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    Carmelics

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    Inverse View

    It is not the case that The form of an abstraction principle alone is insufficient to determine the ontological category of its output, as Frege's own Grundlagen distinguishes directions (abstract) from aggregates (concrete) despite both being definable by abstraction.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Frege's own theory suggests that the *content* of an equivalence relation (not mere form) determines whether outputs are abstract or concrete objects.
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    • 2.If form alone were insufficient, we'd lack principled criteria for individuating abstraction principles—undermining the entire neo-Fregean project.
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    • 3.The distinction between directions and aggregates may reflect different *domains of application* rather than proof that form fails to determine ontological category.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Frege explicitly treats directions and aggregates differently despite both arising from equivalence relations, showing form alone underdetermines ontology.
      ?

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    • 2.Multiple abstraction principles can yield outputs with identical formal structure but different metaphysical status (abstract vs. concrete).
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    • 3.The identity conditions and modal properties of abstract objects differ systematically from concrete ones, requiring additional principles beyond abstraction form.
      ?

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