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It is not the case that Replacing the reflexivity condition on the accessibility relation with seriality allows doxastic models to capture belief rather than knowledge
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Reasons For
2 perspectives
Reason for 1 of 2
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1.
Seriality merely requires that an agent has at least one belief, not that beliefs cohere with any epistemic standards distinguishing belief from fantasy.
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2.
A relation capturing genuine belief must incorporate sensitivity to evidence, but seriality imposes no such constraint, making the resulting operator too permissive.
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3.
Stalnaker's 1996 account shows belief requires a distinct normative structure beyond modal accessibility conditions derivable from weakening knowledge axioms.
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Reason for 2 of 2
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1.
The KD45 axiomatization preserves positive and negative introspection, forcing idealized agents who know exactly what they believe — an implausible condition for fallible believers.
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2.
Williamson's anti-luminosity argument establishes that agents cannot reliably access their own mental states, undermining the introspection axioms retained in doxastic models.
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Reasons Against
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Reason against
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1.
Epistemic models use a reflexive relation to capture knowledge (the Veracity property: what is known is true)
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2.
Seriality (every state has at least one accessible successor) is a weaker condition than reflexivity
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3.
A doxastic model defined with a transitive, Euclidean, and serial relation satisfies all the properties of the knowledge operator except Veracity
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