A New Argument for a Finite Past

Recent Thoughts about Grim Reapers

UPDATE: I recently had the fortunate of discussing this topic in a panel discussion with Alex Pruss and Joe Schmid at the American Philosophical Association. In the course of that discussion, I got a new thought for how dialectical partners could make further progress on this topic and potentially resolve their differences. I’ll share that thought at the end.

The “grim reaper” argument was one of the first arguments for a finite history (finite chain of events) that I found compelling. I offer my latest analysis.

The structure of the argument:

1. The GR scenario is impossible.

2. If causal infinitism is possible, then the GR scenario is possible.

3. Therefore, causal infinitism is impossible.

In support of 1:

See Pruss' paper for a description of a GR scenario. The scenario entails a contradiction, which is a reason to think it is impossible.

In support of 2:

We can setup the GR scenario by rearranging the clock times that determine when the grim reapers kill Fred. Suppose clock A is set to 11:30 and clock B is 11:45. Then A could be set instead to 11:25.

Here is a general principle that supports this (this is the new part):

Principle of Intrinsic Independence (PII): for any objects, their intrinsic properties do not necessarily change merely by changing the intrinsic properties of other objects.

In the clock case, the clock's times are intrinsic to those clocks. So by this principle, for any clocks, their times do not necessarily change merely by changing the times of other clocks. In other words, their times are modally independent.

From here, we can support (2) as follows. Suppose an infinite chain is possible. Then it is possible for a factory to produce an infinite collection of clocks with a randomizer to set its time (from eternity past). In this setup, someone has been installing these clocks into grim reapers who are set to kill Fred at whatever time their clock is randomly set to. Then, by PII, any pattern of times is possible, including the paradoxical GR pattern. Thus, (2) follows.

To be safer, one could treat PII as a defeasible rule of thumb. If there are exceptions, they don't defeat one's reason to apply the principle in a given case. I'm not aware of any clear exceptions to PII.

Objections

1. We can kill off the paradox by appealing instead to a certain application of the law of non-contradiction. So why appeal to causal finitism?

Response. That's where PII comes in. The law of non-contradiction doesn't itself defeat PII. Rather, the law of non-contradiction together with PII defeats an infinite past.

2. Intuitions are less reliable when applied to infinite cases. Why think the intuition behind PII in finite cases carries to infinite cases?

Response. There are intuitions that seem to apply to infinite cases. For example, the intuition behind the law of non-contradiction seems no less reliable when applied to infinite scenarios. Why would the intuition behind PII be any different? It seems to me that if the intuition about the law of non-contradiction applies to infinite scenarios, then I don't see why intuitions about recombination would not as well. I don't see how changing the number of items would make any difference.

3. Causal finitism precludes continuous spacetime, which goes against our best scientific theories.

Response. Causal finitism does not preclude continuous spacetime. It could be like this: intervals of time are infinitely divisible and infinitely divided, whereas causal events are infinitely divisible but not infinitely divided.

Alternatively, one might replace any theory on which spacetime is infinitely divided with an empirically equivalent theory on which spacetime is instead infinitely divisible (and not infinitely divided).

4. PII is true, but it's impossible to setup infinitely many clocks because there can't be that infinite matter.

Response. The setup doesn't require infinite matter because each clock could be half the size of another clock. Or the GR scenario can be setup so that only one clock/reaper is used but is randomized infinitely many times.

5. If there will be an infinite future, then there can be infinite time. 

Response. An infinite future doesn't preclude causal finitism. If each event has a finite causal history, it does not follow that there will be a final event. 

Maybe the setup is impossible for another reason. I welcome further thought on this.

6. Theistic objections: there are objections from particular recombinations that theism is supposed to preclude (e.g., someone being in pain for too long). I'd have to think about the cases. It might be that certain cases put pressure on certain concepts of God, or that certain concepts of God put pressure on certain recombinations. I have nothing definitive to say here. 

I have just a dialectical point, which is that if one has reason to make an exception to a general principle (such as the law of non-contradiction or the recombination principle), one can still treat the principle as a generally reliable rule of thumb.

Related: my Kalam cosmological argument video.

An Avenue for Progress

Disagreements about the implications of the Grim Reaper paradox often come down to disagreements about the legitimacy of certain recombination principles. One side may affirm a principle of recombination that seems to license the Grim Reaper setup, while the other denies the principle, often on the grounds that it leads to contradiction. How can such a dialectical impasse be resolved?

A promising way forward is to seek to find a demarcation (or demarcations) between recombination principles that are true and those that are not. We already know that some recombination principles are true. For instance, we can recombine shapes and symbols to produce meaningful expressions—sometimes even paradoxical ones, such as “this sentence is false.” This form of recombination is clearly possible.

Progress can be made by articulating general principles of recombination that (a) explain the success of clearly true instances and (b) avoid licensing clearly false ones. These general principles function as hypotheses. We evaluate them by testing their predictions: do they entail results that cohere with what we know to be possible? Or do they lead to impossibilities?

In the context of causal finitism, the principle of recombination that underwrites the Grim Reaper argument must be examined in just this way. Is it a principle that tracks the kinds of recombinations we independently know to be possible? Or is it more like those false principles that break down under pressure?

By clearly identifying the criteria that distinguish valid and invalid recombination, dialectical partners can move closer to agreement. Even if we don’t initially share the same conclusions, we can come to share a method: test the principles, examine the cases, and build mutual understanding around the certain structures in the landscape of possibility.