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    The simple theory of types can serve as a prototypical fo... — Carmelics
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    The simple theory of types can serve as a prototypical formal property theory

    Philosophy of Language
    ?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 simple theory of types arranges properties into a hierarchy of types
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    • 2.This hierarchy allows predicates to appear in subject position when higher-type predicates are predicated of them
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    • 3.The simple theory of types, if the principle of extensionality is set aside, captures the structure needed for a property theory
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Frege and Church showed that typed systems individuate properties extensionally at each type level, collapsing distinct co-extensive properties into one.
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    • 2.Properties are intensional entities individuated by meaning or essence, not extension, as Carnap's distinction between intension and extension establishes.
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    • 3.A framework that cannot distinguish necessarily co-extensive properties like 'triangular' and 'trilateral' fails as a prototypical property theory.
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    Reason against 2 of 2
    ?
    • 1.The simple theory of types prohibits self-predication, yet many properties plausibly apply to themselves (e.g., being abstract is itself abstract).
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    • 2.A property theory that structurally blocks self-predication cannot serve as a general theory of properties without stipulating away core cases.
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    Related

    A framework that cannot distinguish necessarily co-extensive properties like 'tr...A property theory that structurally blocks self-predication cannot serve as a ge...Frege and Church showed that typed systems individuate properties extensionally ...Properties are intensional entities individuated by meaning or essence, not exte...
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    The simple theory of types arranges properties into a hierarchy of typesThe simple theory of types prohibits self-predication, yet many properties plaus...The simple theory of types, if the principle of extensionality is set aside, cap...This hierarchy allows predicates to appear in subject position when higher-type ...

    Similar

    The simple theory of types arranges properties into a hierarchy of typ...90%A type-theoretical formal property theory can be constructed that avoi...88%The simple theory of types, if the principle of extensionality is set ...88%A formal theory of properties requires the ability to express basic fa...82%

    Source

    AI-extracted1/3 agreementValid
    SEP: properties
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    Standard second-order logic allows for predicate variables bound by quantifiers. Hence, to the extent that these variables are taken to range over properties, this system could be seen as a formal theory of properties. Its expressive power is however limited, since it does not allow for subject terms that stand for properties. Thus, for example, one cannot even say of a property \(F\) that \(F = F\). This is a serious limitation if one wants a formal tool for a realm of properties whose laws one
    Extraction notes

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

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