An Argument from Contingency is an argument for the existence of God which employs a broad explanatory principle asserting, for every contingent fact, the existence of an explanation, reason or cause of some sort. It proceeds from the existence of contingency via the principle to an explanation of the contingency, whereupon it is inferred that this explanation must be necessary, and that this necessary being must be God. Here’s a basic version of the argument, which I intend to show unsound:
(1) Every contingent fact has an explanation. (The Principle of Sufficient Reason, or PSR)
(2) There is a contingent fact that includes all other contingent facts.
(3) Therefore, there is an explanation of this fact.
(4) This explanation must involve a necessary being.
(5) This necessary being is God.
Before I get to my criticism of this kind of argument, I must mention that ‘explanation’ here is always explanation of a certain sort. Put vaguely, an explanation of some fact serves to make that fact comprehensible, to make it less mysterious and surprising. But two ways to accomplish this. The first way is via descriptive explanation, which tells us in detail what the explanandum1 is, and in doing so makes comprehensible the truth of what is explained – to believe that some fact is true requires a clear conception of the nature of that fact, and descriptive explanations facilitate this semantic prerequisite of belief. The second way is via causal explanation, which tells us why the explanandum is. Unlike descriptive explanations, causal explanations involve the postulation of entities, those to which the explanans and explanandum refer. And unlike descriptive explanations, in which the explanans is identical to the explanandum, a causal explanans is always external to the explanandum. It cites a cause, or set of causes, which make the truth of the explanandum comprehensible by showing us how it is the necessary or likely product of some state of affairs which does not include it2.
Here is an example of what I mean: suppose I request an explanation of Republicanism in the United States from you. Your answer might involve a description of the political system, in terms of its three tiers of representation, the separation of its legislative, judicial and executive branches, the Constitution, and so on. Such an explanation is a descriptive explanation, for it tells me in what Republicanism in the United States consists. But you might instead give me an account of early American history, including the social influences that lead to the American Revolutionary War, and onwards to the drafting of the Constitution. This second explanation would be a causal explanation, for you presume me to know what Republicanism here is, but interpret me as asking after the conditions from which Republicanism could be seen to follow. Both answers count as explanations, as both serve to make comprehensible Republicanism in the United States, but they are obviously explanations of different kinds3.
With the distinction in hand, we see immediately that the sense of explanation relevant to the Argument from Contingency is that of causal explanation. What the PSR is intended to assert is not that every contingent fact has a description which would make it comprehensible, since one could not infer the existence of anything from this, but that for every contingent fact there is something external to it from which the truth of the fact can be seen to follow. So, in what follows I’ll be discussing causal explanations, and I’ll add the qualification to quotations. We proceed to a criticism of the PSR.
Van Inwagen’s Modal Fatalism Argument
Peter Van Inwagen, a theist himself, offers a reductio of the PSR:
(11) No necessary proposition [causally] explains a contingent proposition. (Premise.)
(12) No contingent proposition [causally] explains itself. (Premise.)
(13) If a proposition [causally] explains a conjunction, it [causally] explains every conjunct. (Premise.)
(14) A proposition q only [causally] 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 [causal] 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 [causally] explains itself. (By (13), (15), (17) and (19).)
(22) But q does not [causally] explain itself. (By (12) and (19).)
(23) Thus, q does and does not [causally] explain itself, which is absurd. Hence, the PSR is false.
Both this argument and the basic argument we met earlier have been lifted from Alexander Pruss’s extensive chapter on Leibnizian Cosmological arguments, from the Blackwell Companion to Natural Theology. And as we would expect, Pruss has something to say about Van Inwagen’s reductio. He thinks that the theist should not accept (11). He tells us:
The main reason to accept (11) is the idea that if a necessary proposition q [causally] 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 [causally] 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 [causally] explain p.
Instead of attacking (11) directly, I shall focus my attack on (24).. [which] seems to capture just about all the intuition behind (11). By contraposition (24) is equivalent to:
(27) If q [causally] explains p, then q entails p.
But Pruss thinks (27) is false. Briefly, it is false because a causal explanation need not entail that which it explains. In fact, a causal explanation need not even make probable what it explains, as in the explanation of syphilis by paresis: whereas the cause of paresis is known to be untreated syphilis, it is only in a small percentage of cases of untreated syphilis that paresis does result. But untreated syphilis is a causal explanation of paresis, even if not a sufficient (entailing) one, and so it follows that causal explanations need neither entail nor make probable their explanandum.
Pruss is right, of course, to say that (27) is false, and so that (24) is false. But showing that (24)-(26) is an unsound argument does not show that (11) is false; at most, it shows that one way of attempting to justifying (11) is a failure. So let’s try another way.
(A) Suppose that some necessary proposition q causally explains a contingent proposition p. (Premise for reductio)
(4) A proposition q only causally explains a proposition p if q is true.(Premise)
(B) So, q is a necessary truth. (From A and 4)
(C) The probability of a necessary truth is 1. (Premise)
(D) So, P(q) is equal to 1. (From B and C)
(E) Then, P(p|q) is equal to P(p). (From D4)
(F) But, if q causally explains p, then P(p|q) > P(p). (Premise)
(G) So, q does not causally explain p. (From E and F)
(H) Then, q both does and does not causally explain p, which is absurd. (From A and G)
(11) (Therefore) No necessary proposition causally explains a contingent proposition.
The thought behind (24)-(27) was that causal explanations entailed what they explained. The thought behind the argument I propose is different, and is captured by (F): though causal explanations may neither entail nor make probable what they explain, it is at least true of causal explanations that their being true increases the probability of that which they explain5. Consider again the syphilis-paresis case: though the presence of untreated syphilis does not make paresis probable, as it only rarely leads to paresis, still someone’s having syphilis makes paresis more likely than it otherwise would be, and plausibly this is required in order for it to be explanatory. By contrast, were it not the case that syphilis raised the probability of paresis, then it would be difficult to see in what sense syphilis would make the existence of paresis more comprehensible, less mysterious or surprising. It would be difficult to see what causal relevance syphilis had to paresis at all. We can bring this thought out with the following argument:
(I) To causally explain some fact X, one must cite some fact Y other than X which is yet relevant to X’s obtaining.
(II) To causally explain X is to simultaneously causally explain X’s being true.
(III) So, to causally explain X is to cite some Y other than X’s being true, which is relevant to X’s being true.
(IV) Some Y is relevant to X’s being true only if it either conduces to the truth of X, making it more probable, or conduces to the falsity of X, making it less probable.
(V) Whatever conduces to the falsity of X does not causally explain X.
(VI) Therefore, to causally explain X is to cite some Y other than X’s being true, which conduces to the the truth of X, making X more probable.
So, that a causal explanation increases the probability of its explanandum simply falls out of its being an explanation of some fact’s being true. And now we can see why a necessary fact fails to explain a contingent fact. If a necessary fact did explain a contingent fact, then it would explain why that contingent fact was true. So a necessary fact would have to offer something relevant to the truth of the contingent fact. And whatever is relevant to the truth of the contingent fact, which we could describe as causally explanatory, would have to conduce to the truth of that contingent fact. But a necessary fact is not conducive to the truth of any contingent fact for, what is equivalent, the truth of a necessary fact does not increase the probability of that contingent fact’s obtaining – a necessary fact will obtain whether or not the contingent fact also obtains, and so it tells us nothing about whether the contingent fact also obtains. Hence, Van Inwagen’s modal fatalism argument is sound: the Principle of Sufficient Reason is false, and all arguments which assume its truth are fatally flawed.
If the above argument is sound, then the PSR is false, and so one more argument for the existence of God is unsound. But though that is of interest, there is more we can conclude from the defense of Van Inwagen’s argument: it follows from the fact that no necessary proposition causally explains a contingent proposition that, if God is necessary, then God does not causally explain the universe. And given that part of what we understand by the term ‘God’ is ‘the cause of the universe’, it follows that if God is necessary, God does not exist. In that case I recommend that theists give up the notion that God is necessary, as well as the principle of sufficient reason6.
There are, it is true, potential counterexamples to the principle that “if q causally explains p, then P(p|q)>P(p)“. I’ll address two, taken from the SEP’s article on Probabilistic Causation. The first:
(i) Probability-lowering Causes. Consider the following example, due to Deborah Rosen (reported in Suppes (1970)). A golfer badly slices a golf ball, which heads toward the rough, but then bounces off a tree and into the cup for a hole-in-one. The golfer’s slice lowered the probability that the ball would wind up in the cup, yet nonetheless caused this result.
In response, I deny that it is true that the golfer’s slice lowers the probability of a hole-in-one. That the golfer’s slicing the ball as opposed to hitting the ball cleanly lowers the probability of a hole-in-one is undoubtedly true, and in that case it is true that the golfer’s slicing the ball as opposed to hitting it cleanly does not causally explain the hole-in-one. On the other hand, slicing the ball simpliciter does raise the probability of a hole-in-one, since a hole-in-one is more likely on a slice than on no information regarding the initial conditions at all. Hence slicing the ball simpliciter is causally explanatory of the hole-in-one. The second case:
(ii) Preemption. A different sort of counterexample involves causal preemption. Suppose that an assassin puts a weak poison in the king’s drink, resulting in a 30% chance of death. The king drinks the poison and dies. If the assassin had not poisoned the drink, her associate would have spiked the drink with an even deadlier elixir (70% chance of death). In the example, the assassin caused the king to die by poisoning his drink, even though she lowered his chance of death (from 70% to 30%). Here the cause lowered the probability of death, because it preempted an even stronger cause.
My response here is of the same sort. It is not true that the assassin’s poisoning the king’s drink lowers the probability of the king’s death. What is true is that the assassin’s poisoning the drink as opposed to leaving the poisoning to their associate lowers the probability of the king’s death, and so, it is true that the assassin’s poisoning the drink as opposed to leaving the poisoning to an associate is not causally explanatory. However, as the assassin’s poisoning the king’s drink simpliciter does raise the probability of the king’s death, we can say that the assassin’s poisoning the king’s drink causally explains the king’s death.
As the SEP article notes, both of these are cases of singular causation (they make reference to particular individuals, places, and times). I suggest that this is not coincidental: To judge whether or not some X counts as a cause, we need to come to a conclusion about what causal powers X has, and this can only be done if we abstract away from the particular situation and advert to some comparison class of similar situations including X. But to ask after a cause in a case of singular causation leaves open just which details we are to hold constant in determining our comparison class, and so makes possible the kind of inconsistent treatment above – the probabilistic evaluation of a purported cause erroneously based on the irrelevant features of a singular case.
1 For convenience, I’ll be using the Latin terms ‘explanandum’ and ‘explanans’. An explanandum is what is explained, whereas an explanans is what does the explaining.
2 One response to the Argument from Contingency, and indeed all cosmological arguments, is to observe that they would appear to require a cause of the Big Bang. But, so the objection goes, it is part of the definition of a cause that it precedes its effect in time, and as nothing can precede the Big Bang in time, nothing can be its cause. For this post I’ll assume that the notion of cause is flexible enough to accommodate a timeless cause, which does not precede its effect.
3 There are two other classes of explanation sometimes added to my two. The first is intentional explanation – explanations which cite the beliefs and desires of agents as producing some effect. For my part, I see no good reason to assume that intentional explanations are not a species of causal explanation: though some philosophers may believe intentional explanations do not fit the scientific criteria of a cause, I take the lesson here to be not that they are non-causal explanations, but that there is a broader notion of cause upon which the scientific model is a restriction.
The second potential class is that of justification – explanation in terms of reasons for belief in what is explained. This too, I believe to be a species of causal explanation, for in giving reasons for belief one is often citing such reasons as causally efficacious in producing one’s belief. Cases where this does not happen, say, when reasons for belief are given merely to recommend a belief to others, or where they are cited in support of one’s belief without being productive of that belief, are not cases of genuine explanation – the former because explanation is factive, whereas one may recommend a belief to others without their being some belief which would be explained; the latter because it is an instance of rationalization, but rationalization merely masquerades as explanation.
In any case, it does not appear that insisting on either class in addition to our two would favor the Argument from Contingency: if the PSR is to be interpreted as demanding an intentional explanation for every contingent fact, then the argument from contingency would seem to beg the question; alternatively, if the PSR is interpreted as demanding a reason why one should believe any given contingent fact, then a logical demonstration would suffice to explain the contingent fact which includes all other contingent facts.
4 This follows from Bayes theorem. According to (D), P(q) is 1. Then, P(q|p) is also 1, and we can deduce as follows:
P(q|p) = P(p|q) x P(q) / P(p) [Bayes Theorem]
1 = P(p|q) x 1 / P(p) [Substitution]
1 = P(p|q) / P(p) [Elimination]
1 x P(p) = P(p|q) / P(p) x P(p) [Multiplication of both sides by common factor]
P(p) = P(p|q) [Result]
5 I stress that this is but necessary condition of a causal explanation, and is not intended as an analysis of what causal explanations are.
6 I feel I should add that this concession may not be theologically significant: often, the terms ‘necessary’ and ‘contingent’ are taken to be synonyms of ontological independence and dependence respectively. But as Ex-Apologist has argued, these concepts are not synonymous, and since it seems to me that it is ontological independence which is part of the core conception of God as opposed to necessity, I believe that this is an adjustment the orthodox theist can accept.