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    If the logic of properties used in P3 already treats coex... — Carmelics
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    Challenges→The extensionality of classes is a derived result, not a postulate.

    If the logic of properties used in P3 already treats coextensive properties as identical, extensionality is a hidden postulate smuggled into the definiens, not derived from it.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Property identity criteria in formal logic typically presuppose extensionality when defining coextensional properties as equivalent.
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    • 2.If P3's definiens relies on a property logic that already identifies coextensive properties, then extensionality isn't derived but assumed.
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    • 3.Circular reasoning occurs when the conclusion (extensionality) is embedded in the logical machinery used to establish the premises.
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    Reasons Against

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    Reason against
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    • 1.Coextensionality (same extension) is distinct from identity; treating them as identical requires a separate argument, not a hidden postulate.
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    • 2.P3's logic can consistently distinguish coextensive non-identical properties while remaining neutral on whether they should be identified.
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    • 3.Showing that a framework permits extensionality doesn't prove extensionality was presupposed rather than independently justified by P3.
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    Connections

    2 topics

    Modality & Possibility1 linkedPhilosophy of Language1 linked

    Related

    Circular reasoning occurs when the conclusion (extensionality) is embedded in th...Coextensionality (same extension) is distinct from identity; treating them as id...If P3's definiens relies on a property logic that already identifies coextensive...P3's logic can consistently distinguish coextensive non-identical properties whi...
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    Property identity criteria in formal logic typically presuppose extensionality w...Showing that a framework permits extensionality doesn't prove extensionality was...The extensionality of classes is a derived result, not a postulate.

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    2 (1 for, 1 against)
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