Objections to the Grim Reaper Kalam Argument: Responses, Part II

I have a developed a suite of arguments, based on the Grim Reaper paradox of Jose Benardete (Infinity, 1968) for two related conclusions: the impossibility of infinite causal regresses and the necessary finitude of the past. (See my related posts: The anti-regress argument and the unsatisfiable pair diagnosis.

In my last post, I dealt with the objection based on Shackel’s “Unsatisfiable Pair Diagnosis.” In this post, I take up the second objection, based on Sydney Shoemaker’s “Branching Actualism” theory of modality. I will handle the two remaining objections in the following two posts.

The branching actualism response can be found in a 2023 paper by Joe Schmid and Alex Malpass:

Joseph Schmid and Alex Malpass (2023), Branching Actualism and Cosmological Arguments, Philosophical Studies180(7):1951. https://doi.org/10.1007/s11098-023-01958-y

This response can be seen as an objection to my Patchwork Principle:

(PP) If there is a possible world w₁ containing an event of type E, and there is a possible world w₂ containing a spatiotemporal or causal structure with room for k non-overlapping copies of events of type E (where k is any cardinal number, including transfinite ones), then there is a possible world w₃ containing k non-overlapping copies of events of type E.

So, first, what is the theory of branching actualism? Roughly, the idea is that every possible world “branches off” from the actual world at some point in the causal history of the actual world (past, present, or future). One world branches off another world just in case that the two worlds share an initial causal segment: that is, there are points in the causal history of each world such that the history prior to the point in one world exactly duplicates the history of the world prior to the corresponding point in history. We could even consider that the two worlds share numerically identical facts, things, and events prior to the two points.

This picture of modality fits nicely with a neo-Aristotelian ontology of causal powers, as Alex Pruss recognized in his 2011 book, Actuality, Possibility, and Worlds. Each possible world is possible because it would have resulted from the manifestation of certain powers or potentialities in the actual world that remained unactualized in the actual course of events. Possibility and necessity then have simple and straightforward grounds in actual reality. There is a possible world in which I am a plumber because, at some point in the past, I had the potentiality to become a plumber.

How does Branching Actualism create problems for the Patchwork Principle? The Patchwork Principle entails the existence of worlds that differ from the actual world throughout all of past history (whether it is finite or infinite), but this is not allowed by Branching Actualism.

The first thing to note is that not all non-theists subscribe to Branching Actualism. So, the Grim Reaper argument should still move such non-theists to embrace a First Cause. The GR argument is far from toothless: it establishes the disjunction: either a First Cause, or Branching Actualism (or both).

Nonetheless, since I am attracted to Branching Actualism myself, I cannot deny that it is reasonable for atheists both to accept BA and to object on that ground to the Patchwork Principle. However, there are two forms of Branching Actualism, which Schmid and Malpass fail to distinguish.

First, there is generic branching actualism (GBA): every possible world shares an initial causal segment with the actual world.

Second, there is naturalistic branching actualism (NBA): every possible world shares an initial s temporal segment with the actual world

An initial causal segment includes every event or action in the causal history of the world, up to some limit. An initial temporal segment includes every event or action occurring in spacetime prior to some instant of time (or spacelike hyperplane, in a relativistic setting).

If in every cause-effect pair, the cause precedes the effect in time (i.e., if causal priority entails temporal priority, CPTP), then GBA entails NBA. That is, NBA assumes that every cause occurs in time. GBA is consistent with the hypothesis that all of spacetime depends on one or more non-temporal causes,

NBA conflicts with the IPPP, but GBA does not. So, a compelling objection to the Patchwork Principle would require a defense of the naturalistic assumption that all causes are located within time. In my view, there is no good reason for such an assumption, as I have already argued in several of my books and papers.

Nonetheless, I will try here to produce a new version of the Grim Reaper argument, one that is consistent with NBA and that does not rely on the Patchwork Principle. Another advantage to the new argument that it is not vulnerable (as the PP was) to van Inwagen’s modal skepticism. Van Inwagen has suggested, reasonably, that we do not have real knowledge of what is possible or impossible where this involves very recherche situations, far from the actual world.

The new argument focuses instead on what is conceivable or inconceivable. By ‘conceivable’, I mean roughly what David Chalmers has called ‘negative ideal conceivability’. Somrthing is conceivable if and only if it cannot be known to be false a priori. Something is inconceivable just in case it can be known to be false a priori.

So, what do I mean by ‘a priori knowledge’? Rather than provide a rigorous definition, I will instead rely on a list of conditions, each of which is sufficient for possible a priori knowledge. I will assert that p is knowable a priori if and only if p is  (i) a principle of logic, (ii) an axiom of mathematics or grammar, (iii) a conceptual truth — i.e., something knowable by anyone who grasps the relevant concepts, (iv) a principle of metaphysics, (v) a truth wholly grounded in the essences of things, or (vi) a proposition logically deducible from a set of propositions belonging to (i)-(v). By defining ‘a priori knowable’ in such a generous way, I make the construction of my new argument more difficult, so I cannot be accused of surreptitiously smuggling the conclusion into the premises.

My revised argument proceeds through a series of three scenarios, each of which adds a set of chance events to my original Grim Reaper paradox. The scenarios are the Finite Lucky Case, the Infinitely Lucky Case, and the Unlucky Case. By a ‘scenario’ I mean a set of propositions that fully describe the intrinsic features and causal relations among a set of events and processes. A scenario is intended to describe a causal segment of a single possible worlds, and all the propositions are supposed to be mundane: lacking modal operators (possibility, necessity, subjunctive conditionals). At the same time, they may include facts about causal powers and dispositions, including objective chance.

The Finite Lucky Case:

• A finite regress of Grim Reapers, all determined to act by a prior, mutually independent coin tosses:

• Heads -> The Grim Reaper writes its own number on the slate,
• Tails -> The Grim Reaper transmits the slate’s pre-existing value, if there is one; otherwise, it writes its own number on the slate.
• The first coin toss yields Heads.

In this case, if there are k Grim Reapers, then the first one (Reaper #k) writes its number on the slate, and every subsequent Reaper transmits the slate without change. Clearly, no paradox.

The Infinitely Lucky Case:

• An infinite regress of Grim Reapers, all determined to act by a prior, mutually independent coin tosses:

• Heads -> [right arrow] the Grim Reaper writes its number,
• Tails -> [right arrow] the Reaper transmits the number previously written on the slate, if there is one; otherwise, it writes its own number.
• Every Tails is preceded by a Heads.

This is mathematically possible. Every Reaper preceded by a Tails preserves the number recorded by the most recent case preceded by Heads.

The Unlucky Case: like the Infinitely Lucky Case, except only a finite number of Heads occurs. Consequently, there is a point in the past preceded only by (infinitely many) Tails.

The Unlucky Case is mathematically impossible. It includes an infinite initial segment that is identical to the original Grim Reaper paradox.

I still need just two principles of modality. The first is the rule of necessitation of modal logic (the necessity of theorems).

I also need a second modal principle: a principle of causal independence involving chance events. We know a priori that, if an event is truly a chance event, then both the event and its relevant alternatives are metaphysically possible. If a set of events include only such chance events, then they are causally and metaphysically independent of one another, in the sense that any permutation of results of these chance events corresponds to a possible world. This is a consequence of the very ideas of independence and chance, and so it is also knowable a priori:

The Independence Principle.

If

(i) B is a scenario, true in some possible world w,

(ii) X is a class of mutually independent fair coin tosses whose occurrence and intrinsic character is fully described by B,

(iii) C is a scenario that is exactly like B except with reference to

1. events that are possible outcomes of the coin tosses of X (i.e., Heads or Tails), and
2. possible events that are causally downstream from some of those outcomes and not causally upstream from any of them, and

(iv) C conforms to the same causal laws as B (i.e., associating the same causal powers and potentialities with the same essences),

then C is also a set of possibly compossible propositions (true together in a world possible relative to w).

The Main Argument

1. The Finite Lucky Case is conceivable. (Obvious)
2. If the Finite Lucky Case is conceivable, and an infinite causal regress is conceivable, then the Infinite Lucky Case is conceivable.
3. If the Infinitely Lucky Case is conceivable, then it is conceivable that the Infinitely Lucky Case is metaphysically possible. (From the a priori knowability of modal axiom T)
4. We know the Independence principle a priori .
5. The Independence principle entails that if the Infinitely Lucky Case is metaphysically possible, so is the Unlucky Case.
6. We know a priori that the Unlucky Case is not metaphysically possible. (Easily proved)
7. It is not conceivable that the Infinitely Lucky Case is metaphysically possible. (From 4-6)
8. The Infinitely Lucky Case is not conceivable. (From 3, 7)
9. An infinite regress is not negatively conceivable. (From 1, 2, 8)

The substantive premise is 2.

Here is a possible problem for premise 2: given the other premises, we can know a priori that the Infinitely Lucky Case is inconceivable.

This fact is a feature of the argument, not a bug. Premise 2 is a conditional statement: it is consistent with the inconceivability of the Infinitely Lucky Case. Distinguish the Finite Lucky Case from the Infinitely Lucky Case. Premise 1 is clearly true: the Finite Lucky Case is conceivable. The only relevant difference between the Finite Lucky Case and the Infinitely Lucky Case is the presence of an infinite past in the Infinitely Lucky Case.

In addition, I would argue that the impossibility of the Infinitely Lucky Case must grounded by some fact intrinsic to each scenario containing it. The fact that such a scenario is impossible cannot be wholly grounded by facts that would be possible (via Independence) if the scenario were actual. Such impossible modal consequences of the scenario can be symptoms or indicators of the scenario’s impossibility, but they cannot ground it, since each possible world is causally inert with respect to any other. The explanation for the impossibility of a scenario must be intrinsic to any world supposed to realize it. There is no “modal-logical force” that can prevent scenarios from being possible.

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