Re: Scott Aaronson • Explanation-Gödel and Plausibility-Gödel

Scott Aaronson asks a question arising from Gödel’s First Incompleteness Theorem, namely, what are its consequences for the differential values of explanation, plausibility, and proof?  I add the following thoughts.

A general heuristic in problem solving suggests priming the pump with a stronger hypothesis.  Applying that strategy here would have us broaden the grounds of validity, our notion of validation, from purely deductive proofs to more general forms of inference.  Along that line, and following a lead from Aristotle, C.S. Peirce recognized three distinct modes of inference, called abductive, deductive, and inductive reasoning, and that way of thinking has even had some traction in AI from the days of Warren S. McCulloch on.  At any rate I think it helps to view our questions in that ballpark.  There’s a budget of resources and running thoughts on the matter I keep on the following page.

• Survey of Abduction, Deduction, Induction, Analogy, Inquiry

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