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Inverse View
It is not the case that Without a proven complexity-theoretic Church-Turing thesis, robustness across models remains an empirical regularity, not a principled requirement.
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Reasons For
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Reason for
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1.
Empirical regularity across decades of diverse models creates strong inductive grounds that rivals many 'principled' theoretical frameworks in practice.
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2.
The distinction between 'empirical' and 'principled' requirements is itself philosophically contentious; robust patterns constitute a form of principle.
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3.
Demanding proof before accepting cross-model robustness sets an unreasonably high bar most scientific practices don't meet or require.
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Reasons Against
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Reason against
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1.
Complexity-theoretic equivalence remains unproven; we lack formal proof that all reasonable computational models share identical complexity classes.
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2.
Robustness across models has been observed empirically but derives no logical force from unproven theorems, only from repeated pattern observation.
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3.
Without principled necessity, robustness could be contingent—future models might break established equivalences, making current assumptions provisional.
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