Non-Normal Worlds and Representation

In Michal Peliš & Vít Punčochář (eds.), The Logica Yearbook. College Publications (2012)
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Abstract

World semantics for relevant logics include so-called non-normal or impossible worlds providing model-theoretic counterexamples to such irrelevant entailments as (A ∧ ¬A) → B, A → (B∨¬B), or A → (B → B). Some well-known views interpret non-normal worlds as information states. If so, they can plausibly model our ability of conceiving or representing logical impossibilities. The phenomenon is explored by combining a formal setting with philosophical discussion. I take Priest’s basic relevant logic N4 and extend it, on the syntactic side, with a representation operator, (R), and on the semantic side, with particularly anarchic non-normal worlds. This combination easily invalidates unwelcome “logical omniscience” in- ferences of standard epistemic logic, such as belief-consistency and closure under entailment. Some open questions are then raised on the best strategies to regiment (R) in order to express more vertebrate kinds of conceivability.

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Franz Berto
University of St. Andrews

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References found in this work

Truth in fiction.David K. Lewis - 1978 - American Philosophical Quarterly 15 (1):37–46.
Introduction to Non-Classical Logic.Graham Priest - 2001 - Cambridge and New York: Cambridge University Press.
Relevant Logic: A Philosophical Interpretation.Edwin D. Mares - 2004 - New York: Cambridge University Press.
An Introduction to Non-Classical Logic.Graham Priest - 2001 - Bulletin of Symbolic Logic 12 (2):294-295.

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