The principle Bp → BBp is rejected by most epistemologists as psychologically unrealistic and is explicitly denied in weak S4-alternatives like the logic KD45 without positive introspection.
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Psychologically unrealistic(Philosophers reject this principle because people don't actually have perfect awareness of their own beliefs)
Something that doesn't match how human minds actually work in reality; it's theoretically possible but humans don't actually function this way.
S4 (modal logic system)(A technical framework philosophers use to study beliefs and knowledge)
A formal logical system designed to reason about what is possible and necessary; S4 includes the principle Bp → BBp.
epistemology(Contrasted with purely descriptive scientific inquiry)
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