The paper sketches an analysis of the notion of a self-fulfilling belief in terms of doxastic modal logic. The author points out a connection between self-fulfilling beliefs and Moore’s paradox. Then he looks at self-fulfilling beliefs in the context of neighbourhood semantics. The author argues that the analysis of several interesting self-fulfilling beliefs has to make essential use of propositional quantification.
Pavel Cmorej has argued that the existence of unverifiable and unfalsifiable empirical propositions follows from certain plausible assumptions concerning the notions of possibility and verification. Cmorej proves, it the context of a bi-modal alethic-epistemic axiom system AM4, that (1) ρ and it is not verified that ρ is unverifiable; (2) ρ or it is falsified that ρ is unfalsifiable; (3) every unverifiable ρ is logically equivalent to ρ and it is not verifiable that ρ ; (4) every unverifiable ρ entails that ρ is unverifiable. This article elaborates on Cmorej’s results in three ways. Firstly, we formulate a version of neighbourhood semantics for AM4 and prove completeness. This allows us to replace Cmorej’s axiomatic derivations with simple model-theoretic arguments. Secondly, we link Cmorej’s results to two well-known paradoxes, namely Moore’s Paradox and the Knowability Paradox. Thirdly, we generalise Cmorej’s results, show them to be independent of each other and argue that results (3) and (4) are independent of any assumptions concerning the notion of verification.
The paper outlines an epistemic logic based on the proof theory of sub-structural logics. The logic is a formal model of belief that i) is based on true assumptions (BTA belief) and ii) does not suffer from the usual omniscience properties.
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