In a seminal work Fine (2018), Fine classifies several forms of ignorance, among which are Fitchean ignorance, first-order ignorance, Rumsfeld ignorance, and second-order ignorance. It is shown that there are some relationships among some of them, including that in S4, all higher-order ignorance are reducible to second-order ignorance. This is thought of as a disadvantage by some researchers. It is then natural to ask how to avoid this consequence. We deal with this issue in a much more general framework. In details, we treat the forms of Fitchean ignorance and first-order ignorance as primitive modalities and study them as first-class citizens under neighborhood semantics, in which Rumsfeld ignorance and second-order ignorance are definable. The main contributions include model-theoretical results such as expressivity and frame definability, and axiomatizability. Last but not least, by updating the neighborhood models via the intersection semantics, we extend the results to the dynamic case of public announcements, which gives us some applications to successful formulas. We also show that the result in Fine (2018) stating all higher-order ignorance are reducible to second-order ignorance does not hold in any of our logical systems.
In 'A New Unified Account of Truth and Paradox', Neil Tennant makes the following conjecture: Paradoxes are never strictly classical; all of the classical paradoxes are constructivisable. In this paper, we will present a counterexample to Tennant's conjecture; there are classical paradoxes that cannot be constructivized.
Jc Beall agues that if FDE is logic proper, then there is no logical negation. This claim is largely based on the fact that, in standard proof systems for FDE, there are no stand-alone negation rules that suffice to capture the behavior of negation. In this paper, I show that by adopting a bilateral proof system for FDE, one can maintain that there is a logical negation, it is the very same logical negation that belongs to classical logic, and its basic function is to flip-flop between assertion and denial. I conclude by responding to the objection that it can never be coherent to both assert and deny the very same thing.
This paper concerns three recent results concerning probabilistic deference. The results show interesting things about how various kinds of deference work on finite frames, but in each case the results do not naturally generalise to infinite frames. The nongeneralisation raises interesting philosophical questions about the epistemological significance of the original results, and in the conclusion I briefly note reasons for thinking that epistemologists should be interested in what happens on infinite frames. The main priority, however, is simply showing that the finite and infinite frames behave differently in all three cases.
