I've received some criticisms lately directed toward my version of the Grim Reaper argument for causal finitism. The criticism comes from Alex Malpass and Joe Schmid, My argument depends heavily on a version of David Lewis's Patchwork Principle.

Malpass and Schmid argue (on Schmid's Majesty of Reason web site) that theists must reject the Patchwork Principle, since it seems to entail the existence of a world in which nothing occurs except pointless suffering. It might be supposed that theists hold such a world to be metaphysically impossible. (I'm not so sure--a spacetime world could be filled with suffering, while that suffering might find its point and purpose in a separate spacetime continuum, as in a multiverse. However, I'll concede the point here for the sake of argument.)

Malpass and Schmid are right to point out that the Patchwork Principle needs to be qualified. Here is a plausible version:

Patchwork Principle
If (a) there is a world w1 containing a scenario S, (b) a world w2 containing enough non-overlapping regions of spacetime to accommodate an infinite regress of S-scenarios, (c) an infinite regress of S-scenarios would not violate the principle of causality (i.e., it wouldn’t involve any absolutely uncaused events), and (d) there is no necessary being with necessarily both the causal power and the inclination to prevent the existence of infinite regresses of S-scenarios, then: there is a world w3 in which there is an infinite regress of S-scenarios.

This doesn’t “beg the question” because including clause (d) does not entail that there is any necessary being at all. In fact, it presumes that, if there were such a being, it wouldn’t be necessarily disposed to prevent infinite regresses,

The Grim Reaper does not involve any violations of causality, so condition (c) is irrelevant. So, the correct conclusion should be the disjunction: either (i) infinite causal regresses are impossible (because they cannot be fit into a possible spacetime structure), or (ii) there is a necessary being with the power and inclination to prevent infinite causal regresses.

So, neither disjunct will be acceptable to the atheist,

In Jose Benardete’s paradox, we are to suppose that there is an infinite number of Grim Reaper mechanisms, each of which is engineered to do two things: first, to check whether the victim, Fred, is still alive at the Grim Reaper’s appointed time, and, second, if he is still alive, to kill him instantaneously, and, if he is already dead at the appointed time, to do nothing. The last Grim Reaper (Reaper 1) performs this dual task at exactly one minute after noon. The next-to-last Reaper, Reaper 2, is appointed to perform the task at exactly one-half minute after noon. In general, each Reaper number n is assigned the moment 1/2^(n-1) minutes after noon. There is no first Reaper: for each Reaper n, there are infinitely many Reapers who are assigned moments of time earlier than Reaper n’s appointment.
 
It is certain that Fred does not survive the ordeal. In order to survive the whole ordeal, he must still be alive after one minute after twelve, but, we have stipulated that, if he survives until 12:01 p.m., then Reaper 1 will kill him. We can also prove that Fred will not survive until 12:01, since in order to do so, he must be alive at 30 seconds after 12, in which case Reaper 2 will have killed him.  In the same way, we can prove that Fred cannot survive until 1/2^(n-1) minutes after 12, for every n. Thus, no Grim Reaper can have the opportunity to kill Fred. Thus, it is impossible that Fred survive, and also impossible that any Reaper kill him! However, it seems also to be impossible for Fred to die with certainty and yet to do so without any cause.
 
The original Grim Reaper paradox requires some assumption about causality: that Fred cannot die unless someone or something kills him. I would like to eliminate that dependency. Consider the following variation: the Grim Placer. In place of asking whether a pre-existing victim Fred is dead or alive, we will focus instead on the question of whether or some Grim Placer has issued a death warrant. Let’s say that each Grim Placer #n can issue a death warrant by placing a particular kind of point-sized particle in a designated position, at exactly the distance of d/2^n meters from a plane P. Each Grim Placer #n checks to see if a particle is already at a distance of d/2^i  meters from plane P, for some i > n: that is, he checks to see if any earlier Placer has issued a “warrant”. If a particle has already been placed in one of the designated spots, then the Grim Placer #n does nothing, other than maintaining the status quo.
 
If there is no particle in an appropriate location, then the Grim Placer #n issues his warrant, placing a particle exactly d/2^n meters from P. We can now prove both that at 12:01 that some particle is located within d meters of the plane, and that no particle is located there. Suppose that there is no particle at any location d/2^i meters from plane P, for any i. This is impossible, since if there were no particle d/4 meters from P, then Grim Placer #1 would place a particle in the position d/2 meters from P.
 
Thus, there must at 12:01 pm be some particle in an appropriate position. Suppose that the particle is located at that time in position d/2^n meters from P, for some n. This means that every Grim Placer whose number is greater than n did nothing, contrary to our hypothesis. Thus, this option is also impossible.

​As Alexander Pruss has observed (Pruss 2009), the Grim Reaper paradox suggests not only that no finite time period can be divided into infinitely many sub-periods but also that it is impossible that there should exist infinitely many time periods, all of which are earlier than some event. It seems to provide grounds for thinking that time must be bounded at the beginning: that there must be a first period of time. If not, we could simply construct a new version of the Grim Placer paradox. As in the original version, we postulate the possibility of a Grim Placer, who creates a particle and places it at a designated spot, if and only if no particle is already located at a spot corresponding to any earlier Placer. In this version, Placer 1 is set to act at the first moment of 1 B.C., Placer 2 at the first moment of 2 B.C., and so on ad infinitum. Once again we can generate the contradiction: some particle must be placed within d meters of the plane, but there is no finite distance from the plane such that a particle could have been placed there.

Here again is my Pruss-inspired version of the Kalam argument, relying on causal finitism:

P1. Every event has a finite causal history (no causal loops or infinite regresses).
P2. For everything that begins to exist (at some point in time), the event of its beginning to exist must have a cause.
P3. Every non-eternal thing began to exist at some point in time (since the past of each non-eternal thing is finite in length).
P4. If the yy cause the xx to begin to exist at t, then the yy exist at t or at some time earlier than t or eternally. 
Therefore, every non-eternal thing is ultimately caused to exist by some eternal (godlike) thing.

There is, however, a problem with premise P3. Causal finitism alone does not seem to give us a finite past, not even a finite history for a given thing. 

​Suppose that we have a thing x that exists in time and suppose that causal finitism is true. This means that each event in the history of x must have a finite causal history. Is this enough to entail that x must have begun to exist at some point in the past? Couldn’t the history of x begin with an event or state that is infinitely extended in the past direction? Let’s call such an initial state a simple infinitely long past state or SILPS.
 
We can refute the possibility of a SILPS by posing a dilemma: either time itself has an intrinsic measure (in which sense time can pass in the absence of change) or it does not. If time does not have an intrinsic measure, and the initial state of x is a simple state, without discrete parts, then that state cannot have any temporal duration, much less an infinite duration (since there are, ex hypothesi, no changes concurrent with this state by which time could be extrinsically measured). Hence, we must suppose that time itself has an intrinsic measure.
 
However, this is also inconsistent with a SILPS, since if time has an intrinsic measure, then any extended period of time has discrete proper parts corresponding to the measurable proper parts of that period of time. If an event or state has a duration corresponding to that extended period, then it too must have temporal parts corresponding to the proper parts of the period of time. Thus, the state is not simple or “uneventful” after all. This is a strong argument, although it will not persuade those who think that extended simples (like extended Democritean atoms) are metaphysically possible.
 
Here is a version of the argument without the assumption of a finite past (P3):
 
P1. Every event has a finite causal history (no causal loops or infinite regresses).
P2. For everything that begins to exist, the event of its beginning to exist must have a cause.
P3.1. If something has existed for an infinite period of time, then it must have an infinite causal history (because a simple infinitely long past state is impossible).
Therefore, every non-eternal thing is ultimately caused to exist by some eternal (godlike) thing.
 
Since my argument for P3.1 is less than ironclad, I will argue in future posts both for causal finitism and for the finitude of the past of each temporal thing. This provides support for both arguments: the original argument (which depends on both causal finitism and the finite duration of the past) and the revised argument (which depends on causal finitism and the impossibility of SILPS).

The Kalam argument for God’s existence, which was pioneered by John Philoponus (490-570), developed by Islamic philosophers such as al-Kindi and al-Ghazali, and championed in recent years by William Lane Craig (Craig 1979) and by me (Koons 2014), is an attempt to prove that the universe must have had a cause, a role which God seems best suited to fit. The argument typically takes the following form:
 
1. Whatever begins to exist must have a cause.
2. The universe began to exist, because time itself is bounded in the past.
Therefore, the universe had a cause.
 
The first premise has a great deal of intuitive appeal, and there are severe epistemological costs to countenancing the idea of uncaused origins. For instance, the skeptical scenario popularized by Bertrand Russell—How do we know that the universe didn’t simply appear 5 minutes ago?—would be a live possibility in the absence of an a priori causal principle similar to premise 1. So, let’s focus on premise 2.

The typical Kalam strategy for defending premise 2 is to argue that time past is not eternal, that is, that there is some finite temporal bound to all past events. Now, it is not immediately obvious that a finite bound to the past entails that the “universe” began to exist. First, it is not obvious that there is such a thing as the universe: perhaps the plurality of things that exist at a time t do not compose a single whole at t. We might try to avoid this composition question by modifying premise 2 into 2.1:
 
2.1 There is a time t such that everything existing at t began to exist at t, and nothing existed at any time prior to t.
 
In order to get the desired conclusion, we would also have to modify premise 1 as follows:
 
1.1 If some things xx began to exist at time t, then there must be some thing y or things yy not among the xx such that y (or the yy) caused the xx to begin to exist at t. (I am using double letters as plural variables, following George Boolos’s plural quantification (Boolos 1984). One should read ‘yy’ as ‘the y’s (plural)’.)
 
We will also have to rule out the possibility that the things coming into existence at the first moment of time might have been caused by things existing at later times:
 
3. If the yy cause the xx to exist at t, then the yy exist at t or at some time earlier than t or eternally.

Form 1.1, 2.1, and 3, we can reach the conclusion that something that exists eternally caused the beginning-to-exist of all the things that existed at the first moment of time (if there is such a first moment).
 
There is, however, a further lacuna to fill: from the fact that the past is finite in extent or duration, it does not follow that there is a first moment of time. For example, it could be that no event occurs 14 billion or more years ago, but for every length of time L years less than 14 billion years, there are events that occurred exactly L years ago. That is, there might be a finite bound on the past, with past moments that approach arbitrarily close to that boundary, but no moment that reaches it, i.e., no absolutely first moment. (Think of the set of positive real numbers, which approach arbitrarily close to zero without actually including it.)

Instead of looking for proof of the finitude of the past, we should look instead for support of what Alexander Pruss (2016) has called causal finitism. If we can show that every event has a finite causal history (i.e., no causal loops and no causal infinite regresses), then we can infer that there are uncaused events. If we can further assume that everything that begins to exist at a time must have a cause and that every non-eternal or fully temporal thing must have begun to exist at some time (because the past is finite), then we can conclude that all uncaused things must be eternal in nature (i.e., existing “outside” or “beyond” time itself). At that point, we might be able to show that such an eternal cause of temporal events must be relevantly godlike.
 
Here is a version of this Pruss-inspired argument:
 
P1. Every event has a finite causal history (no causal loops or infinite regresses).
P2. For everything that begins to exist (at some point in time), the event of its beginning to exist must have a cause.
P3. Every non-eternal thing began to exist at some point in time (since the past of each non-eternal thing is finite in length).
P4. If the yy cause the xx to begin to exist at t, then the yy exist at t or at some time earlier than t or eternally. [Premise 3 above]
Therefore, every non-eternal thing is ultimately caused to exist by some eternal (godlike) thing.

This proof assumes (in premise 3) that, for anything that begins to exist, there is a first moment of its existence. That seems pretty reasonable. In addition, one could probably derive this from causal finitism. Suppose, for contradiction, that some x has a finite past but no first moment of existence. Then it seems that there must an infinite regress of periods of x's existence, each caused by its predecessor, in contradiction to the principle of causal finitism.

But suppose one doesn't buy either of these moves. Then there would have to be a single initial period P of x's existence, a period which lacks a first instant. In that case, premises P2 and P4 (suitably modified) would entail that there must be some cause of x's beginning to exist, a cause that is either timeless or active at a time t that is prior to and adjacent to period P. And so the proof will go through.

The proof is pretty simple. Suppose x is some non-eternal thing. By P2 it begins to exist, and by P3 its beginning to exist must have a cause. By P4, this cause must either exist eternally or at the same or earlier time than that of the beginning of x's existence. If the cause is an eternal being, we're done. If the cause is a non-eternal being, then it must have a beginning of its existence. Premise P1 rules out an infinite regress of temporal causes. So, there must be an eternal cause.