explanation for everything. What could such a principle look like? How would we know when we had reached it?
It was Aristotle, in his logical work, Posterior Analytics, who first addressed this matter. There are three ways an explanatory chain might go, Aristotle observed.
First, it might go in a circle: A is true because B, and B is true because A. (The circle might be widened by lots of intermediate explanatory truths: A because B, B because C, … Y because Z, Z because A.) But a circular explanation is no good. Saying “A because B because A” is a roundabout way of saying “A because A.” And no truth explains itself.
Second, the explanatory chain might go on forever: A1 is true because A2, A2 is true because A3, A3 is true because A4, and so on, to infinity. But that’s no good either. Such an endless regress, Aristotle observed, supplies no ultimate explanatory foundation for knowledge.
That leaves the third kind of explanatory chain, one that terminates in a finite number of steps: A1 because A2, A2 because A3, and so on, down to some final truth X. And what sort of truth could X be?
There would seem to be two possibilities. First, X might be a brute fact, lacking any explanation of its own. But if X itself has no explanatory support, Aristotle remarked, it can hardly provide support for other truths. The second possibility is that X is a logically necessary truth, one that could not have been otherwise. And, for Aristotle, this was the only satisfactory way for an explanatory chain to end—the only alternative to circularity, infinite regress, and unjustified explanatory danglers.
But—with due respect to Aristotle—how could a logically necessary truth really explain anything? In particular, how could it explain anything that is logically contingent—like the fact that there is a world? If the existence of a world could be deduced from a logically necessary truth, then it too would be logically necessary. But it isn’t. Although there is a world, there might not have been. Nothingness cannot be dismissed as a logical possibility. Even the most promising attempt to derive being from pure logic—the ontological argument for the existence of God—in the end comes to nothing.
So, in our quest for total understanding, we cannot complete our explanatory chain with a logically necessary truth. We are therefore driven back to a choice among three evils: circularity, infinite regress, and brute fact. Of this trio, brute fact would appear to be the least objectionable. But is there any way the brute-fact dangler at the end of an explanatory chain can be made to seem less arbitrary? Can it be rendered less brutal?
The Harvard philosopher Robert Nozick had an interesting proposal along these lines. The only way an explanation could leave nothing at all unexplained, Nozick began by observing, is if the final truth in the series were somehow self-explanatory. But how could a truth explain itself? “X because X” is an evasion of explanation rather than the real thing. No child is satisfied if you answer the question “Why is the sky blue?” by saying “Because it is.” We are back to the evil of circularity again. That is why philosophers from Aristotle to Richard Swinburne have staunchly maintained that nothing explains itself—that the explanatory relation is, to use the technical term, “irreflexive.”
Nozick, however, saw more to the matter. He conceded that “X because X” is no good as an explanatory paradigm. But there is another way, he observed, that a truth might be deduced from itself. Let’s say our deepest principle—the one that explained all the laws of nature—turned out to have this form:
Any law having characteristic C is true.
Let’s call this deepest-of-all-principles P. The principle P explains why other laws hold true: because they have characteristic C. But what explains why P is true? Well, suppose that P turned out to have characteristic C. Then the truth of P would logically follow from P itself! In that case, principle P would be self-subsuming, to use Nozick’s term.
“Self-subsumption is a way a principle turns back on itself, yields itself, applies to itself, refers to itself,” Nozick wrote. He admitted that explanatory self-subsumption is “quite weird—a feat of legerdemain.” However, compared to the alternatives—circularity, infinite regress, and brute-fact danglers—it doesn’t look so bad.
Of course, showing that a principle is self-subsuming is no proof that the principle in question is valid. Consider the sentence “Every sentence of exactly eight words is true.” Call this sentence S. Since S has