S5's axiom that ◇□P→□P holds only within a single modal system, but the possibility operator in P2 smuggles in a substantive metaphysicalclaim that requires independent justification.
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A logical tool (the ◇ symbol) used to express that something could be true in some situation, even if it isn't true now.
S5(modal logic axiomatization)
A modal logic axiomatizable equivalently by {K,T,B,4} or by {K,T,5}, corresponding to the class of frames with equivalence relations
independent justification(Epistemology of justification transmission)
Justification that appears intuitively independent of the original justification for a proposition q; more precisely, transmitted justification for q that is additional and independent when three counterfactual conditions are met: the subject was already justified in believing q before acquiring the new evidence, remains justified during acquisition, and would have gained a first-time justification via transmission had no prior justification existed
◇□P→□P (the formula)(in modal logic notation)
A symbolic shorthand where ◇ means 'possibly,' □ means 'necessarily,' P is a statement, and → means 'implies.' Together, it says: 'if it's possibly necessary that P, then it's necessary that P.'