David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Philosophical Logic 25 (5):483 - 494 (1996)
The appropriateness of S5 as a logic of knowledge has been attacked at some length in the philosophical literature. Here one particular attack based on the interplay between knowledge and belief is considered: Suppose that knowledge satisfies S5, belief satisfies KD45, and both the entailment property (knowledge implies belief) and positive certainty (if the agent believes something, she believes she knows it) hold. Then it can be shown that belief reduces to knowledge: it is impossible to have false beliefs. While the entailment property has typically been viewed as perhaps the least controversial of these assumptions, an argument is presented that it can plausibly be viewed as the culprit. More precisely, it is shown that this attack fails if we weaken the entailment property so that it applies only to objective (nonmodal) formulas, rather than to arbitrary formulas. Since the standard arguments in favor of the entailment property are typically given only for objective formulas, this observation suggests that care must be taken in applying intuitions that seem reasonable in the case of objective formulas to arbitrary formulas.
|Keywords||knowledge belief entailment property logic of knowledge and belief|
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Lorenz Demey (2011). Some Remarks on the Model Theory of Epistemic Plausibility Models. Journal of Applied Non-Classical Logics 21 (3-4):375-395.
Eric Pacuit (2013). Dynamic Epistemic Logic I: Modeling Knowledge and Belief. Philosophy Compass 8 (9):798-814.
Patrick Allo (2013). The Many Faces of Closure and Introspection. Journal of Philosophical Logic 42 (1):91-124.
Rafał Palczewski (2007). Distributed Knowability and Fitch's Paradox. Studia Logica 86 (3):455--478.
Lloyd Humberstone (2008). Can Every Modifier Be Treated as a Sentence Modifier? Philosophical Perspectives 22 (1):241-275.
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