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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Frege and Church showed that typed systems individuate properties extensionally at each type level, collapsing distinct co-extensive properties into one.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Frege himself distinguished sense from reference; extensional individuation contradicts his core doctrine that properties need intensional identity conditions.
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    • 2.Co-extensive properties (e.g., 'renate' vs 'cordate') are genuinely distinct in natural language; collapsing them loses explanatory power about cognitive content.
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    • 3.Church's Simple Theory of Types permits intensional properties via propositional functions; the extensional reading misrepresents what the system actually allows.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Type theory's formal structure requires identity conditions at each level; extensional individuation follows naturally from this computational framework.
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    • 2.Co-extensive properties being distinct violates the principle that mathematical objects should be individuated by their actual content, not notational variants.
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    • 3.Church's lambda calculus treats functions as extensional; this mirrors how typed property systems achieve clarity and decidability in formal logic.
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