Zero isn't nothing

Chapter 5 addresses “regularity”—whether zero probability requires impossibility. Easwaran argues that in infinite spaces (common in science), some possibilities must have probability zero despite being epistemically possible, creating “miniscule” propositions. This follows from cardinality arguments and continuity assumptions about credence distributions. He examines implications for pragmatic concepts (preference, utility) and alethic evaluation (accuracy measures). The chapter defends countable additivity over mere finite additivity, using Dutch book arguments and the “comparative principle” showing finitely-additive distributions are dominated by countably-additive ones. Easwaran considers whether hyperreals might better represent degrees of belief, but argues they face problems with the Axiom of Choice. He suggests constructible non-Archimedean fields might work if representation theorem axioms are appropriately modified, though details remain open questions requiring further mathematical development.