Knowledge and Truth Value Gluts

The truth condition is embedded in the analysis of propositional knowledge; if S knows that p then p is true.

Whilst a straightforward condition given a classical bivalent system with values true and false, bringing truth value gluts into the picture raises some novel matters.

In a classical framework, ‘true’ is equivalent to ‘not false’, so the condition could simply be rephrased as: if S knows that p then p is not false.

But when the possibility of propositions which are both true and false is introduced, there are three plausible knowledge operators (K):

  • Kp is true if and only if p is true
  • Kp is true if and only if p is not false
  • Kp takes the value of p, so it could be both true and false

The main question is, if one knows that p, does this require that p is true or that p is not false?

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