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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that The process of type construction yields a transfinite hierarchy of mutually non-bisimilar type spaces.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 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.
      ?

      Think about whether this reason is strong or weak

    • 2.Without a terminal object, the type construction process generates a proper class, not a well-defined hierarchy of spaces.
      ?

      Think about whether this reason is strong or weak

    • 3.Brandenburger and Keisler (2006) demonstrated that unrestricted type space construction leads to self-referential inconsistency, undermining claims of mutual non-bisimilarity.
      ?

      Think about whether this reason is strong or weak

    Reason for 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.
      ?

      Think about whether this reason is strong or weak

    • 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.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The process of type construction can be continued indefinitely.
      ?

      Think about whether this reason is strong or weak

    • 2.Each extension of the type hierarchy produces type spaces that are not bisimilar to one another.
      ?

      Think about whether this reason is strong or weak

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