“Not Every Truth Can Be Known: at least, not all at once”, pages 339-354 in New Essays on the Knowability Paradox, edited by Joe Salerno, Oxford University Press, 2009.
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. In this paper, I propose a weakening of the knowability thesis (which I call 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. I show that the conjunctive knowability thesis avoids triviality arguments against it, and that it fares very differently depending on one other issue connecting knowledge and possibility. If some things are knowable but false, 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 quite weak.
Update, April 2005: I’ve added a reference (thanks to Joe Salerno) to a recent paper of Risto Hilpinen, in which he motivates a conjunctive knowability thesis on the grounds of a Peircean pragmatism.