What do Grim Reaper paradoxes actually show about infinity in time and causation, and why might the best response be that the scenario is simply unsatisfiable?
My links: https://linktr.ee/frictionphilosophy.
1. Guest
Alex Malpass's work focuses on philosophical logic, philosophy of time, philosophy of physics, and more. His website is https://useofreason.wordpress.com/, and he runs the Thoughtology YouTube channel.
2. Interview Summary
The conversation opens by framing the topic as a set of arguments about whether the past is finite and whether something like causal finitism is true, and then quickly moves into a core “Grim Reaper” style setup. The host lays out the familiar structure: infinitely many reapers are assigned times converging on a limit (e.g., one minute past noon, 30 seconds past, 15 seconds past, and so on), each instructed to act only if no earlier reaper has already acted—yielding an “impossible” situation that some philosophers take to pressure claims about dense time, infinitary causal structure, or a beginningless past.
Nicholas Shackel’s preferred diagnosis is that these cases are best treated as an “unsatisfiable pair”: once you formalize what the story is requiring, the constraints amount to an inconsistent schema—so nothing (in any domain) could satisfy them. On this view, you don’t need to “escape” the paradox by adding heavyweight metaphysical principles; you can simply say the setup describes an impossible structure. He then addresses the “mysterious force” worry (pressed in the literature by people like Lorenzo Luna) that logic can’t make a reaper fail. The reply is that this is a misunderstanding: logic isn’t a causal agent, but inconsistent stories still don’t correspond to genuine possibilities—much like time-travel “grandfather paradox” cases, where (as David Lewis emphasizes) there are consistent continuations (e.g., the gun jams) and the inconsistent one is simply not a real option.
The interview then pivots toward modality and whether principles about recombining possibilities could undercut the “unsatisfiable pair” move. The host raises a Lewis-style “patchwork” idea: if separate spacetime regions are each possible, perhaps they can be “patched” into a single world (e.g., to build a world containing arbitrarily many reapers). Malpass argues that while this feels intuitive, stating it in a defensible way is surprisingly hard (since even toy examples generate constraints about overlap, size/shape, etc.), so it’s not a reliable guarantee that you can freely combine any set of individually possible “patches.” He also sketches a branching picture of metaphysical possibility—often associated with Aristotle and Saul Kripke—on which genuinely possible worlds must overlap the actual world and then diverge; with an infinite coin-flip case, this yields the striking result that you can secure “any finite divergence” but not a world that differs at every past point, which provides a principled stopping point for “keep adding one more reaper” challenges. The broader methodological thread is a kind of epistemic humility: you can’t survey every consideration at once, so inquiry involves taking informed leaps and seeing what survives pressure.
3. Interview Chapters
00:00 - Introduction
01:42 - Grim Reaper paradox
20:34 - Mysterious forces
25:09 - Consistent?
30:47 - Metaphysically possible?
40:58 - Dense time case
43:48 - Branching view of modality
47:56 - Choosing modalities
51:42 - True modality
57:09 - Patchwork principle
1:07:56 - Patchwork principles and theism
1:13:48 - Principle of logic/metaphysics?
1:18:04 - Counterexample
1:22:11 - Amending the principle
1:23:56 - Guilt by association
1:28:31 - Hilbert’s hotel
1:32:43 - Finite vs. infinite sets
1:38:31 - Questioning principles of logic
1:42:29 - Counting arguments
1:47:40 - When are conditions sufficient?
1:53:42 - Explaining the entire count
1:57:53 - Conclusion
