Wednesday, May 6, 2009

The PSR and inference to best explanation

Sam Cole, one of the students in my upper level metaphysics class, wrote an interesting paper (I am writing this with his permission) where he argued that if we do not accept the Principle of Sufficient Reason (PSR), then the following question will be unanswerable:

  1. Under what circumstances should we accept a given explanatory hypothesis instead of the hypothesis that the phenomenon in question simply has no explanation?

I think this is a really neat question. We have some idea of the sorts of criteria we employ in choosing between alternate explanatory hypotheses: simplicity, prior probability (perhaps I repeat myself), etc. But if we do not accept the PSR, then the no-explanation hypothesis is going to be, presumably, always available. On what grounds do we judge between our best explanatory hypothesis and the no-explanation hypothesis?

It is tempting to say: If the best explanatory hypothesis is pretty good, then we go for it. But the evaluation of the quality of hypotheses seems to be innately comparative. So this "pretty good" does not seem like it should be absolute. But if it is relative, then what is it relative to? If it is relative to other explanatory hypotheses, then its being "pretty good" seems irrelevant when comparing it against the no-explanation hypothesis. The hypothesis that JFK was shot by a bunch of gorillas escaped from the zoo is pretty good as compared to the hypothesis that JFK was killed by a rifle-toting clam, but that is irrelevant when we compare the gorilla hypothesis to the Oswald hypothesis. So what we need to know is whether the explanatory hypothesis is "pretty good" as compared to the no-explanation hypothesis. But we have no criteria for that sort of comparison!

Another tempting suggestion is this: Whenever any narrowly logically coherent explanation has been offered (asking for more than that may run into Kripkean problems), we should reject the no-explanation hypothesis. This is a more promising answer to (1). Note, however, that an opponent of the PSR who takes this route cannot oppose the use of the PSR in the Cosmological Argument. For in the context of the Cosmological Argument, the PSR is employed to claim the existence of explanations for phenomena for which narrowly logically coherent explanations—namely, theistic ones—have indeed been offered.


James said...

I suppose some kind of Ockham's razorish premise could also be thrown into the mix. That is, if the PSR-denier accepts a premise like "All things being equal, one shouldn't multiply one's explanatory entities beyond necessity", then--if she has no other way of deciding between a given explanation and no-explanation--Ockham's razor gives her a positive reason to embrace the no-explanation option.

On a separate note, I've often wondered if the naturalist who denies the PSR suffers from an extension of the epistemic difficulties that Plantinga alleges that the believer in N&E suffers from. That is, on N&-PSR, our beliefs are, I assume, explicable in terms of our brainstates. But then there might be no explanation as to the pertaining of these brainstates. Hence, even if we grant that evolutionary forces will tend to produce properly functioning brains (or something along these lines), this still doesn't seem to make the believer in N&-PSR's beliefs epistemically proper. For her brainstates might not be the product of evolutionary forces inasmuch as they might have no explanation for their pertaining at all. Hence, the person who affirms N&-PSR seems to have a reason to doubt that her belief that N&-PSR pertains. Or something along those lines, I don't know.

Alexander R Pruss said...

Pretty much this epistemological argument was explored by Rob Koons in the first Oxford Studies in Philosophy of Religion volume.

James said...

Darn. Returning to the original argument then: Wouldn't we go for an explanatory hypothesis that seems to explain the most available data or has the most predictive power or something along those lines? So, explaining ball B's movement in terms of ball A's hitting it (as opposed to regarding A's hitting B as being explanatorily irrelevant to B's movement) would be preferable since it would explain a range of other data as well (e.g. car A's crumpling having collided with a brick wall). Sure, you could say such other data had no explanation too. But then it would seem odd that the physical law-type explanations were so predictively successful wouldn't it (since presumably there could be no necessary or sufficient conditions for an explanationless event's occurring)?

Alexander R Pruss said...

It would indeed be an odd fact. It would be an odd fact with no explanation. But if we do not balk at violations of the PSR in general, why balk at violations of the PSR in the case of odd facts?

James said...

Fair point. Though couldn't the same argument be put positively? Say,

(1) Good explanations will explain a wide range of data and/or have decent predictive power
(2) Explaining things in terms of physical laws often satisfies (1)
(3) Positing "no-explanation explanations" doesn't
(4) So, let's go for the physical-law-type explanations?

Heath White said...

This is very thought-provoking. Here is one thought it provokes. We sometimes have to choose between accepting and not accepting an explanation. E.g. in the first minutes after Kennedy was shot, perhaps somebody posited that he was shot by rifle-toting gorillas escaped from the zoo. I think your average Secret Service agent would have said, "I don't know how the President got shot, but it wasn't by gorillas." That is, faced with the choice between a bad explanation and no explanation, the agent opts for no explanation. Epistemically, sometimes nothing is better than something.

If we are right to do this, then presumably there is some criterion for deciding what is an explanation worth accepting when the alternative is not having an explanation. And then perhaps we could use this criterion to distinguish between explanations worth accepting, versus the belief that there is no explanation.

Alexander R Pruss said...


"I don't know how the President got shot, but it wasn't by gorillas" is opting not to opt for an explanation, but it is different from opting for the no-explanation hypothesis. The no-explanation hypothesis of his being shot would be something like this: "A loaded gun materialized ex nihilo, and the trigger got depressed for no cause." Moreover, the "materialized ex nihilo" would need to be understood not in terms of any quantum vacuum stuff.

Now, I don't think your Secret Service agent will opt for that.

Heath White said...

Right - I was trying to bring out the distinction you make. My point was that sometimes we do say, "That is not a good enough explanation"--that is, we reject explanations non-comparatively, without having a better one. It is an interesting question when we ought to do this; I do not know. But I think the anti-PSR person would say there are cases where we should just reject all explanations non-comparatively. Would this fly? I don't know either that it would or that it wouldn't.

(And I think your student's line of reasoning has important consequences for how we think of free will, too.)

James said...

I think that's an interesting point, Heath. Presumably, when we say "E is not a good enough explanation", we do so because we think there's bound to be a better explanation out there somewhere. In which case, could it be that, even if some state of affairs didn't have an explanation, given that we're not omniscient, we'd still be unjustified in concluding as much?

Alexander R Pruss said...


I wonder, though, what we'd do if we eliminated all the explanations other than the team of marksgorillas. Maybe then we'd go for it? Sherlock Holmes says that once the impossible has been eliminated, what remains must be true, however unlikely. What he means by that (context makes this clear) is precisely that if all the explanations except one have been eliminated, that one must be accepted. (It does not occur to him to suppose that the PSR might be false. :-) )

As for free will, that's going to depend on whether libertarian free will does or does not violate the PSR. I have argued that it does not as long as we bear in mind the possibility of non-entailing explanations.

Heath White said...


Good question. I’m really not sure about any of this.


I dunno. There seem to be whack-job explanations that I would probably not accept under any circumstances; marksgorillas teleporting in from the planet Mars, for example. I think I would give up the PSR first.

About free will: can you explain to me why the appeal to non-entailing explanations isn’t just giving up the ship? If the explanans doesn’t entail the explanandum, then there are multiple possibilities compatible with the explanans, only one of which is the thing that actually happened. Why, then, that actual happening rather than one of the other possibilities? It seems by definition we have no explanation of this and, assuming we have given the whole explanation, no explanation exists. So if we embrace non-entailing explanations, then there are cases in which the question “Why P1 rather than P2?” has no explanation.

But now I think I can run your student’s argument. In ANY case of “Why P1 rather than P2?” (why did my wife give birth to a human being rather than to a lizard?) the no-explanation answer is, in principle, available. And maybe there is no way to say why we should accept some explanation rather than none.

If we want to say that any explanation is better than no explanation, as you suggest in your post, then why don’t we say this for the free will case? That is, any explanation of why P1 rather than P2 is better than the (libertarian) hypothesis that there is no such explanation. So we should never be willing to accept the libertarian hypothesis.

Alexander R Pruss said...


I have lots of stuff on this in my PSR book. To summarize, there are at least two ways out:

1. The PSR says every proposition has an explanation. Then deny that "p rather than q" expresses a proposition distinct from (p and not q). (Two ways of doing that: (1) deny that "p rather than q" expresses a proposition; (2) admit that it expresses a proposition, but argue it is the same proposition as p&~q.) No problem explaining "p and not q".

2. Insist that contrastive explanations can be given even in these free will cases. This works best using Kane's strategy, though Kane I think doesn't think this saves the PSR: Sally is thinking whether to help someone who is being attacked, or get to her meeting on time. She has one reason, R1, in favor of helping, and another reason, R2, in favor of going to the meeting. If she helps, it is because of R1. If she goes to the meeting, it is because of R2. Of course, both R1 and R2 obtain. But even though they both obtain, only one is explanatory. If she in fact helped, then R1 explains why she helped rather than went.

Natural question: But what explains why she (say) acted on R1 rather than on R2? A regress threatens.

Response: The answer to the natural question is: R1 does. It is Sally's being impressed by R1 that explains why she acted on R1 rather than on R2, even though she was also impressed by R2. ("Impressed" is a technical term I use: x is impressed by R provided that x takes R into consideration in deciding what to do.) But what explains why it was that her being impressed by R1 that proved explanatory? Answer: R1 does. There is no regress, R1 (or, being impressed by R1) explains it all.

The apparent regress resembles the one that one might think results from the question: "If E (deterministically or not) caused F, what caused the occurrence of a causal relation between E and F?" But this question does not yield a regress. For what caused the ocucrrence of the causal relation is, simply, E, and it caused the occurrence of the causal relation in causing F.

I have argued that the libertarian has to say something basically like this. For if libertarian choice violates the PSR, then libertarian choice is objectionably random, and libertarianism is incoherent. So if libertarianism is coherent, it is not a violation of the PSR.

Heath White said...


1. Suppose we are flipping a coin. By hypothesis the coin flip is indeterministic. However we’ve modified the coin slightly. There is a magnet glued to each side of the coin, and we are flipping over an iron tabletop. So the tail-side magnet tends to make the coin land Heads, and the heads-side magnet tends to make the coin land Tails. We flip and the coin lands Heads.

What made it land Heads? Well, the flipping motion, gravity, and in particular the tail-side magnet.

Natural question: what made it land Heads rather than Tails? Response: the flipping motion, gravity, and the tail-side magnet. Objection: But all those factors would still have been in play if the coin had landed Heads. This is an insufficient explanation. Response: *thumps table* Those were the factors that made the coin land Heads; a fortiori they are the factors that made it land Heads rather than Tails.

It seems to me that the objector has the better case here; by definition, indeterministic events cannot be given sufficient explanations. (Put it this way: suppose that, per impossibile maybe, contrary to the PSR some event did not have a sufficient explanation. Wouldn’t that event just be an indeterministic event?) Moreover, I don’t see how the coin with magnets glued to the sides differs in an interesting way from Kane-style explanations of libertarian free actions.

2. Suppose we have some indeterministic event E1, for which there is a partial (non-entailing) explanation X. In particular, X does not rule out E2. If we ask “What explains E1?” then X is the right answer. But the function of the question, “What explains why E1 rather than E2?” is to rule out the factors common to explanations of both E1 and E2 and focus only on the factors which would differentiate between them. And to this question, there is no answer. So I guess there are different kinds of PSR but I would think that a principle of sufficient explanation would want to rule out this scenario. And that means there are no indeterministic events.

Put it the other way around. If we deny this, then it is very easy to defend a PSR because the principle rules out very little. Suppose the world is full of random, arbitrary events which have necessary but no sufficient causes. We ask the explanation of one of these events E1. The answer comes, “Because its necessary condition X obtained.” “But why E1 rather than E2?” If we say that, once again, “Because X” is an adequate answer, then it seems even a very arbitrary world will support a PSR. That however seems wrong.

3. If we adopt the stance that “any explanation is better than no explanation” then we should believe anything rather than believe that a question like “Why E1 rather than E2?” has no answer. For example, we should believe anything rather than believe “Why go to a meeting rather than aid a victim?” has no answer. But that means that any deterministic hypothesis is more credible than the libertarian hypothesis.

I tend to agree that "If libertarianism is coherent, it is not a violation of the PSR." But one man's modus ponens....

OK, that’s enough for now. Sorry for the length.

Alexander R Pruss said...

Dear Heath,

1. I think there may be a difference between the coin case and the free will case. In the free will case, the reasons do not merely incline--together with the agent's choice, they do explain. Of course to say that simply begs the question against you. But it does seem to be at least a coherent statement.

2. I think there is a difference between fully accounting for why A happened and giving a sufficient condition for A. To fully account for why A happened requires that we give a sufficient explanation. But the sufficient explanation need not be a sufficient condition, pace Leibniz.

3. I do not think the causes cited in the indeterministic explanation are merely necessary conditions. They are, rather, the actual causes of the event. (This, almost surely, requires causal particularism.)

Compare the fact that it is a perfectly fine explanation of why the apple fell that it was dropped in a gravitation field, even though that the apple was dropped in a gravitational field by no means entails that it fell.

4. Not just any random world satisfies the PSR. Note that the account of free will that I give has a very specific structure: (a) there are two or more countervailing sets of "forces" pulling towards different respective outcomes; (b) each set of forces satisfies the condition that were the other sets absent, the outcome associated with this set would occur automatically and deterministically; and (c) the outcome does in fact occur, and occurs because of the associated set of forces, and despite the other forces. We do not, at least in this case, need to cite the things despite which something happens in the explanation, so the explanation is just in terms of the associated set of forces.

5. It might even be the case that the only sort of indeterminism that satisfies the PSR is that involved in libertarian choice. But I don't have a good argument for this.

6. Let's try this thought experiment. Suppose that the coin is being pulled in two directions. It is pulled down by gravity and up by magnetism. Suppose further (and perhaps contrary to fact) that the way this works is this: When the two forces are balanced, the coin will still end up going up or going down, but the outcome is not determined. However, when the forces are not balanced, the coin goes with the stronger force. Let A be a measure of the force of gravity and B a measure of the force of magnetism. Let S(A,B) be the above situation with these specified forces.

Then, in S(1,2), the coin goes up. Why? Because of the magnetism. Shouldn't we say something about the gravity? Well, we can if we like. But we don't have to. The gravity had nothing to do with the coin's going up. It was pulling the coin down. It made no contribution to the coin's going up, so we don't need to cite it. The full cause of the motion was the magnetism. (Maybe we should cite that gravity was weaker than magnetism? But then we have to also cite that there were no other forces present that were sufficient to counteract the magnetism. And if we go down that path, we may end up having an explanans that contains the explanandum. See my book. :-) )

OK, what about S(1.5,2)? Well, the coin goes up due to magnetism. If we didn't cite the gravity in S(1,2) when we were explaining the coin's motion, we shouldn't cite it here, because in S(1,2) the gravity is even more opposed to the effect in question.

So, the stronger the gravity, the more clear it is that we shouldn't cite it in the explanation of the coin's going up, because the more it is opposed to this, the further it is from needing to be included.

Therefore, in S(2,2) if the coin still goes up, the gravity is even less to be cited. It had nothing to do with the coin's going up.

Moreover, if in S(1,2) the magnetism was the explanation, I think in S(2,2) the magnetism will also be the explanation. No further force is present in S(2,2). Gravity is stronger then, and more able to counteract the magnetism, but what moves the coin up is the magnetism.

Charlie said...

Most would agree that not all explanations are causal. But now suppose the converse is true: perhaps not all causal phenomena are translatable into propositions flanking the explanation relation. So consider some event E1 that causes E2; there is no p that clears up mystery about why q is true, where p reports E1 and q reports E2. (Presumably a minimal constraint on explanation is that the explanans should clear up some mystery about the explanandum.)

It would only be when we observe phenomena of this sort that we must choose the no-explanation option over any other hypothesis.

I leave it open whether there are phenomena of this sort. (Events involving libertarian agent causation would be the best candidates, though.)

Unknown said...

"if we do not accept the Principle of Sufficient Reason (PSR), then the following question will be unanswerable: Under what circumstances should we accept a given explanatory hypothesis instead of the hypothesis that the phenomenon in question simply has no explanation?"

If the PSR is false, then we always have two broad options: 1) no explanation exists; 2) an explanation exists

When are we justified in accepting 2? I disagree that we should accept 2 just because we have SOME explanation (e). There is always the comparative: e and ~e. One should accept e only if it is arguably more probable than ~e.