The boundary between 'small' and 'large' large cardinals is itself set-theoretically defined, making the claim epistemically circular when used to ground a philosophical distinction about possibility.
?Rate how convincing each reason is below to see the overall strength.
No one has weighed in yet. Be the first to share reasons for or against this statement.
Sign in or register to share your perspective on this statement.
A normative enterprise that tells us how we ought to reason from evidence and how we ought to justify our beliefs, as distinct from merely describing how we do reason or justify beliefs
grounding(Drawn from contemporary metaphysics; proposed as potentially applicable to understanding the foundations of legality.)
A metaphysical relation in which some entities or facts are more foundational than others, providing a hierarchical structure of the world.
large cardinals(Contemporary set theory proposes large cardinal axioms as a remedy for the incompleteness of ZFC.)
Set-theoretic principles positing the existence of very large infinite cardinal numbers, used as candidate new axioms to extend ZFC and potentially settle open questions such as the Continuum Hypothesis.