A Demonstration of the Incompleteness of Calculi of Inductive Inference
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 Deduc...
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| Format: | Article |
| Language: | English |
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Oxford University Press
2019
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| Online Access: | View Fulltext in Publisher |
| Summary: | 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 2.1Finite Boolean algebras of propositions2.2Symmetries of the Boolean algebra3Deductively Definable Logics of Induction: The Formal Expression of Completeness 3.1Strength of inductive support3.2Explicit definition3.3Implicit definition4The Symmetry Theorem 4.1An illustration4.2The general case5Asymptotic Stability 5.1Illustrations5.2The general condition6The No-Go Result 6.1Illustration: the principle of indifference6.2The result7Incompleteness8Unsuccessful Escapes 8.1Enriching the deductive logic8.2Enrich the inductive logic8.3Preferred refinements and preferred languages8.4The subjective turn9ConclusionsAppendices. © 2018 The Author(s). Published by Oxford University Press on behalf of British Society for the Philosophy of Science. All rights reserved. |
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| ISBN: | 00070882 (ISSN) |
| DOI: | 10.1093/bjps/axx004 |