Nonmonotonicity and Knowability: As Knowable as Possible

According to the anti-realistic theory of meaning, everything that is true is knowable. Fitch’s (1963) paradox—based on very standard assumptions made in modal logic—is seen as a challenge to this theory. In this paper I argue that there is something wrong with Fitch’s derivation of the absurdity. Assuming—for the sake of argument— the thesis of anti-realism, I argue with Beall (2000) that this doesn’t lead to disaster in case we allow some contradictions to be true. By making use of a nonmonotonic consequence relation, I show that for all of Tennant’s (1997) so-called ‘Cartesian propositions’ that are true, we can derive that it is true and not false that they are knowable.