From Gödel's Incompleteness Theorem to the completeness of bot beliefs (Extended abstract)
This addresses foundational issues in logic and AI theory, but it appears incremental as it builds on established philosophical and mathematical concepts.
The paper tackles the problem of extending incomplete theories to complete ones, inspired by Gödel's incompleteness theorem, by analyzing logical processes that lead to testable but unfalsifiable theories, with a focus on convergence in automated learners like bots.
Hilbert and Ackermann asked for a method to consistently extend incomplete theories to complete theories. Gödel 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 Gödel's construction answered his question, and in his late writings and lectures, Gödel 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.