In analytic epistemology, the propositional ignorance of an agent is consistently defined in terms of an agent not having knowledge or true belief that something is the case. Recently, however, Piedrahita (2021) and Pritchard (2021) have argued that ignorance involves some kind of epistemic fault. Pritchard claims that ignorance is the product of an intellectual defect in the agent as an inquirer, whereas Piedrahita claims that ignorance involves an agent being in a certain kind of epistemically suboptimal position. This article (...) uses willful ignorance in Anglo-American criminal law as a lens through which to assess these claims. First, I argue that willful ignorance is a counterexample to Piedrahita’s view of ignorance. Second, I argue that Pritchard’s view of ignorance illuminates the epistemic culpability of willful ignorance, but the view faces challenging questions about the relationship between epistemic norms and epistemic values. (shrink)

In the logical context, ignorance is traditionally defined recurring to epistemic logic. In particular, ignorance is essentially interpreted as “lack of knowledge”. This received view has - as we point out - some problems, in particular we will highlight how it does not allow to express a type of content-theoretic ignorance, i.e. an ignorance of φ that stems from an unfamiliarity with its meaning. Contrarily to this trend, in this paper, we introduce and investigate a modal logic having a primitive (...) epistemic operator I, modeling ignorance. Our modal logic is essentially constructed on the modal logics based on weak Kleene three-valued logic introduced by Segerberg (Theoria, 33(1):53–71, 1997). Such non-classical propositional basis allows to define a Kripke-style semantics with the following, very intuitive, interpretation: a formula φ is ignored by an agent if φ is neither true nor false in every world accessible to the agent. As a consequence of this choice, we obtain a type of content-theoretic notion of ignorance, which is essentially different from the traditional approach. We dub it severe ignorance. We axiomatize, prove completeness and decidability for the logic of reflexive (three-valued) Kripke frames, which we find the most suitable candidate for our novel proposal and, finally, compare our approach with the most traditional one. (shrink)

In a recent paper, Kit Fine presents some striking results concerning the logical properties of (first-order) ignorance, second-order ignorance and Rumsfeld ignorance. However, Rumsfeld ignorance is definable in terms of ignorance, which makes some existing results and the axiomatization problem trivial. A main reason is that the accessibility relations for the implicit knowledge operator contained in the packaged operators of ignorance and Rumsfeld ignorance are the same. In this work, we assume the two accessibility relations to be different so that (...) one of them is an arbitrary subset of the other. This will avoid the definability issue and retain most of the previous validities. The main results are axiomatizations over various proper bi-frame classes. Finally we apply our framework to analyze Fine’s results. (shrink)