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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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.