Set theories that determine more and more busy beaver numbers must become more and more complicated (e.g. via large cardinal axioms asserting larger infinities), and there is no surefire systematic way to discover such axioms while being confident they remain consistent — sometimes proposed large cardinal axioms turn out inconsistent.
factualpending
Speaker
Scott AaronsonEvidence Quote
“as soon as you can build a turing machine that enumerates all of the theorems of that set theory then however many states there are in that touring machine that then sets a bound on how many busy beaver numbers that set theory can ever determine”
Created: 6/13/2026, 7:00:25 PM
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