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    If the biconditional holds only relative to a privileged ... — Carmelics
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    Challenges→A function f(x) is in FP if and only if it is definable by a Σ^B_1-formula relative to which it is provably total in V^1

    If the biconditional holds only relative to a privileged encoding scheme, it expresses a representation artifact rather than an intrinsic mathematical equivalence, undermining its status as a foundational characterization.

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    Key Terms

    Biconditional(in formal logic)
    A logical statement that says two things are true if and only if each other is true; it's a two-way relationship (like saying 'you can vote if and only if you're 18').
    Encoding scheme(in philosophy of mathematics and representation)
    A system or method for representing information or data, like how we might write numbers in binary versus decimal.
    Foundational characterization(in philosophy of mathematics)
    A basic, fundamental description that serves as the starting point for understanding something—the essential explanation that everything else builds on.
    Intrinsic(describing the kind of continuities that ground identity)
    Something that belongs to or is part of something by its very nature, rather than coming from outside or being relational.

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    Privileged(suggesting that body size shouldn't be treated as more important than other properties)
    Given special treatment or considered more important or fundamental than other things.
    Representation artifact(what the superposition might be)
    Something that appears to exist only because of how you've chosen to describe or measure it, not because it's fundamentally real.

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    2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked

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    A function f(x) is in FP if and only if it is definable by a Σ^B_1-formula relat...

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