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    If set-theoretic claims are fully translatable into claim... — Carmelics
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    Challenges→Claims about sets are claims about objects of a different kind from ordinary physical objects

    If set-theoretic claims are fully translatable into claims about physical pluralities without ontological remainder, sets require no distinct object-kind beyond ordinary physical entities.

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    Key Terms

    Object-kind(as used in metaphysics)
    A category or type of thing that exists. For example, 'chairs' and 'numbers' might be different object-kinds.
    Ontological remainder(as used in metaphysics)
    Extra stuff or entities left over after you've explained something else—things that don't fit into your explanation and require their own separate existence.
    Ontology(Carnap argues this enterprise is based on a mistake)
    The philosophical discipline that tries to answer hard questions about what there really is.
    Physical pluralities(as used in metaphysics)
    Multiple concrete, physical things that actually exist in the world (like tables, atoms, or people), as opposed to abstract ideas.
    Set-theoretic claims(as used in logic and mathematics)

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    Statements about mathematical sets—collections of objects grouped together according to specific rules, like how you might group all even numbers together.
    Translatable(as used in philosophy of language)
    Able to be converted or expressed in a different way while keeping the same meaning, like translating English to Spanish.

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    2 topics

    Modality & Possibility1 linkedPhilosophy of Language1 linked

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    Claims about sets are claims about objects of a different kind from ordinary phy...

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