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    The space of all epistemic types is universal in the sens... — Carmelics
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    Home/Modality & Possibility
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    The space of all epistemic types is universal in the sense that every relational model can be mapped in a truth-preserving manner to the space of all types.

    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.Each state in a relational model can be sent to a full description of the agents' corresponding first- and higher-order informational attitudes.
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    • 2.This mapping preserves truth across the relational model.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Harsanyi's type space construction assumes common knowledge of the prior, but this assumption is not derivable from the relational model structure alone.
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    • 2.A mapping that presupposes what it is meant to ground cannot count as a truth-preserving reduction without circularity.
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    Reason against 2 of 2
    ?
    • 1.Brandenburger and Keisler (2006) demonstrated that universal type spaces generate self-referential paradoxes when agents can reason about all possible belief hierarchies including their own.
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    • 2.A space that cannot consistently contain all epistemic types without contradiction cannot be universal in the truth-preserving sense the claim requires.
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    Topics

    Modality & PossibilityTruth & Knowledge

    Connections

    1 topic

    Philosophy of Language1 linked

    Related

    A mapping that presupposes what it is meant to ground cannot count as a truth-pr...A space that cannot consistently contain all epistemic types without contradicti...Brandenburger and Keisler (2006) demonstrated that universal type spaces generat...Each state in a relational model can be sent to a full description of the agents...
    +2 moreShow less
    Harsanyi's type space construction assumes common knowledge of the prior, but th...This mapping preserves truth across the relational model.

    Similar

    The truth-preserving map from relational models to the space of all ty...80%A result that holds by arbitrary construction of a type space does not...80%Transfinite types become relevant when the epistemic language is enric...75%Empirical universality is merely an arbitrary augmentation from 'valid...75%

    Source

    AI-extracted1/3 agreementValid
    SEP: logics-for-games
    View source passageHide passage
    To fix all of the agents’ beliefs, the analysis moves to types \(\mathfrak{f}=\langle f_0,f_1,\ldots\rangle\), containing some \(f_n\) for every natural number n. In this extended framework the situation becomes more complicated. The space of all such types is universal in the following sense: every relational model can be mapped in a truth-preserving manner to the space of all types by sending each state to a full description of the agents’ corresponding first- and higher-order informational at
    Extraction notes

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

    Details

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