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How to Refute Principles of Sufficient Reason

Does everything have an explanation, either in terms of the causal/creative power of something else, or in a necessity of its own nature?

The principle that everything must have some such explanation is a version of what is called the Principle of Sufficient Reason. In one version or another, PSR is presupposed in certain fundamental philosophical arguments, including perhaps most famously an argument for the existence of God -- the First-Cause or Cosmological Argument -- as well as arguments to the effect that there must always be something science and reason cannot explain.

No matter how hallowed by common sense and tradition, PSR today is in deep trouble. For one thing, PSR appears to conflict with the indeterminacy characteristic of many of the processes studied by quantum physics. For another, a conceptual argument against PSR has recently been constructed, an argument based on deductive inferences from PSR's own concept of explanation. The argument concludes that not everything can have an explanation of the sort claimed by PSR.

The argument is developed in detail in John Post's book The Faces of Existence, Chapter 2, §§2.1-2.4. Here in outline is how it goes.

Most explanations, if known, would provide materials out of which one could construct a justification of the belief that the thing to be explained exists or occurs, though normally that belief already is justified in some other way as well. Let us call such explanations justification-affording explanations; or, shorter still, J-A explanations. (Note that a J-A explanation, even if known, is not in general itself a justificatory argument, but merely provides materials out of which such an argument could be constructed by someone who knew the explanation.)

The category of J-A explanations is very broad. It includes explanations in which the explaining factors necessitate or entail the existence or occurrence of the thing explained, as in PSRs. And it includes those in which the explaining factors merely make it rather more probable that what is explained will occur than not. As to the nature of the explaining factors, they may range from law-like regularities to statistical regularities, from physical events and processes to mental states, from atoms and the void to minds and intentions, from the observable to the unobservable, from the trivial to the profound. Clearly, J-A explanations range from scientific to nonscientific, and from the mundane to the other-worldly.

Now, could there be an infinite parade of J-A explanations, in which each factor that does the explaining in one explanation is itself explained in the next? Suppose there were such a parade. Because each explanation in it would afford a justification, the whole parade would afford or give rise to an infinite parade of justifications, in which each premise in one justification is itself justified by a further justification in the parade.

But could there be an infinite parade of justifications? The argument will be that if we allowed even one such parade, we could arbitrarily construct a justification of any contingent statement whatever, hence another justification of the contingent statement's own negation (where "contingent" means "neither logically necessary nor logically impossible"). But being able arbitrarily to justify any contingent statement whatever, hence any together with its negation, is absurd. Such arbitrariness and inconsistency are inconsistent with our concepts of justification.

So we must conclude that it is logically impossible for there to be an infinite parade of justifications. From this it follows that it is logically impossible for there to be an infinite parade of J-A explanations (since if there were one, it would afford or give rise to an infinite parade of justifications, in which each premise in one justification is itself justified by a further justification in the parade). A parade of explanation-seeking why-questions must end, at least when the explanations sought are J-A, as is typically the case. We may call what they end with "final explainers."

All versions of PSR postulate explanations that are justification-affording. The sufficient reasons they postulate are supposed to be logically sufficient for the explained states of affairs. Does every state of affairs (every "stoa") have a J-A explanation, or at least every stoa in some restricted class or kind? Since stoas get stated by statements, or perhaps are merely the shadows cast by statements, we may treat this question as though it asks whether every statement has a J-A explanation, or at least whether every statement in some restricted class of statements has a J-A explanation. Even if stoas (or events or things) are in the first instance what get explained, or what have explanatory significance, still the explanation, being J-A, would provide materials (statements) out of which a justificatory argument could be constructed, in which what is to be explained is justified by what does the explaining (conjoined if need be with other material).

Now, if not every statement has a J-A explanation, perhaps every true statement does, or else every contingently true statement, or else every true statement merely that a given thing or being exists, or whatever. But whether every statement in a given class has a J-A explanation depends crucially on what concept of J-A explanation is being used. In particular, it depends on whether the property that singles out the stoas in the class is "hereditary" with respect to that concept. A property P is hereditary with respect to a given concept of explanation if and only if whenever statement S is explained by T, and S has P, then T has P. The idea is that in any parade of such explanations, P gets passed from each statement to the next.

The property of being true, for example, is hereditary with respect to any concept of explanation according to which the explanans statement T must be true. And the property of being contingently true is hereditary with respect to any concept of explanation according to which T must both be true and logically entail the explanandum statement S . For if S is contingent and entailed by a true T, then T must be contingent as well as true. It follows that the property of being contingently true is hereditary with respect to the concepts of explanation presupposed by PSRs. For according to PSRs, the statement T of the sufficient reason is supposed to be true, and the sufficient reasons are supposed to be logically sufficient, so that T entails the statement S of what is to be explained.

Next we prove the Heredity Theorem for J-A explanation:

HT. Given any concept of J-A explanation for which property P is hereditary, not every P-statement has such an explanation,

One immediate consequence of the Heredity Theorem is that not every true statement -- not every truth -- has a J-A explanation for which being true is hereditary. Thus any version of PSR is false which implies that every fact or stoa that obtains has an explanation in any such sense. For facts and stoas get stated by true statements. Hence if every fact or obtaining stoa had some J-A explanation for which truth is hereditary, then every true statement would have such an explanation, contrary to the Heredity Theorem.

The Heredity Theorem is then applied to other versions of PSR, with the result that they too are false. So far from being a presupposition of reason itself, as some think, PSR can be refuted by reason, arguing only from PSR's own concepts of explanation.

To repeat, this argument is developed in detail in John Post's book The Faces of Existence , Chapter 2, §§2.1-2.4; for further applications and implications, see §2.5 ("Ultimate Explanation"); §2.7, ("Science and Ultimate Explanation"); and in Chapter 3, §3.2, "Mystery and the Universe," and §3.3, "First Cause."

A possible reply to all this may be found, in effect, in Richard Gale's book, On the Nature and Existence of God (Cambridge University Press, 1991). He thinks the cosmological arguer can easily respond to a denial of PSR by recasting the argument "so that its conclusion is no longer that there is in fact a theistic type explanation [of the universe] ... but that this is the only possible explanation.... Only God can satisfy our rational longing to have a really satisfying explanation of the universe" (280).

Here Gale is assuming what he calls Weak PSR, about which "there is little question": for any entity, it should be at least possible that there is an explanation for its existence (203-204). Well, not physically possible, where physical possibility means consistency with the laws of physics, since by the quantum physical laws there are entities that have no explanation of the kind required by PSR, the universe included if quantum-tunneling accounts of its origin prove sound. But what about logical or conceptual possibility?

Well, the foregoing argument against PSR, which proceeds from PSR's own concept(s) of explanation, also works against Weak PSR (if it works at all). It is a consequence of the argument, as noted, that there must be "final explainers" which themselves can have no explanation (not even in their own nature), since if even they had one, this would give rise to an infinite sequence of explanations, which in turn would give rise to an infinite regress of justifications (the relevant notions of explanation being "justification affording"); but such a regress is impossible, for, given even one such justificational regress, then for any contingent belief whatever, another such regress is constructible that would justify it (and still another that would justify its negation).

Given a final explainer, then, it is not logically or conceptually possible for there to be an explanation of its existence; not even a theistic explanation could be its only possible explanation, there being no possible explanation whatever. Nor could there be a rational longing to have an explanation of it, since a longing is rational only if it is consistent with rationally acceptable principles. All this applies as well to the universe if, as some have long argued, it is a final explainer.