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    Frege and Church showed that typed systems individuate pr... — Carmelics
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    Challenges→The simple theory of types can serve as a prototypical formal property theory

    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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    1 reason for
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    Reasons For

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    Reason for
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    • 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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    Reasons Against

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    Reason against
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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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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Church's Simple Theory of Types permits intensional properties via propositional...Church's lambda calculus treats functions as extensional; this mirrors how typed...Co-extensive properties (e.g., 'renate' vs 'cordate') are genuinely distinct in ...Co-extensive properties being distinct violates the principle that mathematical ...
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    Frege himself distinguished sense from reference; extensional individuation cont...The simple theory of types can serve as a prototypical formal property theoryType theory's formal structure requires identity conditions at each level; exten...

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