A Demonstration of the Incompleteness of Calculi of Inductive Inference. (24th January 2018) - Norton, John D
Abstract: 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 Introduction 2 The Deductive Structure 2.1 Finite Boolean algebras of propositions 2.2 Symmetries of the Boolean algebra 3 Deductively Definable Logics of Induction: The Formal Expression of Completeness 3.1 Strength of inductive support 3.2 Explicit definition 3.3 Implicit definition 4 The Symmetry Theorem 4.1 An illustration 4.2 The general case 5 Asymptotic Stability 5.1 Illustrations 5.2 The general condition 6 The No-Go Result 6.1 Illustration: the principle of indifference 6.2 The result 7 Incompleteness 8 Unsuccessful Escapes 8.1 Enriching the deductive logic 8.2 Enrich the inductive logic 8.3 Preferred refinements and preferred languages 8.4 The subjective turn 9 Conclusions Appendices