The Ideal of the Completeness of Calculi of Inductive Inference: An Introductory Guide to its Failure
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Non-trivial calculi of inductive inference are incomplete. This result is demonstrated formally elsewhere (Norton, manuscript). Here the significance and background to the result is described. This note explains what is meant by incompleteness, why it is desirable, if only it could be secured, and it gives some indication of the arguments needed to establish its failure. The discussion will be informal, using illustrative examples rather than general results. Technical details and general proofs are presented in Norton (manuscript).