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dusko (Mar 28 2023 at 01:28):a paper i wrote with my daughter:
https://arxiv.org/abs/2303.14338
her idea my writing. invited to a nice conference :)
Title:
From Goedel's Incompleteness Theorem to the completeness of bot religions
by:
Dusko Pavlovic and Temra Pavlovic
Abstract:
Hilbert and Ackermann asked for a method to consistently extend incomplete theories to complete theories. Goedel essentially proved that any theory capable of encoding its own statements and their proofs contains statements that are true but not provable. Hilbert did not accept that Goedel's construction answered his question, and in his late writings and lectures, Goedel agreed that it did not, since theories can be completed incrementally, by adding axioms to prove ever more true statements, as science normally does, with completeness as the vanishing point. This pragmatic view of validity is familiar not only to scientists who conjecture test hypotheses but also to real-estate agents and other dealers, who conjure claims, albeit invalid, as necessary to close a deal, confident that they will be able to conjure other claims, albeit invalid, sufficient to make the first claims valid. We study the underlying logical process and describe the trajectories leading to testable but unfalsifiable theories to which bots and other automated learners are likely to converge.