ABSTRACTIn this paper, I offer an account of propositional learning: namely, learning that p. I argue for what I call the “Three Transitions Thesis” or “TTT” according to which four states and three transitions between them characterize such learning. I later supplement the TTT to account for learning why p. In making my case, I discuss mathematical propositions such as Fermat's Last Theorem and the ABC Conjecture, and then generalize to other mathematical propositions and to non-mathematical propositions. I also discuss (...) some interesting applications of the TTT, and reply to some noteworthy objections. (shrink)

One of the most venerable and enduring intuitions in epistemology concerns the relationship between true belief and knowledge. Famously articulated by Socrates, it holds that true belief does not suffice for knowledge. I discuss a matching intuition about ignorance according to which true belief does not suffice for the absence of ignorance. I argue that the latter intuition undercuts the New View of Ignorance and supports the Standard View of Ignorance.

According to the Ignorance Factivity Thesis, for every proposition p, one is ignorant of p only if p is a truth. By contrast, according to the Ignorance Non-Factivity Thesis, it is false that, for every proposition p, one is ignorant of p only if p is a truth. I argue that, on balance, the case for the latter thesis is stronger than the case for the former.

I argue that the Standard View of ignorance is at odds with the claim that knowledge entails truth. In particular, if knowledge entails truth then we cannot explain away some apparent absurdities that arise from the Standard View of ignorance. I then discuss a modified version of the Standard View, which simply adds a truth requirement to the original Standard View. I show that the two main arguments for the original Standard View fail to support this modified view.