If the knowability proof's contradiction K(p ∧ ¬Kp) produces a glut rather than absolute falsehood, then ¬◇K(p ∧ ¬Kp) does not follow, since the world realizing the glut remains accessible.
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A logical argument that tries to show something can be known or understood, often used in debates about what kinds of things are possible to know.
Modal logic(logic)
A system of logic that deals with concepts like possibility, necessity, and what could or must be true.
contradiction(Relevant to distinguishing contradictions from false contingent statements in the logic student variant of the preface paradox.)
A statement that is necessarily false in all interpretations; in this context, specifically the negation of a tautology or any falsehood drawn from a list containing only tautologies and contradictions.
¬ (negation symbol)(used in formal logic notation)
The ¬ symbol means 'not'—so ¬Q means 'not Q.'
◇ (diamond symbol)(modal logic (logic of possibility and necessity))
In logic, this symbol means 'it is possible that' the thing following it could happen or be true.