Not Every Truth Can Be Known (at least, not all at once)

According to the 'knowability thesis', every truth is knowable. Fitch's paradox refutes the knowability thesis by showing that if we are not omniscient, then not only are some truths not known, but there are some truths that are not knowable. This chapter proposes a weakening of the knowability thesis (called the 'conjunctive knowability thesis') to the effect that for every truth p there is a collection of truths such that (i) each of them is knowable and (ii) their conjunction is equivalent to p. It shows that the conjunctive knowability thesis avoids triviality arguments against it, and that it fares very differently depending on another thesis connecting knowledge and possibility. If there are two propositions, inconsistent with one another, but both knowable, then the conjunctive knowability thesis is trivially true. On the other hand, if knowability entails truth, the conjunctive knowability thesis is coherent, but only if the logic of possibility is weak.