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    Replacing the reflexivity condition on the accessibility ... — Carmelics
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    Home/Modality & Possibility
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    Replacing the reflexivity condition on the accessibility relation with seriality allows doxastic models to capture belief rather than knowledge

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Topics

    Modality & PossibilityTruth & Knowledge

    Key Terms

    knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
    Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.

    Related

    A doxastic model defined with a transitive, Euclidean, and serial relation satis...A relation capturing genuine belief must incorporate sensitivity to evidence, bu...Epistemic models use a reflexive relation to capture knowledge (the Veracity pro...Seriality (every state has at least one accessible successor) is a weaker condit...
    +5 moreShow less
    Seriality merely requires that an agent has at least one belief, not that belief...Stalnaker's 1996 account shows belief requires a distinct normative structure be...The KD45 axiomatization preserves positive and negative introspection, forcing i...The resulting operator captures a softer informational attitude — belief — which...Williamson's anti-luminosity argument establishes that agents cannot reliably ac...

    Similar

    Both informational attitudes share a common formal structure differing...78%Epistemic models use a reflexive relation to capture knowledge (the Ve...77%A doxastic model defined with a transitive, Euclidean, and serial rela...76%The accessibility relation R on possible worlds should be reflexive73%

    Source

    AI-extracted1/3 agreementValid
    SEP: epistemic-game
    View source passageHide passage
    So far we have looked at relational models of hard information. A small modification of these models allows us to model a softer informational attitude. Indeed, by simply replacing the assumption of reflexivity of the relation \(\sim_i\) with seriality (for each state \(w\) there is a state \(v\) such that \(w\sim_i v\)), but keeping the other aspects of the model the same, we can capture what epistemic logicians have called “beliefs”. Formally, a doxastic model is a tuple \(\langle W, \{R_i\}_{
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit