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It is not the case that A framework that cannot distinguish necessarily co-extensive properties like 'triangular' and 'trilateral' fails as a prototypical property theory.
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Reasons For
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Reason for
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1.
A property theory's job is to identify what properties *are*, not to preserve every cognitive or linguistic distinction we make.
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2.
The claim confuses properties themselves with concepts or definitions of properties—different concepts can refer to the same property.
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3.
Many successful scientific frameworks identify distinct phenomena as identical (e.g., water and H₂O) without theoretical failure.
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Reasons Against
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Reason against
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1.
Property theories should capture conceptual distinctions that are cognitively and linguistically real, even if extensionally identical.
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2.
A framework that treats 'triangular' and 'trilateral' as indistinguishable cannot explain why we have two distinct concepts for one property.
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3.
Necessary co-extensionality is compatible with distinct modes of presentation; good theories should preserve this distinction.
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