The basic argument

3.2.1.1. The effect would not have occurred without the cause

I will formulate this argument in terms of the cause of a contingent state of affairs. "States of affairs" here are understood as concrete things that can stand in causal relations, rather than as abstracta, and that exist if and only if they obtain. Moreover, I shall assume that states of affairs are individuated in such a way that in every world where Socrates is sitting at t0, his sitting at t0 is the very same state of affairs, just as the proposition that he is sitting at t0 is the same proposition in every world. States of affairs are, thus, fine-grained, and Kripkean essentiality of origins does not hold for them - the state of affairs of Socrates' sitting at t0 is the same state of affairs regardless of what caused it.

The argument now bootstraps its way from the possibility of a cause to the actuality of a cause. Thomas Sullivan (1994) has tried to find an argument for the CP based on the idea that a cause was a necessary condition for the effect. While this requirement is too strong, something in the vicinity of the following fact should be true:

(29) That C causes E entails that were C not to exist or take place, E would not have taken place.

Claim (29) is not meant to be a complete analysis of causation, and, anyway, it requires that in cases of causal overdetermination we describe C carefully, for instance, as a disjunctive state of affairs. But something like this counterfactual claim is certainly a part of our notion of causation. David Lewis thought that this counterfactual claim was at the root of a complete analysis of causation, but this further controversial claim will not be needed.15

Suppose now that an airplane crashes due to metal fatigue in the ailerons. Then the following nested counterfactual is true:

(30) Were the plane earlier hit by a surface-to-air missile, then the plane would have crashed and it would have been the case that were the plane not hit by a surface-to-air missile, the plane would, or at least might, still have crashed.

The plane would or might still have crashed because of the metal fatigue in the ailerons. Analogously, one might say this. Suppose that an airplane crashes for no reason at all. Then the following nested counterfactual should be true by parallel to (30):

(31) Were the plane hit by a surface-to-air missile, then the plane would have crashed and it would have been the case that were the plane not hit by a surface-to-air missile, the plane would, or at least might, still have crashed.

Presumably, the consequent of the inner counterfactual can be taken to say that the plane would or might still have crashed for no reason at all. But this results in the absurdity that in the counterfactual world w where the plane is hit by a surface-to-air missile, and where no other crash-inducing causes are available (since the counterfactual that moved us to that world presupposed only one added cause - the surface-to-air missile), it is the case that were the missile not to have hit, the plane would or might still have crashed, contradicting the fact that the missile is the cause in w of the plane's crashing. Therefore, we should reject the possibility of the assumption that an airplane crashes for no reason at all.

As it stands, the argument may be thought to rest on improperly assimilating the case where the plane crashes because of no reason at all to the case where the plane crashes for some specific reason. In the latter case, when we move to a counterfactual world by positing

15. One might argue as follows against Lewis's more general claim. The recently shown failure of Lewis's own semantics for counterfactuals to properly exclude absurd cases of backtracking counterfactuals where the consequent is in the antecedent's past (Elga 2001; Pruss 2004b) strongly suggests that a semantics for counterfactuals will have to presuppose an asymmetry between the past and the future. One might further argue that there are no scientific asymmetries to sufficiently ground an asymmetry of such philosophical significance, and this might lead one to the Kantian view that the asymmetry in time supervenes on the asymmetry of causation: the past is just that region of time where (at least most of) the causes of present events are situated and the future is just that region of time where (at least most of) the effects of present events are situated. But if the asymmetry of time is presupposed in a semantics for counterfactuals, and the asymmetry between cause and effect is presupposed in the asymmetry of time, then at the pain of circularity one cannot analyze causation in terms of counterfactuals.

a new cause, we generate a case of overdetermination, and hence a case where the effect would still happen even without the new overdetermining cause. But in the case where the plane crashes because of no reason at all, the counterfactual world where a cause is posited is a world where there is only one cause, and hence the counterfactual that were the cause not to have occurred the effect would not have taken place is intact.

We will see, however, that we can make a variant of the said argument into a valid and plausible argument for a CP. We will need a certain precise version of the observation that were the cause to have taken place, the effect would not have. This version says that if a state of affairs E is in fact caused by C, then E would not have occurred were no cause of E to exist:

(32) (C causes E) => ((-3D (D causes E)) □—>E did not occur), where "p □—> q" stands for "were p to hold, q would hold," and where "=>" marks entailment. We will also need a might operator: "p O—> q" will stand for "were p to hold, q might hold." The two operators are related as follows: (p □—> q) <=> ~(p 0—> ~q).

Premise (32) takes into account the possibility of overdetermination, where more than one state of affairs takes place, each of which is sufficient to cause E. It also takes into account the possibility that perhaps, were C not to have occurred, some other state of affairs D would have caused E. For instance, if members of some group are asked to volunteer to execute a traitor, then it might well be that Jones's shooting the traitor causes the death of the traitor, although were Jones not to have shot the traitor, someone else would have, and hence the traitor would still have died.

I shall now argue that if E is a state of affairs that can have a cause, then E is a state of affairs that does have a cause. Since every step in the argument will be a conceptual truth if the argument works, it will follow that if E has a cause in one possible world, then in every world in which E takes place, E has a cause.

David Lewis proposed the following analysis of counterfactuals for a possible proposition p: p □—> q holds providing there is a (p&q)-satisfying world that is more similar to the actual world than any (p&~q)-satisfying world is (Lewis 1986, sec. 1.3). While this analysis is, doubtless, not correct in all its details,16 the intuitive idea of a connection between counterfactuals and possible worlds should remain. When we try to see whether p □—> q is true, we move to worlds relevantly similar to our world, but in which p holds, and see whether q holds in all such worlds. What features we must carry over from the actual world to the counterfactual world for it to count as "relevantly similar" is a difficult question. One might well say that, to the extent that p allows, one needs to carry over laws of nature and the past of p, while Lewis insists that "relevant similarity" has to do with being as similar as possible to the actual world. If, on the other hand, we think that there is some world relevantly similar to our world in which p holds but q does not, then we say that were p to hold, q might not hold.

16. See, for instance, Edgington (1995), Elga (2001), and Pruss (2004b, 2007). See also Section 3.2.2.1, below.

In modal logic, the Brouwer Axiom, which is entailed by S5, says that if a proposition p is actually true, then necessarily that proposition is possible. In terms of accessibility, this says that if we were to move to a world accessible from the actual world, the actual world would be accessible from that world: the accessibility relation is symmetric. But perhaps the best intuitive way to think about the Brouwer Axiom is to think of it as encapsulating the observation that in any nonactual situation we might consider, the events of the actual world remain relevant as alternative possibilities.

There is an analogue of this observation in the case of counterfactuals:

(33) (q&p&M~p)=>(~pn-»(p«-»i/)), where M indicates metaphysical possibility. If we actually have both p and q holding, and then move to a relevantly similar world w in which p does not hold, so as to evaluate a counterfactual with antecedent ~p, the events of the actual world are going to be relevant for the evaluation of counterfactuals in w. Hence, if we ask in w what would happen were p to hold, we need to say that q might happen, since q in fact happens in the actual world.

Consider how (33) plays out in some paradigmatic cases. Suppose p claims that Jones freely chose to set fire to a barn and q claims that Jones was arrested. Then, were Jones not to have set fire to the barn, it would certainly have been true that were he to have set fire to the barn, he at least might have been arrested. In the case where p reports the occurrence or nonoccurrence of some punctual event in time, we can think of the space of possibilities as a branching structure. Were p not to have occurred, we would have gone on a different branch from the one we had in fact gone on. But were we to have gone on that branch, it would have been true that were p to have occurred, things might have gone just as they have actually gone. The fact that things have gone a certain way witnesses to the relevant possibility of them going this way. In this sense, (33) is an analogue to the Brouwer Axiom.

We also need two further obvious axioms dealing with counterfactuals, where is entailment:

(35) ((pa—>q) & (p□—»-<?)) => ~Mp.

Entailment relations are stronger than counterfactual conditionals, and it cannot be that both q would hold were p to hold and ~q would happen were p to hold, unless p is itself impossible.

But now (33)-(35) imply that anything that can have a cause does have a cause. Let q be the true proposition that event E occurs, and suppose that E can have a cause. For a reductio, let p be the true proposition that there is nothing that causes E, that is, ~3D (D causes E). However, since E can have a cause, M~p. Thus, by the Brouwer analogue (33), we have:

Let w be any possible world at which ~p holds. Then, w is a world at which E has a cause. Since nonexistent and nonoccurrent things can neither cause nor be caused, E occurs at w, as does a cause, call it C. Applying (32), we see that it is true at w that were no cause of E to have existed, E would not have occurred, that is, it is true at w that p □—> ~q. Since this is true at every world at which E has a cause, that is, at every world at which ~p holds, it follows that:

But p □—> ~q is equivalent to ~(p o—» q). Thus, by (34):

By (35) and (36) it follows that ~Mp. But p was assumed to be true, and true propositions are possible, and hence absurdly ~Mp and Mp.

Thus, the assumption for the reductio is false, and so p is false. Hence, there is a cause of E.

This is enough to show that Humeans are wrong to think that a brick could come into existence for no cause at all. For it is plain that there can be a cause of the state of affairs of a brick's coming into existence at t, and hence by the argument, there is such a cause.

It is plausible that for any physical kind of object identified de dicto and in a positive way, such as a galaxy containing exactly n stars and having total mass M, the state of affairs of that kind of object existing can have a cause, and hence does. Similarly, if we have a positive de dicto description D of all the physical stuff in the universe, it seems that it ought to be possible for there to be a cause of the state of affairs described by D. For instance, we could imagine D being satisfied in a larger world w* where D describes a proper part P of the contents of w*, a proper part that has a cause in another proper part Q of the contents of w*, where Q might not actually exist in the actual world. That the description D is positive is important, since a nonpositive description could rule out the existence of Q, for example, by saying that there is nothing outside of what D describes.

From such considerations, we get a CP for physical objects, and by the same reasoning for causal chains of physical objects (surely there could be a cause of the whole chain). And this can yield a cosmological argument for a nonphysical being (see Section 4.2, below).

But let us slow down for a moment, and try for a more expansive result.

3.2.1.3. Which contingent states of affairs can have a cause?

If I could argue that all contingent states of affairs can have causes, then a CP for contingent states of affairs would follow from the conclusion of the previous section. However, there are several concerns about this idea.

A contingent state of affairs that contains a part that obtains necessarily perhaps cannot be expected to possibly have a cause. We do not expect the state of Socrates' having existed in a world without square circles to have a cause. Consider now the notion of a wholly contingent state of affairs, that is, one that has no component part that is necessary. Thus, the state of affairs of Socrates' having existed is wholly contingent, but the state of affairs of Socrates' having existed in a world that has no square circles is not wholly contingent. On a plausible set of mereological axioms for states of affairs, one can establish that every contingent state of affairs S contains a maximal wholly contingent part S* such that, necessarily, S obtains if and only if S* does.17 We can now reasonably expect the possibility of causes for the wholly contingent substates.

A second problem is that if essentiality of origins holds, then that the state of affairs of Socrates' existing can have a cause immediately implies that the state of affairs does have a cause, since a cause of the state of affairs will presumably have to be a cause of Socrates, and hence will have to exist in every world where Socrates does. So if essentiality of origins holds, the atheist is likely not to grant that all contingent states of affairs can have causes. (Note that essentiality of origins could, in principle, hold for an uncaused being - such a being would then be essentially uncaused.)

Likewise, the smart atheist is likely not to grant that, in general, nonpositive contingent states of affairs can have causes, since granting that would yield the existence of a necessarily existent, causally efficacious being too quickly. For instance, the atheist is likely to think that there is a possible world that consists of only a single photon, and no necessarily existent, causally efficacious beings. But then, consider the state of affairs of there being one photon and nothing else. That state of affairs cannot have a cause, since that cause could not be the photon on pain of circularity and could not be anything else on pain of contradiction.

Consider now the following pair of claims:

(39) If all wholly contingent, positive states of affairs that do not de re involve entities for which essentiality of origins holds have causes, then all wholly contingent, positive states of affairs have causes.

(40) Every wholly contingent, positive state of affairs that does not de re involve contingent entities for which essentiality of origins holds can have a cause.

Claim (40) is an extension of the observation that states of affairs of the existence of de dicto described physical entities all can have causes. There is no reason to limit that observation to physical entities. If there can be a ghost that is 7-feet tall, then there can be a 7-foot tall ghost with a cause.

17. Koons (1997, Lemma 2) shows that every contingent state of affairs ("fact" in his terminology) contains a wholly contingent part. Let S* be the aggregate of all wholly contingent parts of S. Note that S* must itself be wholly contingent. For suppose, for a reductio, that it has a necessary part N. Then N has to overlap at least one of the wholly contingent parts of S, since every part of an aggregate must overlap at least one of the aggregated things. Thus, N will have a part in common with a wholly contingent part P of S. Thus, there will be a part Q that N and P will have in common. Any part of a necessary state of affairs is necessary (Koons 1997, Lemma 1), and so Q is necessary, contrary to the claim that P is wholly contingent, which is absurd. So S* is wholly contingent. Moreover, it is a maximal, wholly contingent part of S. The only remaining question is whether it is the case that, necessarily, S obtains if and only if S* does. One direction is clear: necessarily, if a state of affairs obtains, so do its parts, so, necessarily, if S obtains, so does S*. For the converse, let N be the aggregate of all necessary parts of S. Clearly, N is itself necessary. Let S** be the aggregate of N and S*. Since N is necessary, necessarily if S* obtains, so does S**. If we can show that S** = S, it will follow that, necessarily, if S* obtains, so does S. For a reductio, suppose that S** is not equal to S; then there is a U that overlaps one but not the other (Koons 1997, Axiom 3). Since S** is a part of S, it must be that U overlaps S but not S**. But then, let V be a part that S and U have in common. If V is contingent, it will have a wholly contingent part (Koons 1997, Lemma 2), and this part will then be a part of S**, and so V will overlap S**, and hence so will U, which contradicts what was already said. So V must be necessary. But then V is a part of N, and hence overlaps S**, and hence U overlaps S**, which again contradicts what was already said.

I now argue for (39). Say that a kind of entity is "essentially origined" if essentiality of origins holds for that kind of entity. I claim that any contingent state of affairs S that does de re involve essentially origined entities has an associated state of affairs Sf that does not. We obtain Sf by taking a canonical description D of S in some ideal language and Ramseyfying it as follows. If the description D made reference to essentially origined entities ei, e2, . . . , so that D = D(e1, e2, . . .), then let Ei be the maximally specific, positive description of ei that does not involve the de re occurrence of any essentially origined entities (I shall assume there is a unique maximal description, since we can just conjoin any descriptions that meet the criteria other than maximality). A positive description is one such that the state of affairs of its being satisfied is a positive state of affairs. Descriptions that use words such as "unique" are not positive. And now we can Ramseyfy by letting Df be:

(41) 3x13x2 . . . (D(x1, x2, . . .) & E1(x1) & E2(x2) & . . .).

Finally, let Sf be the state of affairs described by Df.

Say that a world is "nice" if every pair of distinct essentially origined entities in that world differs in the maximally specific, positive, definitive descriptions that do not involve the de re occurrence of any essentially origined entities. On a plausible way of understanding Leibniz's doctrine of identity of indiscernibles, any world for which identity of indiscernibles holds is a nice world. It is very plausible that our world is nice - it seems very likely that our world, in fact, lacks indiscernibles.

Now, plausibly, in a nice world, a cause C of Sf is also going to be a cause of S. First of all, C will be the cause of everything in S except maybe of the numerical identities of the satisfiers of D being what they, are since perhaps different individuals could play the same roles and satisfy D(x1, x2, . . .). But, plausibly, there is no further step in causing particular individuals to occupy roles. Sophroniscus and Phainarete were causes of the existence of a philosopher executed by hemlock. There was nothing further that they did to cause the existence of Socrates. Moreover, if we include all of the causes of Sf in C, then the numerical identities of the essentially origined individuals will also be taken care of, since it is plausible that for essentially origined entities, once their full causes have been given, their identity is thereby explained.

Therefore, (39) holds in nice worlds, and our world seems to be nice.

To amplify on the argument, observe that there are three plausible kinds of entities, with "entity" broadly understood, that might be essentially origined: substances, events, and some natural kinds. We might be a bit more worried about natural kinds. If all natural kinds were essentially origined, then the maximal descriptions introduced in the Ramsey-fication would be unable to include reference to natural kinds, and that might make the descriptions not be specific enough to ensure niceness of our world. However, plausibly, only some natural kinds are essentially origined. The thesis of essentiality of origins for natural kinds is highly implausible for basic kinds such as electron, star, and organism. Suppose the first electron, star, or organism could have arisen from a different cause. It would perhaps be a numerically different electron, star, or organism (respectively) from the first one in our world, but it would nonetheless still be an electron, star, or organism (respectively). Let us suppose that electrons arose from collisions between certain other particles. Then even had these collisions happened earlier or later, and had different individuals been involved in the collisions, it would still be electrons that arose. The only natural kinds for which essentiality of origins is plausible are biological taxa defined in evolutionary terms. It is somewhat plausible that had an animal with a different evolutionary history had the same DNA as the first horses, that animal would not have been a horse. But the limitation on descriptions that they do not involve taxa defined in evolutionary terms is not much of a limitation for our purposes - we can use phenotypic or genotypic descriptions instead, and if these are maximally specific, we will capture sufficient detail for the purposes of niceness.

And it seems that typical substances and events of our world can be captured by positive de dicto descriptions quite well. This may not capture their numerical identity, but it gives a maximal description strong enough that we would say that the cause of that description's being satisfied is the cause of the entity.

Now, given the conclusion of the previous section, together with (39) in nice worlds as well as (40), we get the claim that all wholly contingent, positive states of affairs in nice worlds have causes. But it is highly plausible that if the CP holds in nice worlds for wholly contingent, positive states of affairs, it also holds in non-nice worlds. The niceness condition is a version of the identity of indiscernibles. It would be odd indeed if there could not be a world consisting of a single uncaused brick, but there could be a world consisting of two indiscernible uncaused bricks. Hence, plausibly, the CP holds in all worlds for all wholly contingent, positive states of affairs.

One objection to this line of argument is that if libertarianism holds, it seems that states of affairs such as of George's freely choosing A are wholly contingent and positive, but cannot have a cause. One may worry whether freely choosing can be part of a positive state of affairs, since perhaps it entails the absence of external compulsion; but whether that worry is a good answer to the objection is unclear because many libertarians may accept that freedom is an intrinsic property of an action, and the absence of external compulsion is only relevant insofar as external compulsion would remove something from the intrinsic character of the action. However, the libertarian can say that the state of affairs of George freely choosing A has a cause. Maybe George is the cause. Or maybe George's making a choice between A and B while impressed by reasons R is the cause. Whether this cause provides a sufficient explanation of George's freely choosing A is a further question (see Section 2.3.2.3, above), but the mere claim of the existence of a cause is plausible.

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