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It is not the case that Absence of proof of superpolynomial lower bounds is not equivalent to absence of superpolynomial lower bounds in those systems.
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Reasons For
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Reason for
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1.
In mathematics, 'existence' claims require construction or proof. Without evidence, asserting hidden bounds is unfalsifiable speculation, not justified belief.
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2.
The claim conflates epistemology with ontology illegitimately. Absence of proof may genuinely indicate absence of fact in formal systems designed precisely to capture computability.
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Reasons Against
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Reason against
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1.
Proof limitations reflect current mathematical tools, not reality. Gödel showed formal systems can't prove all true statements within them.
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2.
Complexity theory distinguishes between existence of phenomena and our epistemic access to them. Bounds may exist but remain formally unprovable.
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3.
Historical precedent: negative results about algebraic methods (Razborov-Rudich) show certain proof techniques fundamentally cannot establish superpolynomial bounds.
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