EXPLANATORY RATIONALISM AND CONTINGENT TRUTHS

The argument of this paper is that current scepticism about explanatory rationalism is unjustified in one respect. It is widely assumed and sometimes argued that it is impossible to explain why there are positive contingent truths. In this paper, I shall challenge this contention and demonstrate that the following principle of explanatory rationalism is possibly true:

To begin with, let us make a first approximation at defining the relevant notions. A truth is a proposition with the truth value of true. A positive and contingent truth is a proposition that entails that some contingent concrete object exists and is true in some but not all possible worlds. The proposition that the stone is being warmed is positive and contingent since it entails that some stone exists and is true in some but not all possible worlds.

A sufficient reason for the truth of a positive contingent proposition p is another proposition q, such that (i) necessarily, p is true if q is true and (ii) q relevantly entails p (in the sense of relevant logics), and (iii) q explains why p is true. The sufficient reason for the truth of that the stone is being warmed is the conjunctive proposition that the sun is shining on the stone and whatever the sun shines upon is warmed.

The sufficient reason for the truth of any necessarily true proposition is that proposition itself. ' p has a sufficient reason for being true within its own nature' is logically equivalent to' p is necessarily true '. That every triangle has three sides is true by virtue of its nature.

I shall argue in this paper that it is possible that there is a sufficient reason why there are positive contingent truths. This reason cannot be a necessary truth (see Section 11). It must be a positive contingent truth, but it cannot be a reason why each positive contingent truth is true (see Sections III and IV).

I I

It is a logical contradiction to assert that a necessary truth is a sufficient reason for there being positive contingent truths. But this is not because it is a contradiction to assert that a necessary truth is a sufficient reason for there being contingent truths. We need to distinguish the proposition

The proposition that there are contingent truths is necessarily true and thus has a sufficient reason, namely, itself. The fact that this proposition is necessarily true follows from the fact that there is more than one possible world. A possible world is a maximal proposition W, such that for every proposition p, W entails p or not-p. If there are at least two possible worlds W₁ and W₂, it follows that there is at least one proposition q that is true in W₁ but not in W₂. (If W₁ contains all and only the same true propositions as W₂, then W₁ is identical with W2.) Ifq is true in W₁ and not in W₂, then q possesses its truth value contingently. If W₁is actual, then q is contingently true and if W₂ is actual, then the negation of q is contingently true. In either case, some proposition will be contingently true. Since this argument is generalizable to each possible world, it follows that some proposition will be true contingently regardless of which possible world is actual. Thus, it is true in each possible world that there are contingent truths. The claim that it is necessarily true that there are contingent truths is not, of course, the contradiction that contingent truths are necessarily true, since the fact that there are contingent truths is necessarily true does not entail that some contingent truth is necessarily true. To suppose otherwise is to confuse

(4) is a contradiction since it ascribes necessary truth to propositions that are contingently true, but (5) is consistent since it ascribes necessary truth to a proposition stating there are contingent truths.

(2) There are positive contingent truths. If (2) were necessarily true, then some necessary truth, namely (2) itself, would be the sufficient reason for the truth of (2), and there would be no logical contradiction. However, (2) is contingently true. Since a positive contingent truth entails that some contingent concrete objects exist, (2) is true only in the worlds in which there are contingent concrete objects. It is not true in the worlds in which it is true that no contingent concrete objects exist. In these worlds, there exist only necessary objects, such as propositions, properties and numbers.

(6) Some necessary truth is a sufficient reason for that there are positive contingent truths

is an implicit logical contradiction, since we can construct an explicit logical contradiction by conjoining with (6) the necessary truth

(7) The proposition that there are positive contingent truths has a contingent truth value and whatever has a sufficient reason in a necessary truth has a necessary truth value.

This shows that if the project or explanatory rationalism is logically tenable, and it is possible to specify a sufficient reason for there being positive contingent truths, then the only hope is to identify this reason with some positive contingent truth.

III

Some philosophers believe that it is impossible for a positive contingent truth to be a sufficient reason for there being positive contingent truths. A case in point is William Rowe.[1] Rowe enunciates a proposition similar to our (2):

Rowe considers states or affairs to be abstract objects that either obtain or do not obtain and exist even if they do not obtain. His' states or affairs' are identical or isomorphic to our propositions and the following equivalence obtains: ‘states or affairs either obtain or do not obtain and exist even if they do not obtain’ is logically equivalent to ‘propositions either are true or false f and exist even if they are false’. For Rowe, a state or affairs is positive if it t entails that at least one concrete object exists and is contingent if it obtains in some but not all possible worlds.

Rowe assumes that t is contingent, which is a plausible view given our foregoing considerations that there is some possible world in which there are no contingent concrete objects but only necessarily existent objects, such as numbers, properties and propositions. If t is positive and contingent, Rowe, argues, no state or affairs can be a sufficient reason for the obtaining or t and thus it is impossible for there to be a sufficient reason why there are positive contingent truths (why positive contingent states or affairs obtain). Let q be a state or affairs that allegedly explains t and let ‘actual state or affairs’ mean ‘obtaining state or affairs’. Rowe argues as follows:

Suppose that q is the state of affairs that explains t and that' q explains t' is made true by the fact that the actual state of affairs q stands in a certain relation R to t. The actual state of affairs qRt must entail the state of affairs t, otherwise the fact that qRt would not make it true that q explains t… Now the actual state of affairs qRt is either necessary or contingent. It cannot be necessary, for t would then be necessary… This means that the actual state of affairs qRt is a positive, contingent state of affairs. This being so, it is clear that qRt cannot make it true that q explains t. For to explain t, q must explain why there are positive, contingent states of affairs -and clearly q cannot serve this explanatory role by virtue of standing in relation R to t, if the fact that q stands in relation R to t is itself a positive, contingent state of affairs.[2]

I do not believe that it is 'clear' that q cannot explain t if qRt is contingent. Rowe does not offer further argument but he does offer an example. Suppose , ‘that God willed that positive contingent states of affairs be actual’.[3] In this case, God wills that positive contingent states of affairs be actual is a positive contingent state of affairs, since it obtains contingently and entails that some contingent concrete objects exist. This shows, Rowe concludes, that this state of affairs cannot explain why t is actual, for' clearly, the fact that accounts for why there are positive, contingent states of affairs cannot itself be a positive, contingent state of affairs '.[4] But this is not clear. In the argument at hand, Rowe is willing to countenance the supposition that God necessarily exists and thus that God exists is a necessarily obtaining state of affairs. Given this supposition, the state of affairs God exists is not one of those needing to be explained by the fact of God's willing that positive contingent states of affairs obtain. All that needs to be explained is that there obtain positive contingent states of affairs, which is logically equivalent to the state of affairs that thtTe are contingent concrete objects. Now this state of affairs does appear to have an explanation, namely, by the state of affairs

(s) is a sufficient reason for t, since (i) necessarily, if s obtains, t obtains, (ii) s relevantly entails t and (iii) s explains t. Thus, it seems that Rowe is mistaken in believing that there can be no sufficient reason for t.

Suppose a defender of Rowe argues that s is a positive, contingent state of affairs and itself obtains for no sufficient reason. (It obtains for no sufficient reason since God is free in the libertarian sense. ) I t follows, therefore, that there is at least one positive contingent state of affairs that obtains for no sufficient reason. Now if there is one positive contingent state of affairs that obtains for no sufficient reason, it follows that t obtains for no sufficient reason. Therefore, s cannot explain t.

But this does not follow, even though it may appear to follow. The illusion that s cannot explain t is due to a failure to realize that the following two states of affairs are consistent:

(u) There is a sufficient reason why there are positive contingent states of affairs.

(v) There is some positive contingent state of affairs that obtains for no sufficient reason.

(w) Each positive contingent state of affairs that obtains has a sufficient reason why it obtains.

If u is true, then it is the case that if the sufficient reason mentioned, call it SR, obtains, then there obtain positive, contingent states of affairs. If u obtains, then it also follows that there is some positive contingent state of affairs that obtains for a sufficient reason. But it does not follow that every positive contingent state of affairs obtains for a sufficient reason, be it SR or another sufficient reason. By analogy, suppose that some human actions are causally determined by prior psychological states and that some human actions are not determined but are free in the libertarian sense. This is consistent with

The issue about the sufficient reason for t ( or that there are positive contingent truths) is not parallel to the issue about the sufficient reason for the conjunction of all positive contingent truths. There is a sufficient reason for the conjunction of all positive contingent truths if and only if there is sufficient reason for each positive contingent truth, whereas there is a sufficient reason for there being positive contingent truths if and only if there is a sufficient reason for a certain one of the positive contingent truths, namely, the positive contingent truth that there are positive contingent truths.

The foregoing considerations suggest that it is desirable to become perfectly clear about the difference between these two projects of explanatory ration- alism, one of which is logically impossible and the other possible. The impossible project is to explain why each positive contingent truth is true. Let us consider an argument by Jonathan Bennett about contingent truths in general, which is relevantly analogous to the argument about positive contingent truths, Bennett writes :

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,[5]

Bennett is correct that if Q is contingent, then it is a conjunct in P. But why should the fact that Q is a conjunct in P entail that Q cannot explain P? Bennett does not say. I believe the reason is similar to the reason that Rowe (mistakenly) gave as a reason why a contingent proposition cannot be a sufficient reason for there being positive contingent truths. Suppose Q is contingent and thus a conjunct of P. Q is a sufficient reason for P if and only if Q is a sufficient reason for each conjunct in P and thus only if Q is a sufficient reason for Q. But Q cannot be a sufficient reason for Q, because only necessary truths are sufficient reasons for themselves and Q is not a necessary truth. Thus, Q cannot be a sufficient reason for P.

A similar argument shows that no positive contingent truth can be a sufficient reason for the conjunction of all positive contingent truths. In order to be such a reason, a positive contingent truth would have to be a sufficient reason for itself, violating the principle that no contingent truth can be a sufficient reason for itself.

However, this argument does not show that a positive contingent truth cannot explain why there are positive contingent truths. It shows merely that no positive contingent truth can explain the conjunction of all positive contingent truths. As I have argued above, it is possible for some positive contingent truth, such as God's willing that there be contingent concrete objects, be a sufficient reason why there are positive contingent truths.

The moral of the story is that the project of explanatory rationalism is not as hopeless as some have maintained. There can be no sufficient reason for each positive contingent truth, but there can be a sufficient reason why there are positive contingent truths at all.[6]

[1] William Rowe, The Cosmological Argument (Princeton University Press, 1975), pp. 103 ff.

[2] Ibid., p. 103

[3] Ibid., p. 106

[4] Ibid., p. 106

[5] Jonathan Bennett, A Study of Spinoza’s Ethics (Hackett Pubs., 1984), p, 115.

[6] It is also possible to explain why there are positive contingent truths on naturalistic assumptions alone, in terms of a wave function law of nature. See Quentin Smith, 'The Wave Function of a Godless Universe' in William Lane Craig and Quentin Smith, Theism, Atheism and Big Bang Cosmology (Oxford: Clarendon Press, 1993).