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    A correspondence between entities of different ontologica... — Carmelics
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    Challenges→There is an intrinsic connection between Gentzen's ordinal assignment to deductions in PA and the standard ordinal assignment to infinite deductions in PA_ω

    A correspondence between entities of different ontological categories can at most be extrinsic and representational, as Kreisel's work on informal rigor suggests proof-theoretic notions must be grounded in their specific domains.

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    Key Terms

    Extrinsic(whether the artist's intentions are separate from the work itself)
    Coming from outside something; not part of its core nature or identity.
    Informal rigor(as developed by Kreisel in philosophy of mathematics)
    The idea that mathematical arguments can be carefully reasoned and convincing without being spelled out in completely formal symbolic notation.
    Kreisel(as a historical figure in logic and philosophy of mathematics)
    Georg Kreisel (1923–2015), a mathematical logician who studied how mathematical reasoning works and whether we can be certain about mathematical truths.
    Proof-theoretic notions(what must be grounded in specific domains according to the statement)
    Ideas and concepts that are specific to how mathematical proofs work, rather than abstract universal principles.

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    grounded in(whether distinctness or identity is explained by intrinsic features)
    To be explained by or to have its reason or basis in something else—like how a tree being wet is grounded in (explained by) recent rain.
    ontological categories(Thomasson's system; used to address mutual exclusiveness and exhaustiveness requirements)
    Classifications of purported entities distinguished by the relations of dependence they have or lack — specifically dependence on mental states and dependence on spatio-temporally located objects.
    representational(used to discuss whether experiences can be captured in some form that others can understand)
    Something that stands for or describes something else—like how words represent ideas, or how a painting represents a scene.

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    All sources support it1 linkedProof of definition segments1 linked

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    There is an intrinsic connection between Gentzen's ordinal assignment to deducti...

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