As far as I understand it, in Priest's "Logic of paradox" there is a proof to the effect that $\phi$ is classically valid IFF $\phi$ is valid in the Logic of Paradox (LP), that is: $\vDash_C \phi$ IFF $\vDash_{LP} \phi$.

Priest says that

the proof from right to left is immediate since every two valued model is a three valued model

Why so?

Moreover, how does it work the proof from left to right?

  • The result follows by examining the truth tables. If you take the three-valued tables for LP and remove the rows and columns for the value p, those that remain are identical with those for classical logic. Conversely, if you replace all the p values with t, the f values are preserved. This holds because p and t are the designated values that are preserved. The weird consequence is that the deduction rules are different, and modus ponens only works with restrictions.
    – Bumble
    Mar 22 at 13:39


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