Regress, Infinite

Infinite regress arguments are used by philosophers as methods of refutation. A hypothesis is defective if it generates an infinite series when either such a series does not exist or its supposed existence would not serve the explanatory purpose for which it was postulated.

The English philosopher John Locke (1632–1704) criticized the view that an act is free only if we freely choose whether to perform that act. Because freely choosing is itself an act, he argued, this commonly held theory is absurd because that act of choice must then, according to the theory, be preceded by still another act of choice that is free. It generates an infinite series of acts of free choice, one act of choosing determining the acts of another, and so on ad infinitum. Because such a series does not in fact occur, he argues, this account of what it is to act freely must be wrong.

Infinite regress arguments are frequently used to demonstrate that an explanatory hypothesis cannot in principle explain what it is supposed to explain. It would be absurd to suppose that the only way we can justify any of our beliefs is by appealing to other beliefs. Such an explanation is fatally flawed, because it generates either an endless chain of beliefs or a circular chain. And because we certainly don't entertain an infinite number of beliefs, the chain must circle back on itself. But a circular explanation doesn't explain anything; hence an alternative account of belief-justification is needed. The foundationalist answer is to say that the foundation of some beliefs is experience itself, not just beliefs about experience.

Some infinite regresses are linear, not circular. Suppose someone thinks the explanation as to why anything at all exists is that God made things exist. Then the God-hypothesis, when thus invoked, simply adds to the burden of explanation. On pain of infinite regress, we cannot explain why anything at all exists by invoking the existence of still another entity (God). For then that entity's existence calls for explanation.

Merely generating an infinite series is not in itself objectionable. The claim “Every natural number has a successor” entails an infinite series of natural numbers. Likewise, the claim “For every event there is a temporally precedent event that is its cause” entails both an infinite series of events and an infinite series of moments of time at which they occur. Yet the existence of an infinite series of natural numbers is mandated by logic and mathematics, and the concept of a beginningless series of events and temporal moments is not self-contradictory. There is no warrant in logic therefore for Thomas Aquinas's claim that these infinite series “cannot” go on forever. This is a misuse of an infinite regress argument.

Throughout the history of philosophy, infinite regress arguments have sometimes been used to demonstrate that ultimately some features of the universe cannot, on pain of infinite regress, be explained at all. The brute fact that some things exist is just one example.