A Demonstration of the Incompleteness of Calculi of Inductive Inference
John D. Norton · The British Journal for the Philosophy of Science · 2017
A complete calculus of inductive inference captures the totality of facts about inductive support within some domain of propositions as relations or theorems within the calculus. It is demonstrated that there can be no complete, non-trivial calculus of inductive inference. 1. Introduction2. The Deductive Structure 2.1. Finite Boolean algebras of propositions2.2. Symmetries of the Boolean algebra3. Deductively Definable Logics of Induction: The Formal Expression of Completeness 3.1. Strength of inductive support3.2. Explicit definition3.3. Implicit definition4. The Symmetry Theorem 4.1. An illustration4.2. The general case5. Asymptotic Stability 5.1. Illustrations5.2. The general condition6. The No-Go Result 6.1. Illustration: the principle of indifference6.2. The result7. Incompleteness8. Unsuccessful Escapes 8.1. Enriching the deductive logic8.2. Enrich the inductive logic8.3. Preferred refinements and preferred languages8.4. The subjective turn9. ConclusionsAppendices