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    Parikh's own work on feasible arithmetic shows that opera... — Carmelics
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    Challenges→The theory PA^F, though technically inconsistent, is practically consistent because any proof of a contradiction in PA^F must be infeasibly long.

    Parikh's own work on feasible arithmetic shows that operationally motivated length restrictions require a fully rigorous alternative proof theory, not a reinterpretation of classical inconsistency.

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    Key Terms

    Classical inconsistency(as used in formal logic)
    The traditional logical problem where a system contains a statement and its opposite, making the entire system logically broken according to standard rules.
    Feasible arithmetic(The field Parikh worked on)
    A branch of mathematics that deals with what computations are actually possible given real limits on time, memory, and resources—rather than theoretical limits.
    Length restrictions(these require a new proof theory according to the statement)
    Limits on how long or complex mathematical proofs or numbers can be before they become practically impossible to work with.
    Operationally motivated(describes the length restrictions being discussed)
    Based on what actually works in practice or what you can physically do, rather than what might be theoretically possible.

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    Parikh(as the mathematician whose theorem is referenced)
    Rohit Parikh is a logician and philosopher who proved important mathematical results about how long formal proofs need to be—basically, he showed there are limits to how short you can make certain logical arguments.
    Proof theory(philosophy of logic)
    The branch of logic that studies how proofs work and what makes an argument logically valid.
    Rigorous(as used in academic and philosophical discourse)
    Careful, thorough, and following strict rules—the opposite of loose or casual reasoning.

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    Truth & Knowledge1 linkedModality & Possibility1 linked

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    The theory PA^F, though technically inconsistent, is practically consistent beca...

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