An Insufficient Argument against Sufficient Reason

This is an emended version of an entry that first saw the light of day on 21 May 2016. It is a set-up for a response to a question put to me by Tom Oberle.  I'll try to answer Tom's question tomorrow.

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Explanatory rationalism is the view that there is a satisfactory answer to every explanation-seeking why question. Equivalently, it is the view that there are no propositions that are just true, i.e., true, contingently true, but without explanation of their being true. Are there some contingent truths that lack explanation? Consider the conjunction of all contingent truths. The conjunction of all contingent truths is itself a contingent truth. Could this contingent conjunctive truth have an explanation? Jonathan Bennett thinks not:

Let P be the great proposition stating the whole contingent truth about the actual world, down to its finest detail, in respect of all times. Then the question 'Why is it the case that P?' cannot be answered in a satisfying way. Any purported answer must have the form 'P is the case because Q is the case'; but if Q is only contingently the case then it is a conjunct in P, and the offered explanation doesn't explain; and if Q is necessarily the case then the explanation, if it is cogent, implies that P is necessary also. But if P is necessary then the universe had to be exactly as it is, down to the tiniest detail -- i.e., this is the only possible world. (Jonathan Bennett, A Study of Spinoza's Ethics, Hackett 1984, p. 115)

A clever little argument, this. Either Q is contingent or Q is necessary. If Q is contingent, then it is a conjunct in P and no explanation of P is to be had. But if Q is necessary,  then so is P.  So explanatory rationalism fails: there is no explanation of P's contingent truth.

Bennett's point is that explanatory rationalism entails the collapse of modal distinctions.  To put it another way, the principle of sufficient reason, call it PSR, according to which every truth has a sufficient reason for its being true, entails the extensional equivalence of the possible, the actual, and the necessary.  These modal words would then differ at most in their sense but not in their reference. If we assume, as most of us will, the non-equivalence of the possible, the actual, and the necessary, then, by modus tollens, we will infer the falsity of explanatory rationalism/PSR.  

This is relevant to the God question.  If PSR is false, then cosmological arguments for the existence of God which rest on PSR will be all of them unsound.

Now let's look at Bennett's argument in detail.

The world-proposition P is a conjunction of truths all of which are contingent. So P is contingent. Now if explanatory rationalism is true, then P has an explanation of its being true.  Bennett assumes that this explanation must be in terms of a proposition Q distinct from P such that Q entails P, and is thus a sufficient reason for P. Now  Q is either necessary or contingent. If Q is necessary, and a proposition is explained by citing a distinct proposition that entails it, and Q explains P, then P is necessary, contrary to what we have assumed. On the other hand, if Q is contingent, then Q is a conjunct in P, and again no successful explanation has been arrived at. Therefore, either explanatory rationalism is false, or it is true only on pain of a collapse of modal distinctions.  We take it for granted that said collapse would be a Bad Thing.  

Preliminary Skirmishing

Bennett's is a cute little argument, a variant of which  impresses the illustrious Peter van Inwagen as well,  but I must report that I do not find the argument in either version  compelling. Why is P true? We can say that P is true because each conjunct of P is true. We are not forced to say that P is true because of a distinct proposition Q which entails P.

I am not saying that P is true because P is true; I am saying that P is true because each conjunct of P is true, and that this adequately and non-circularly explains why P is true. Some wholes are adequately and non-circularly explained when their parts are explained.  In a broad sense of 'whole' and 'part,' a conjunction of propositions is a whole the parts of which are its conjuncts. Suppose I want to explain why the conjunction Tom is broke & Tom is fat is true.  It suffices to say that Tom is broke is true and that Tom is fat is true. Their being conjoined does not require a separate explanation since for any propositions their  conjunction automatically exists. Nor does the truth of a conjunction need a separate explanation since the truth of a conjunction supervenes upon the truth of its conjuncts. It is an aletheiological free lunch.

Suppose three bums are hanging around the corner of Fifth and Vermouth. Why is this threesome there? The explanations of why each is there add up (automatically) to an explanation of why the three of them are there. Someone who understands why A is there, why B is there, and why C is there, does not need to understand some further fact in order to understand why the three of them are there. Similarly, it suffices to explain the truth of a conjunction to adduce the truth of its conjuncts. The conjunction is true because each conjunct is true. There is no need for an explanation of why a conjunctive proposition is true which is above and beyond the explanations of why its conjuncts are true.

Bennett falsely assumes that "Any purported answer must have the form 'P is the case because Q is the case'. . ." This ignores my suggestion that P is the case because each of its conjuncts is the case. So P does have an explanation; it is just that the explanation is not in terms of a proposition Q distinct from P which entails P.

Going Deeper 

But we can and should go deeper.  P is true because each of its conjuncts is true.  But why are they each true?  Each is true because its truth-maker makes it true.  A strong case can be made that there are truth-makers and that truth-makers are concrete facts or states of affairs.  (See D. M. Armstrong, et al.)  A truth-making fact is not a proposition, but that which makes a contingently true proposition true.  Contingent truths need ontological grounds. Armstrong finds the thought already in Aristotle. My being seated, for example, makes-true 'BV is seated.'  The sentence (as well as the proposition it is used to express) cannot just be true: there must be something external to the sentence that makes it true, and this something cannot be another sentence or anyone's say-so.  As for Bennett's "great proposition P," we can say that its truth-maker is the concrete universe. Why is P true?  Because the concrete universe makes it true.  'Makes true' as used in truth-maker theory does not mean entails even though there is a loose sense of 'makes true' according to which a true proposition makes true any proposition it entails.  Entailment is a relation defined over propositions: it connects propositions to propositions.  It thus remains within the sphere of propositions. Truth-making, however, connects non-propositions to propositions.  Therefore, truth-making is not entailment.  

We are now outside the sphere of propositions and can easily evade Bennett's clever argument.  It is simply not the case that any purported answer to the question why P is the case must invoke a proposition that entails it. A genuine explanation of why a contingent proposition is true cannot ultimately remain within the sphere of propositions.  In the case of P it is the existence and character of the concrete universe that explains why P is true.

Going Deeper Still

But we can and should go deeper still.  Proposition P is true because the actual concrete universe U -- which is not a proposition -- makes it true.  But what makes U exist and have the truth-making power?  If propositional truth is grounded in ontic truth, the truth of things, what grounds ontic truth?  Onto-theological truth?

Theists have a ready answer: the contingent concrete universe U exists because God freely created it ex nihilo.  It exists because God created it; it exists contingently because God might not have created it or any concrete universe.  The ultimate explanation of why P is true is that God created its truth-maker, U.

Now consider the proposition, God creates U.  Call it G.  Does a re-run of Bennett's argument cause trouble?  G entails P.  G is either necessary or contingent.  If G is necessary, then so is P, and modal distinctions collapse.  If G is contingent, however, it is included as a conjunct within P.  Does the explanation in terms of divine free creation therefore fail?

Not at all.  For it is not a proposition that explains P's being true but God's extra-propositional activity, which is not a proposition. God's extra-propositional activity makes true P including G and including the proposition, God's extra-propositional activity makes true P.

Conclusions 

I conclude that Professor Bennett has given us an insufficient reason to reject the Principle of Sufficient Reason.

I apply a similar critique to Peter van Inwagen's version of the argument in my "On An Insufficient Argument Against Sufficient Reason," Ratio, vol. 10, no. 1 (April 1997), pp. 76-81.

Arguments to God a contingentia mundi that rely on PSR are not refuted by the Bennett argument. 

Comments

[Tom]

Thanks Dr. BV,

two points I have on this post.

First, it doesn't seem to me the case that conjunctions are always explained fully in terms of their conjuncts. In the case of the three bums, Pruss points out that there might be some further explanation for why all three are where they are, say they are terrorists about to detonate themselves in a coordinated attack. In that case, knowing that A is there, that B is there, and that C is there doesn't suffice to explain why all three are where they are at the same time.

Second, I had thought that maintaining that conjunctions are grounded in their conjuncts thereby removes the need for an 'outside' explanation of the series. Thus, we get to keep the PSR from the objection of modal collapse, yet this undermines the use of the PSR for arguing that there must be an 'outside' explanation (God) of the collection as a whole.

You seem to agree with me here, if I'm not mistaken, because your strategy to nonetheless argue for God involves saying that God's creating the world is not a proposition (which I agree with). But now you're moving beyond the PSR. Why not just avoid all this and adopt the unrestricted PSR? It is the PSR restricted to contingently true propositions that leads to all this hassle, as far as I can tell.

Thanks for your time!

[BV]

First, don't confuse propositions with bums. If you have two propositions, p, q, then automatically, so to speak, you have their conjunction p & q. Nothing more is needed to explain the existence of the conjunction beyond the conjuncts. Now suppose both propositions are true. Nothing more is needed to explain the truth of the conjunctive proposition beyond the truth of the conjuncts.

Suppose you have a bolt and a nut. The existence of these two logically suffices for the existence of the set of the two, and for the mereological sum of the two. But it does not suffice for the existence of nut-threaded-onto-bolt. In this case, an additional explanatory factor must be invoked.