220.127.116.11. The basic argument
Peter van Inwagen (1983, pp. 202-4) has formulated an influential and elegant reductio ad absurdum of the PSR. Let p be the conjunction of all contingent truths. If p has an explanation, say q, then q will itself be a contingent truth, and hence a conjunct of p. But then q will end up explaining itself, which is absurd. We can formulate this precisely as follows:
(11) No necessary proposition explains a contingent proposition. (Premise)
(12) No contingent proposition explains itself. (Premise)
(13) If a proposition explains a conjunction, it explains every conjunct. (Premise)
(14) A proposition q only explains a proposition p if q is true. (Premise)
(15) There is a Big Conjunctive Contingent Fact (BCCF), which is the conjunction of all true contingent propositions, perhaps with logical redundancies removed, and the BCCF is contingent. (Premise)
(16) Suppose the PSR holds. (for reductio)
(17) Then, the BCCF has an explanation, q. (by (15) and (16))
(18) The proposition q is not necessary. (by (11) and (15) and as the conjunction of true contingent propositions is contingent)
(19) Therefore, q is a contingent true proposition. (by (14) and (18))
(20) Thus, q is a conjunct in the BCCF. (by (15) and (19))
(21) Thus, q explains itself. (by (13), (15), (17), and (19))
(22) But q does not explain itself. (by (12) and (19))
(23) Thus, q does and does not explain itself, which is absurd. Hence, the PSR is false.
Versions of this argument has been defended by James Ross (1969, pp. 295-304), William Rowe (1975, 1984), and, more recently, Francken and Geirsson (1999).
The argument is plainly valid. Thus, the only question is whether the premises are true. Premise (14) is unimpeachable.10
Premise (13) bears some discussion. In favor of it, one might note that the explanation of the conjunction might have more information in it than is needed to explain just one of the conjuncts, but if it has enough information to explain the conjunction it also has enough information to explain the conjuncts. We may, however, worry about Salmon's remark that irrelevancies spoil explanations (Salmon 1990, p. 102). If we are worried about this, however, we can replace "explains" with "provides material sufficient for an explanation" throughout the argument, and whatever was plausible before, will remain plausible.
10. That aliens shot John F. Kennedy would be a good explanation of JFK's death were it true, but since it is false, it is not an explanation. False propositions can be putative explainers, but not actual explainers.
Alternately, we may say that if q explains a conjunction, then the only reason it might fail to explain a conjunct r is because q might contain irrelevant information. But, surely, when the conjunct r is equal to q itself, this worry will not be real - how could q contain information irrelevant to itself? So even if (13) is questioned, (21) still very plausibly follows from (15), (17), and (19).
This leaves the technical Premise (15) about the existence of a BCCF, and two substantive claims, (11) and (12), about explanation. Leibnizian cosmological arguments based on the PSR need something like a BCCF, so questioning (15) is probably not a fruitful avenue for questioning for a defender of the Leibnizian cosmological argument (see further discussion in Section 18.104.22.168, below, as well as in Pruss 2006, sec. 6.1).
But we should not accept (11). We shall see that the main reason for believing (11) rests on a misunderstanding of how explanation works. Moreover, I shall argue that someone who accepts the logical possibility of libertarian free will should deny at least one of (11) and (12).
Premise (11), that no necessary proposition can explain a contingent one, needs some justification. The main reason to accept (11) is the idea that if a necessary proposition q explained a contingent proposition p, then there would be worlds where q is true but p is false, and so q cannot give the reason why p is true. This sketch of the argument can be formalized as follows:
(24) If it is possible for q to be true with p false, then q does not explain p. (Premise)
(25) If q is necessary and p is contingent, then it is possible for q to be true with p false. (a theorem in any plausible modal logic)
(26) Therefore, if q is necessary and p is contingent, then q does not explain p.
Instead of attacking (11) directly, I shall focus my attack on (24). Without (24), Premise (11) in the modal fatalism argument does not appear to be justified. Now, granted, someone might one day find a powerful argument for (11) not dependent on (24), in which case more work will need to be done, but (24) seems to capture just about all the intuition behind (11).
By contraposition, (24) is equivalent to
Let me start with a quick ad hominem argument against (27). It seems a perfectly good explanation of why the dog did not bark that neither a stranger came by the dog nor did any other potential cause of the dog's barking occur. But the explanans here only entails the explanandum if we suppose that it is a necessary truth that if the dog barked, its barking had a cause. But opponents of the PSR are unlikely to grant that this is a necessary truth, unless they have some principled to reason to argue that dogs' barkings metaphysically require causes, but some other things do not need any explanation, whether causal or not. But I doubt that there is a good way of drawing the line between barkings and other states of affairs.
Now, (27) does seem to hold in the case of many conceptual explanations. These explain a state of affairs by saying what the state of affairs is constituted by or consists in. For instance, in Metaphysics Z, Aristotle suggests explaining an eclipse of the sun by noting that an eclipse of the sun is identical with the earth's entry into the moon's shadow. Likewise, one might explain a knife's being hot by noting that its being hot consists in, or maybe is constituted by, its molecules having high kinetic energy.
However, (27) is falsified by just about every modern scientific nonconceptual explanation that I know of. Scientific causal explanations, in general, simply do not give conditions that entail the explanandum. This is obvious in the case of statistical explanations, since in these, the explanans gives laws of nature and states of affairs that do not entail the explanan-dum but either render the explanandum more probable than it would otherwise be, or at least are explanatorily relevant to the explanandum. Why did the cream spread throughout the coffee cup? Because it is very likely that random molecular motion would disperse cream in this way.
But the falsity of (27) also follows in the case of nonstatistical explanations. Why are the planets moving in approximately elliptical orbits? Because the main gravitational influence on them is that of an approximate point mass (the sun), the secondary gravitational influences on them from other objects, including other planets, being weak. But what I just said does not entail that the planets move in approximately elliptical orbits. It only entails that absent other influences, the planets move in approximately elliptical orbits.
Perhaps we can build that proviso into the explanation. Why do the planets move in approximately elliptical orbits? Because the main gravitational influence is that of an approximate point mass, and there are no other relevant influences. But the word "relevant" is crucial here, for, of course, there are many other influences, such as electromagnetic ones. The word "relevant" here seems to mean "relevant to affecting the approximate shape of the planets' orbits." But that is not quite right. Electromagnetic influences of the sort that the planets undergo are, in general, relevant to affecting the approximate shape of the planets' orbits. They are just not relevant in this case because the gravitational influence of the sun swamps the other effects.
So what we are really saying when we give the proviso is that the main gravitational influence is that of an approximate point mass, and no other influence prevents the orbits from having elliptical shape. Perhaps now we have entailment? Actually, the objector to the PSR should not say so. For if the PSR is false, then surely things can come into existence for no reason at all and can likewise pop out of existence for no reason at all. Thus, it is quite possible for all of the aforementioned to be true, and yet for the planets to pop out of existence, thereby preventing them from having any orbits at all.
Do we add, then, to the our explanans the conjunct "and the planets remain in existence"? Perhaps then we will get entailment, although even that is not at all clear. For if the PSR is false, and if the laws of nature are of such a nature as not to rule out the possibility of external influence, then it seems likely that the laws of nature cannot rule out the possibility of a brute, unexplained departure from the laws of nature.
Or perhaps objectors to the PSR will admit that by their own lights (27) is false, but insist that the defenders of the PSR are committed to (27). Then the argument against the PSR becomes ad hominem. I have no objection against ad hominem arguments, but one would need to give an argument that while the opponents of the PSR can reasonably reject (27), for some reason the proponents of the PSR should accept (27). But then an argument is needed as to why the proponents of the PSR must accept a theory of the nature of explanation that requires (27) just because they happen to think that all contingent facts have explanations. Yet since the PSR is incompatible with (27) given some plausible other assumptions, this would be a hard case to make!
In any case, suppose that through a lot of careful work we have somehow managed to come up with an explanans that entails that the planets have approximately elliptical orbits. An easy point I can make here is that the resulting explanation is unlike standard scientific explanations in more than one way.
First, note that with the provisos we have loaded into the explanans, the explanation becomes logically odd. What we end up saying is essentially that the planets move in approximately elliptical orbits because the gravitational influence of an approximate point mass moves them in approximately elliptical orbits. The provisos all add up to saying that the gravitational influence of the sun succeeds in moving the planets in elliptical orbits. But now the explanandum is in effect there in the explanans, and our explanation is like "He died because he died of being stabbed." But that is not how we give explanations. He died because he was stabbed. The planets move approximately elliptically because the sun gravitationally influences them. He did not die because he died of being stabbed, and the planets do not move approximately elliptically because the sun moves them approximately elliptically.
Second, the proponents of the PSR have an epistemic right to reject the loading up of the explanation of provisos, a right grounded in reasons apparently independent of their need to reject the van Inwagen argument. Our provisoed explanation basically was: "The planets move approximately elliptically because the sun gravitationally influences them as an approximate point source and nothing prevents them from moving approximately elliptically." But if the PSR is a necessary truth, then that nothing prevents the planets from moving approximately elliptically entails that they in fact move approximately ellipti-cally, since if they did not, there would have to be a reason why they do not. However, it is an odd sort of explanation where one of the conjuncts in the explanans is sufficient by itself to entail the explanandum. One wonders why one bothers mentioning the sun's gravitational influence at all! In fact, this worry may be there even for the PSR's opponent, if one of the provisos has to be something like "and the PSR is not relevantly violated in this case."
Third, the claim that nothing prevents the planets from moving approximately elliptically involves universal quantification over all entities in existence, whether natural or not. It is a claim that each of these entities is a nonpreventer of the planets' elliptical motion. But while scientific claims have entailments about nonnatural entities (e.g. that the planets are moving approximately elliptically entails that God is not making them move along logarithmic spirals), they should not quantify over nonnatural entities. Thus, our heavily provisoed explanation does not appear any longer to be a scientific one.
Let me end this section with the following argument for (27). The PSR had better understand "explains" as "gives a sufficient reason for." But a sufficient reason is, surely, a logically sufficient reason, that is, an entailing reason. And, indeed, Leibniz thought that the reasons said by the PSR to exist would be entailing.
A simple answer to this is to say that I am not defending Leibniz's PSR, but a PSR sufficient for the cosmological argument. We do not, in fact, need entailing reasons for the cosmological argument, as shall be clear when we discuss cosmological arguments. A fuller answer is that when I talk of the PSR, by "sufficient reasons" I mean reasons that are sufficient to explain the explanandum. Leibniz may have erroneously thought that a reason is only sufficient to explain something that it entails, but we do not need to follow him in his error - and should not, since that route leads to modal fatalism. But if the reader is not convinced, I can just rename the principle I am defending the "Principle of Good-Enough Explanation."
Let me now offer an argument that someone who accepts the possibility of libertarian free will must reject the van Inwagen argument. Since van Inwagen is a libertarian, he too must reject his own argument. To make this more than an ad hominem, I would need to argue for the possibility of libertarian free will (or for its actuality), for which, of course, there is no space here.
Libertarian free will is nondeterministic. From the condition of the mind of the chooser prior to the choice, one cannot deduce what choice will be made. This has given rise to the randomness objection to libertarianism: libertarian free choices are not really caused by the person, but are merely random blips, as some people think quantum events are. We would not account a person free if acts of will occurred randomly in a person's mind or brain.
Libertarians are, of course, committed to a denial of the randomness objection. However they manage it, they must reject the claim that libertarian free actions are random - they may, for instance, insist that they are not random because they are caused by agent causation. Now suppose that a libertarian allowed that in the case of a libertarian free choice between options A and B, where in fact A was chosen, there is no sufficient explanation of why A was chosen. Such a libertarian has succumbed to the randomness objection. If there is no explanation for why option A was chosen, then that A was chosen is a brute, unexplained, uncaused fact - a random fact. Thus, the libertarian cannot allow that there is no explanation of why A was chosen.
Look at this from another direction. Suppose someone is externally determined to choose A instead of B, so that the explanation for why A was chosen was that some external puppet master has caused the agent to choose A rather than B. In that case, there would indeed be an explanation for why A was chosen rather than B - the causal efficacy of the puppet master. The libertarian will insist that in that case, there is no free will. Now take this situation and subtract the puppet master, without adding anything. We get a situation where there is no explanation for the choice of A rather than of B. We get a genuine case of randomness, having replaced the puppet master by nothing at all. And this mere removal of the puppet master does nothing to give freedom to the agent. Libertarian freedom is not supposed to be something purely negative, the lack of a puppet master, but something positive like self-determination. To go from the choice determined by the puppet master to a genuine libertarian free choice, we cannot merely delete the explanation of the action in terms of the puppet master: we must add something to the situation. It is plausible that what needs to be done is to substitute the free agent and/or her free will for the puppet master: the action must be explained in terms of the agent now, instead of in terms of something external. The basic intuition of a libertarian is that determinism places the ultimate point of decision outside the agent, in the environment that forms and influences the agent. This external determinism, to produce freedom, must not only be removed but must be replaced by something causal, though still indeterministic in the case of agents that have a cause of their existence,11 within the agent.
Thus, the libertarian should hold that there is an explanation for why one rather than another choice was freely made. Otherwise, the randomness objection to libertarianism succeeds. This either forces the libertarian to say (a) that a description of a mind in a state that is equally compatible with either of two actions, A or B, can be used to explain why A was in fact freely chosen - a denial of (27) - or (b) that the claim that action A was freely chosen, or perhaps freely chosen for reason R, is "almost" a self-explanatory claim, despite its contingency, with the only thing unexplained being why the agent existed and was free and perhaps impressed by R. If the agent were a being that necessarily exists and is necessarily freely and omnisciently, then in case (b), nothing would be left unexplained, and we would have a counterexample to (12).
Nonetheless, how there can be explanation of exercises of libertarian free will is mysterious. I shall here defend option (a), that a choice of A can be explained in terms of a state that was compatible with choosing B. I shall defend this by offering a hypothesis about how libertarian free will works. If this hypothesis is false, perhaps another can do the same job, but I find this one plausible. For simplicity, I will assume a binary choice between A and B. On my hypothesis, free choices are made on the basis of reasons that one is "impressed by," that is, that one takes into consideration in making the decision. Some of the reasons are in favor of one choice, and others are in favor of another choice. Reasons that are neutral between the options are not taken into account by the agent in the choice between A or B.
I now suppose that when the agent x chooses A, there is a subset S of the reasons that favor A over B that the agent is impressed by, such that x freely chooses A on account of S. My explanatory hypothesis, then, is that x freely chooses A because x is making a free choice between A and B while impressed by the reasons in S. On my hypothesis, further, had the agent chosen B, the agent would still have been impressed by the reasons in S, but the choice of B would have been explained by x's freely choosing between A and B while impressed by the reasons in T, where T is a set of reasons that favor B over A. Moreover, in the actual world where A is chosen, the agent is also impressed by T. However, in the actual world, the agent does not act on the impressive reasons in T, but on the reasons in S.
This explanation fits well with how agents in fact describe their choices. They say things like: "I chose this graduate school because it was important to me that my spouse be able to study at the same institution." Sure, another school might have better fit with their academic interests, and that may also be important to them. But while the latter consideration is one they are also impressed by, they did not in fact choose on the basis of it, and hence it does not enter into the explanation.
11. The reason for the proviso is this: If agent x is caused by y to exist, and is internally determined to do A, then y by causing x to exist has caused x to do A. But if agent x has no cause of its existence, then this argument no longer works, and internal determinism may be compatible with freedom. This is important for the question whether a God who cannot choose evil can be free (see, for instance, Pruss 2003).
Note that I am not claiming that the same thing explains the choice of A as would have explained the choice of B. That sameness of explanation claim might seem absurd, so an opponent might try to push me to admit that there is a single explanation in both cases. Thus, one might say that if p (a proposition about the choice being made while impressed by the reasons in S) explains the choice of A, and q (which is like p but with T in place of S) is true, then p&q also explains the choice of A. However, "irrelevancies [are] harmless in arguments but fatal in explanations" (cf. Salmon 1990, p. 102). Thus, even though p explains the choice of A, and q is true, one can coherently deny that p&q explains the choice of A. If, on the other hand, this point is denied, I will regroup by saying that the idea that the same proposition should explain A in our world and an incompatible B in another world is defensible. Salmon (1990, pp. 178-9) argues that one must accept the possibility that the same kinds of circumstances can explain one event on one occasion and an incompatible kind of event on another occasion if one is to have any hope of explaining stochastic outcomes.12 For instance, if a carcinogen causes cancer 12 percent of the time, with 60 percent of the time its being type A cancer and 40 percent of the time its being type B cancer, these statistical facts can explain both an occurrence of type A cancer in one patient and an occurrence of type B cancer in another.
For the cosmological argument, the most important case of libertarian choice is God's choice what world to create. In this case, I actually think it is a necessary truth that God is impressed by the reasons S on account of which he created the actual world, just as it is a necessary truth that God was impressed by a different set of reasons on account of which he might have created another world. After all, necessarily, an omniscient and morally perfect God is impressed by all and only the good reasons. What the reasons on the basis of which God created this world are is something largely beyond my ken, although we can say a few standard things about the value of beings that participate in God's life.
As a modification of my hypothesis, I should note that it might be that what matters explanatorily is not only the fact of the agent's being impressed by the reasons, but also the degree to which the agent is impressed by them. It is easy to modify the account to take this into account, by explaining not just in terms of a set of reasons but in terms of a set of reason-weight pairs.
There is, still, something uncomfortable about the proposed explanation of libertarian action. I think a reader is likely to have the sense that while it is correct to say that the choice of graduate school might be explained by what is better for a spouse, even though this reason would have equally been present had a choice not supported by this reason been made instead, this kind of explanation is explanatorily inferior to, say, deterministic causal explanation or explanation in terms of a necessitating metaphysical principle. That may be. But there is no need to take the PSR to say that there is always the best kind of explanation - the PSR I am defending merely says that there is an explanation of every contingent proposition. And that is all I need for the cosmological argument.
12. Note that Salmon's definition (Salmon 1990, p. 67) of a statistical relevance explanation of a fact as simply being an assemblage of statistically relevant facts implies the claim that the explanation of p in one world will be an explanation of ~p in another if we add the observation that sometimes, maybe even always, whatever is relevant to p will also be relevant to ~p.
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