The Anti-Regress Argument for a First Cause

This is the first of two new arguments for a first cause. Check out an earlier post that contains the relevant definitions.

1. Causation is a strict partial order (transitive and asymmetric).
2. The Universe exists (i.e., there are some broadly causable things).
3. Every member of the Universe (the class of broadly causable things) has a cause (Simple Universal Causation).
4. There are no infinite regresses.

Therefore, everything in the universe is caused by one or more strictly uncausable things.

Consequently, there is a plurality of one or more strictly uncausable things (the First Cause) that jointly causes the existence of all the members of the Universe. The conclusion of the argument follows from the four premises by a theorem of set theory (including the Axiom of Dependent Choice)—see Bernays 1942, p. 84 and Clark 1988.

Premise 1 is a plausible assumption about causation, and premise 2 follows from the fact that there are actual cases of causation. I will discuss premise 3 in a later post. This leaves premise 4 as the crucial assumption.

In arguing for premise 4, the impossibility of infinite regresses, I will draw on a thought experiment invented by Jose Bernadete (Bernadete 1964), the Grim Reaper story. I will tell here a slightly simpler version of the story. Let’s suppose that there is an infinite regress of Grim Reapers, each of which is assigned a particular time on which to perform its duty. Grim Reaper 1 is assigned noon, January 1^st, 1 B.C., Reaper 2 the same day in 2 B. C, 3 in 3 B. C., and so on throughout an infinite past. Each Grim Reaper n + 1 passes a death warrant on to its successor (Reaper n) at the end of its assigned period (Jan. 1^st n B. C.). Each Grim Reaper n follows the following script: (1) If the warrant already contains a numeral larger than n, then Grim Reaper n leaves the warrant unchanged and passes it on, in turn, to Reaper n – 1; (2) otherwise, Grim Reaper n signs the warrant by writing on it the numeral n.

This story obviously involves some kind of impossibility, since we can derive from it a contradiction. We can prove both that the warrant will and will not contain a numeral on Jan. 1^st, 1 A. D. First, it must have a numeral on it on Jan. 1^st 1 A. D. The warrant either did or did not have a numeral on it on the morning of Jan. 1^st 1 B. C. If it did, then Grim Reaper 1 would have passed it on unchanged, and it would still have that numeral on it on Jan. 1^st 1 A.D. If it did not have a numeral in 1 B. C., then Grim Reaper 1 would have written the numeral ‘1’ on it. So, in either case, the warrant will contain some numeral in 1 A. D.

However, there is no number n such that the corresponding numeral could be on the warrant at that time. Suppose for contradiction that the warrant in 1 A. D. contains the numeral n. Then Grim Reaper n must have received a blank warrant from Reaper n + 1 and then written the numeral n on the warrant. Now, either the warrant already had a numeral m on it at the beginning of n + 1 B. C., or not. If it did, then Reaper n + 1 would have passed this warrant unchanged to Reaper n, and Reaper n would not have written his own number on it. If the warrant did not contain a numeral the beginning of n + 1 B. C., then Reaper n + 1 would have written his numeral on it, and, again, Reaper n would not have written his numeral. This argument applies to any natural number, so the warrant cannot have a number on it in 1 A. D. Contradiction.

Since we can prove that the Reaper story is impossible, it is inconceivable. Here is an argument from the inconceivability of the Grim Reaper story to the inconceivability of infinite regresses:

1. If infinite regresses were conceivable, then the Grim Reaper story would be conceivable.
2. The Grim Reaper story is not conceivable.

Therefore, infinite regresses are not conceivable.

Premise 1 is a consequence of a version of David Lewis’s Patchwork Principle (Lewis 1986), a recombination principle, adapted to the property of conceivability

Patchwork Principle for Conceivability. If (i) a certain causal structure S is conceivable, (ii) a finite process P is conceivable, and (iii) scenario A consists of inserting one or more copies of P into slots in S, each of which is large enough to accommodate P, then scenario A is also conceivable.

S is the “frame”, P is the “patch”, and A is the “quilt”. If we have a frame and an unlimited supply of copies of a patch, then we can build the quilt by inserting copies of the patch into the frame.

Some form of Recombination is relied on by all of us implicitly every day in planning possible programs or scenarios. For example, suppose that I want to schedule soccer games on a series of dates in the coming month. Given the conceivability of the arrival of the coming month and the conceivability of scheduling a soccer game on a particular date, we conclude that any assignment of games to dates in the month is at least conceivable.

In the case of the Grim Reaper story, the structure S is the infinite regress of dates (1 BC, 2 BC, etc.). The “patch” is the behavioral program of an individual Grim Reaper. The patch is obviously possible, and a copy of the patch will obviously fit into each of S’s year-long slots. So, if S itself is conceivable, then the whole Grim Reaper story would be conceivable. But it is not conceivable: in fact, it involves a provable mathematical impossibility.