P has an explanation and so does Q). I don't see how that can be reasonably denied. It looks obviously true to me.

SRB

Thomas Metcalf

Originally posted by SRB :

Gale and Pruss speak to this issue in their response to Graham Oppy, who brings it up directly as an objection to their cosmological argument. See "A Response to Oppy, and to Davey and Clifton", Religious Studies 38 no. 1 (pp. 88-99). If I remember correctly, their response back to Oppy is that just because accepting some principle leads you logically to one you don't like, that's not grounds for going back on your original intuitions with respect to the first premise.

I think your response is still forceful, however. Properly understood, W-PSR entails S-PSR with a very short chain of reasoning. The idea that our BCCF has an explanation (rather than some other possible world's BCCF) seems immediately connected to S-PSR. So I don't think this is a case of accepting P, accepting P --> Q, but not accepting Q and therefore going back and denying P; I think this is a case of accepting P at first without fully understanding P. And our intuitions speak to us about every particular fact and maybe a few conjunctive facts, but mine, at least, start to stretch quite a bit when I try to intuit whether a BCCF would have an explanation in some possible world. It's just too different, and I suspect that to say "it's possible that our BCCF has an explanation" is literally to say something about the actual world rather directly. After all, what is a possible world but a maximal consistent conjunction of facts? True, that includes some necessary truths, but I think that point is minor in the end.

Perhaps Gale and Pruss could frame an inductive argument based on our intuitions that every "atomic" fact has an explanation, to the conclusion that, probably, the BCCF has an explanation.

I would be interested to read your evaluation of my objection to part 2. I say that if part 1 is sound, then it's a necessary truth that the BCCF has an explanation. But then the atheist can claim that the necessary truth is fact E: "the contingent fact determination event occurs", which happens in every possible world to fix the truth-values of all the contingent facts with truth-values. E seems to be a necessary truth, so it requires no explanation and is not vulnerable to the criticism Gale and Pruss attempt to bring to bear against a "scientific" explanation.

SRB

They would do well to take their own advice! Pruss and Gale originally said that S-PSR is something that informed atheists can reasonably deny. Since W-PSR entails S-PSR, it follows that W-PSR is something that informed atheists can reasonably deny. So the cosmological argument they present has no force. [If an informed person can reasonably deny q and p->q then that person can reasonably deny p]. Now, apparently, because they have found out that W-PSR entails S-PSR, Pruss and Gale want to backtrack on their concession that S-PSR is something that atheists can reasonably deny. I should think that is because their original concession had unfortunate consequences for their argument. Why should anyone go along with them and how do they defend their U-turn?

In any case, there are other good reasons to think W-PSR is false. Explanation is surely distributive over conjunction, as I earlier noted. From this it follows that if q explains the Big Conjunctive (Contingent) Fact (BCCF), then q explains every conjunct of the BCCF. But one of the conjuncts of the BCCF is q itself, since q is contingent. So q explains q! In other words, W-PSR entails that there is such a thing as self-explanation. But I would say that necessarily there is no such thing as self-explanation. If x explains y then x must be somehow better known, or more clearly grasped, than y. No proposition can be better grasped, or more clearly known, than itself. So no proposition can explain itself. No conjunct of the BCCF could explain the BCCF itself. Since that idea is incoherent and is entailed by W-PSR, W-PSR must be false.

Pruss and Gale try to forestall that objection. You would need to address something specific in response to their claim that propositions are contingent if they report the occurrence of events:

"It cannot be the case that q gives a scientific explanation of p. The reason is that q must contain some law-like proposition, as well as a proposition reporting a state of affairs at some time, but such propositions seem to be contingent, especially the latter. And, since they are contingent they are members of the Big Conjunctive Contingent Fact."

SRB

Thomas Metcalf

Originally posted by SRB :

This is the big question. Can you think of any other examples of this occurrence? Suppose I have the intuition that earth is stationary and the rest of the solar system orbits around it. This is my belief in p. Now, our p->q is that if earth is stationary and the rest of the solar system orbits around it, then certain observations about Jupiter's moons and the phases of Venus will probably obtain (at least, in the Galileo story). But these observations don't obtain. Therefore, I will abandon my original intuition.

In general, suppose I hold some belief intuitively, and you show that such a belief entails some deniable conclusion. I decide to abandon that original belief. There's nothing rationally wrong with that, I don't think. And the same situation goes through with W-PSR and S-PSR. I have a belief that W-PSR is true, you show that it entails S-PSR, and I abandon W-PSR.

I wonder whether this works for intuitive principles the way it works for empirical observations.

I don't think it needs to be. Why can't q be a necessary truth? For example: "God performs some action that fixes the truth-values of all contingent facts with truth-values."

Remember, the explaining proposition I am proposing is: the contingent fact determination event occurs. I don't think this seems law-like, or even that it reports a state of affairs at some time, if I understand their description. But moreover, Gale and Pruss require that my proposition be contingent for them to rule it out as an explanation, and it's certainly epistemically possible for the contingent fact determination event occurs to be a necessary truth. Gale and Pruss seem to think of their necessary truth explanation as something like "God creates the universe", and this is a necessary truth that depends upon God's existence. But I'm within my rights to posit a competing necessary event that requires no explanation, because if Gale and Pruss show that every BCCF requires an explanation, then that's a necessary truth and the nature of the explanation is left wide open.

SRB

The "->" here denotes logical entailment. So I don't think your example is a good one. Here is a better example. p is the proposition that 2+2=5 and swans are white; q is the proposition that 2+2=5.

The statements "S-PSR is false" and "W-PSR is true" are incompatible, both with prima facie appeal. Indeed, Gale and Pruss erroneously thought they were compatible. They would say that since they are incompatible, and since the latter is plausible, then the former is implausible. But one could just as well say that since they are incompatible, and the former is plausible, then the latter is implausible. Why prefer one argument to the other? We need some reason to think "S-PSR is false" is less plausible than "W-PSR is true" to break the deadlock. None appears to be forthcoming.

This is taken up by Pruss and Gale:

"A more effective argument for q’s contingency is the following reductio ad absurdum argument from the assumption that q is necessary. If q is necessary, q is a conjunct in every possible world’s Big Conjunctive Fact. But q entails p, since that a necessary being intentionally brings it about that p entails that p, and thus p also is a conjunct in every possible world’s Big Conjunctive Fact. Given that p is the actual world’s Big Conjunctive Contingent Fact and that a possible world is individuated by its Big Conjunctive Contingent Fact, it follows that every possible world is identical with the actual world. Therefore, there is only one possible world. And this, surely, is absurd."

A proposition that reports the occurrence of an event necessarily reports a state of affairs at some time, since all events occur in time.

That's not their view. Read premise (14) of their argument and the prior notes.

SRB