Yanjing Wang
Department of Philosophy Peking University
AWPL
Publication Types:
The Quest for Ultimate Ignorance. I: Iterated Ignorance is Complex!
Abstract. This is the first paper on a project where we aim to explore the concept of ultimate ignorance of an agent, depending on the underlying logic of knowledge. By “ultimate ignorance” we mean an operator obtained by iterating the ignorance operator I (possibly transfinitely), where Iφ intuitively saying that “The agent is ignorant whether φ is true”, until stabilisation up to logical equivalence, if that stabilisation ever occurs. Here, we set the stage for the project and explore the logical behaviour of the finite hierarchy of ignorance I, I_2, . .. and its limit operator I^ω anddemonstrate that, contrary to common expectation, that behaviour is generally rather complex, both in terms of the valid consequences betweenthese operators and in terms of the semantic conditions corresponding to the respective implications between them, over relatively weaker underlying logics of knowledge.