Fitchean Ignorance and First-order Ignorance: A Neighborhood Look
Jie Fan

TL;DR
This paper studies different forms of ignorance using neighborhood semantics, providing new axiomatizations, expressivity results, and dynamic extensions with public announcements, to better understand and avoid the reduction of higher-order ignorance.
Contribution
It introduces a neighborhood semantics framework treating Fitchean and first-order ignorance as primitive, with new model-theoretic results and dynamic extensions.
Findings
Neighborhood semantics for ignorance forms
Axiomatizations and expressivity results
Dynamic updates with public announcements
Abstract
In a seminal work~\cite{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 is interesting relationship among some of them, which includes that in , all higher-order ignorance are reduced to second-order ignorance. This is thought of as a bad consequence 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 detail, 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 axiomatizations.…
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Epistemology, Ethics, and Metaphysics
