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    The process of type construction yields a transfinite hie... — Carmelics
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    The process of type construction yields a transfinite hierarchy of mutually non-bisimilar type spaces.

    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.The process of type construction can be continued indefinitely.
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    • 2.Each extension of the type hierarchy produces type spaces that are not bisimilar to one another.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Mirimanoff and von Neumann showed that transfinite hierarchies require a stopping point—an ur-element or foundation axiom—to avoid paradox.
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    • 2.Without a terminal object, the type construction process generates a proper class, not a well-defined hierarchy of spaces.
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    • 3.Brandenburger and Keisler (2006) demonstrated that unrestricted type space construction leads to self-referential inconsistency, undermining claims of mutual non-bisimilarity.
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    Reason against 2 of 2
    ?
    • 1.Bisimilarity is a relation defined relative to a fixed modal signature; varying the signature across levels makes cross-level non-bisimilarity trivially true but philosophically uninformative.
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    • 2.Heifetz and Samet argued that universal type spaces can be constructed that embed all smaller type spaces, collapsing the hierarchy into a single structure rather than a transfinite sequence of distinct ones.
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    Related

    Bisimilarity is a relation defined relative to a fixed modal signature; varying ...Brandenburger and Keisler (2006) demonstrated that unrestricted type space const...Each extension of the type hierarchy produces type spaces that are not bisimilar...Heifetz and Samet argued that universal type spaces can be constructed that embe...
    +3 moreShow less
    Mirimanoff and von Neumann showed that transfinite hierarchies require a stoppin...The process of type construction can be continued indefinitely.Without a terminal object, the type construction process generates a proper clas...

    Similar

    Each extension of the type hierarchy produces type spaces that are not...87%The simple theory of types arranges properties into a hierarchy of typ...73%Infinite hierarchies of higher-order information require transfinite t...72%No type-theoretically admissible function or operation can have a doma...72%

    Source

    AI-extracted1/3 agreementValid
    SEP: logics-for-games
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    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