Steelman: the infinite regress reply

The argument deserves to be stated in its strongest form. Many cosmological arguments, especially Kalam-style arguments and some finitist versions of the first-cause argument, claim that the causal history of the world cannot be actually infinite. If every event needed a prior cause, and if there were no first event, then causal explanation would allegedly never get started. Therefore, so the argument goes, there must be a first, uncaused cause.

The atheist or naturalist reply is that this step is not established. Actual infinities are not incoherent. Cantorian set theory gives a rigorous account of infinite sets. Mathematicians routinely reason about infinite series, transfinite numbers, and structures with no first member in one direction. So it is not enough to say that an infinite causal sequence feels strange. One needs an argument that such a sequence is metaphysically impossible.

Philosophers such as J.L. Mackie, Graham Oppy, Quentin Smith, Adolf Grunbaum, and Wes Morriston have pressed objections of this general kind against Kalam and related arguments. Their point is not that mathematics directly proves an infinite past exists. Rather, it is that the alleged impossibility of an actual infinite is far harder to show than many popular apologetic presentations suggest.

The view can be put like this:

If every event in a beginningless causal series has a sufficient prior cause, then no event in the series is left without a cause of the relevant sort. Demanding a first cause is not a neutral requirement of reason; it is an additional thesis that causal or explanatory series must be well-founded. That thesis needs an argument. If a beginningless causal series is metaphysically possible, then one cannot infer a first cause merely from the fact that every event has a cause. At most, the defender must add a further principle about global explanation or dependence.

This argument also challenges a common reply: "Even if each member of the series is explained by a prior member, the whole series still needs an explanation." The critic says that this inference is not automatic. It may commit a fallacy of composition if it moves from "each member is caused" to "the collection is caused" without a further principle; or it may treat the totality as though it were one more object alongside its members. Bertrand Russell made a famous version of this point in his debate with Frederick Copleston: if every human has a mother, it does not follow that the human race has a mother. Likewise, if every event has a cause within the series, it does not obviously follow that the series as a whole has the same kind of cause outside it. The serious dispute is whether a stronger principle of sufficient reason can justify that further demand.

What this argument gets right

First, the appeal to mathematics is a real caution against overconfident finitism. The mere phrase "actual infinite" does not name a contradiction. Cantorian infinities are not incoherent in standard mathematics. A critic of infinite causal regress cannot simply point to the strangeness of infinity and declare victory.

Second, the common popular argument from examples such as Hilbert's Hotel is weaker than many suppose. Hilbert's Hotel shows that infinite sets have counterintuitive properties. It does not by itself show that infinite collections cannot exist in reality. Many true ideas are counterintuitive. Relativity, quantum mechanics, and non-Euclidean geometry all warn us against using intuition as a final court of appeal.

Third, it is correct that "every member has a cause" is not logically equivalent to "the series has a cause." Those are different claims. A defender of a first cause must explain why explanation must apply not only locally, member by member, but globally, to the entire structure.

Fourth, the argument rightly distinguishes a temporal beginning from a metaphysical ground. Even if the universe had a beginning, further argument would be needed to infer a cause beyond the universe. And even if the universe had no beginning, some cosmological arguments would remain on the table. The debate is not settled merely by cosmology or by one position on the age of the universe.

Where the argument is less decisive

The strongest internal critique of the infinite-regress reply is that it often moves from "an infinite regress has not been shown impossible" to "there is no need for a first cause." That move is too quick.

There are at least three distinct claims here:

  • An actual infinite is logically or mathematically coherent.
  • An actual infinite causal regress is metaphysically possible.
  • An actual infinite causal regress is explanatorily sufficient.

The first is widely accepted. The second is more controversial. The third is still stronger. Even if the first two are granted, the third does not automatically follow.

Mathematics shows that infinite structures can be described without contradiction, at least within standard mathematical frameworks. It does not show that every mathematically coherent structure can be instantiated in concrete reality. This is not special pleading for theism. Philosophers of modality commonly distinguish formal consistency, metaphysical possibility, and physical possibility. A model with no first moment may be formally coherent, but the further claim that such a history is metaphysically possible requires argument beyond the existence of transfinite arithmetic.

Still, the finitist should be careful. Saying "mathematics is abstract, reality is concrete" is not yet an argument against a concrete infinite. It is only a distinction. To show that a concrete infinite past is impossible, one needs a principled reason: perhaps about traversal, causal generation, temporal becoming, or the impossibility of completing an infinite by successive addition. But each of these is disputed. Morriston, for example, has argued that if the past is beginningless, it was never "completed" from a starting point, so the language of traversing an infinite may be misleading.

The most serious first-cause reply, then, should not pretend that the impossibility of an infinite past is obvious. It should instead ask whether an infinite causal series explains itself merely because each member is explained by another member.

The totality question

The proponent of infinite regress says: every event is explained by a prior event, and causal explanation need not terminate in a first event. Therefore, no first temporal cause has been established. The defender of a cosmological argument replies: even if that is granted, why does this whole dependent order exist at all, or why does it have the laws and character it has?

Is that reply question-begging? Sometimes it is presented in a question-begging way. If one simply asserts, "the totality is dependent and therefore needs an external ground," then the opponent is right to object. That assumes what needs to be argued.

But the more careful version does not rely on treating the totality as a thing in the same way that its members are things. It relies on a principle about explanation. For example, a Leibnizian cosmological argument asks not merely for a prior cause of each event, but for an explanation of why there is this contingent reality rather than none. Philosophers such as Richard Swinburne, Alexander Pruss, Robert Koons, and Joshua Rasmussen have defended versions of this explanatory demand. One need not accept their arguments to see that they are not simply the Kalam argument repeated.

The issue is whether local explanation is enough. Suppose there is an infinite chain of books, each copied from an earlier book, with no first manuscript. We can explain why each book has the text it has: it was copied from the previous book. But one may still ask why this entire pattern of books and copying exists at all, and why that text rather than another is transmitted through the chain. The example does not prove theism. It illustrates the difference between explaining each link by another link and explaining the existence or character of the whole chain.

The atheist can reply that this demand for a global explanation rests on a controversial Principle of Sufficient Reason. Many philosophers reject strong versions of that principle. They allow that some facts may be brute: not necessarily uncaused events within time, but facts about the total structure of reality that have no further external explanation. Oppy, for example, is known for arguing that naturalism may take natural causal reality as ultimate rather than posit a further supernatural being beyond it; on that view, the demand for an external explanation of the whole order is precisely what is being denied, not something the naturalist has forgotten.

That reply has force. If brute facts are allowed, then the cosmological argument loses one of its key engines. The dialectical result should be stated plainly: the infinite regress by itself does not provide an ultimate explanation in the strong Leibnizian sense; it offers a different stopping point or rejects the demand for that kind of stopping point altogether. Instead of stopping with a necessary first cause, the naturalist may stop with the total causal order, perhaps beginningless, perhaps law-governed, perhaps brute. That may be a coherent position, but it is not the same as demonstrating that every demand for ultimate explanation is confused.

Causal regress and dependent being

There is also an important difference between a temporal causal regress and a regress of dependence. Kalam-style arguments focus on whether the universe began to exist and whether an infinite temporal past is possible. But contingency arguments often ask whether dependent realities can be self-sufficient even if they have always existed.

A beginningless universe would not automatically be a necessary universe. Something can exist at every time and still be contingent, in the sense that it might not have existed or might have been otherwise. If so, an infinite past would answer one question - "Was there a first moment?" - but not another - "Why does this contingent order exist?"

Here again, the theistic argument must not overstate itself. It must defend the claim that contingent reality requires a necessary ground. It cannot simply assume that dependence must terminate. But the infinite-regress reply also must not overstate itself. Showing that a first temporal event is unnecessary does not show that a necessary ground is unnecessary.

The strongest atheist reply

The strongest reply is that explanatory demands must end somewhere, or that not every explanatory demand is legitimate. If the theist is allowed to stop with a necessary being, why may the naturalist not stop with a necessary universe, a necessary totality, or a brute causal order? The theist may answer that a necessary being has explanatory virtues that the universe lacks: unity, independence, modal necessity, simplicity, or the capacity to ground contingent things. But those are further arguments, not automatic wins. They require showing that the natural order is contingent or explanatorily incomplete in a way that a necessary ground would not be.

The atheist can also say that "necessary being" is obscure. We understand mathematical necessity, perhaps logical necessity, but what does it mean for a concrete entity to exist necessarily? Some philosophers defend such a notion; others find it doubtful. The infinite-regress defender can therefore maintain that positing an eternal natural order is no worse, and perhaps less metaphysically extravagant, than positing a necessary transcendent cause.

This is a serious reply. It prevents the cosmological argument from being a quick proof. It forces the defender of a first cause to justify not only the rejection of infinite regress, but also the positive idea of a necessary ground.

What the infinite regress argument establishes

The infinite-regress objection succeeds against simplistic first-cause arguments that merely assert that infinity is impossible or that every causal chain must obviously have a first member. Those claims are not obvious, and the existence of coherent infinite structures in mathematics makes crude dismissals of infinity intellectually weak.

It also succeeds in showing that Kalam-style finitism needs serious support. One cannot infer a first cause merely from discomfort with a beginningless past. The impossibility of an actual infinite causal regress remains a debated metaphysical thesis, not a settled result.

But the objection does not establish atheism. It does not show that the actual world contains an infinite causal regress. It does not show that a concrete actual infinite is metaphysically possible simply because mathematical infinities are coherent. It does not answer every version of the cosmological argument, especially those based on contingency rather than temporal beginning. And it does not remove the question of why there is a dependent or contingent order at all, unless one is willing to deny that such a question needs an answer.

The fairest conclusion is modest. A beginningless causal regress is a serious philosophical possibility and cannot be dismissed by slogans about infinity. But its possibility, even if granted, undercuts only certain routes to a first cause. It does not by itself make theism unnecessary in every explanatory sense, and it leaves open whether naturalism owes, or can coherently refuse, a further account of the existence and character of the causal order. The debate turns less on whether infinity is strange, and more on what standards of ultimate explanation we are entitled to demand.