A Demonstration of the Incompleteness of Calculi of Inductive Inference
A Demonstration of the Incompleteness of Calculi of Inductive Inference
复制标题
归纳推理计算不完备性的证明
DOI：
--
复制
发表时间：
2018
影响因子：
3.4
通讯作者：
J. Norton
中科院分区：
文献类型：
--
作者：
J. Norton
完整的归纳推理演算捕获了有关命题某些领域内归纳支持的全部事实，作为演算中的关系或定理。事实证明，不可能存在完整的、非平凡的归纳推理演算。 1. 简介2.演绎结构 2.1。命题的有限布尔代数2.2。布尔代数的对称性3。演绎可定义的归纳逻辑：完整性的形式表达 3.1。感应支持的强度3.2。显式定义3.3。隐式定义4.对称定理 4.1。插图4.2。一般情况 5. 5.1 渐近稳定性插图5.2。一般情况 6.不可行的结果 6.1。插图：冷漠原则 6.2．结果 7.不完整8. 8.1. 不成功的越狱丰富演绎逻辑8.2．丰富归纳逻辑8.3．首选改进和首选语言8.4。主观转向9．结论 附录 引言 演绎结构 2.1。命题的有限布尔代数2.2。布尔代数的对称性 命题的有限布尔代数 布尔代数的对称性 演绎可定义的归纳逻辑：完备性的形式表达 3.1。感应支持的强度3.2。显式定义3.3。隐式定义 归纳支持的强度 显式定义 隐式定义 对称定理 4.1。插图4.2。一般情况 插图 一般情况 渐近稳定性 5.1。插图5.2。一般情况 插图 一般情况 不合格结果 6.1。插图：冷漠原则 6.2．结果说明：冷漠原则 结果不完整 不成功逃脱 8.1．丰富演绎逻辑8.2．丰富归纳逻辑8.3．首选改进和首选语言8.4。主观转向 丰富演绎逻辑 丰富归纳逻辑 首选细化和首选语言 主观转向 结论 附录
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. Conclusions Appendices Introduction The Deductive Structure 2.1. Finite Boolean algebras of propositions2.2. Symmetries of the Boolean algebra Finite Boolean algebras of propositions Symmetries of the Boolean algebra Deductively Definable Logics of Induction: The Formal Expression of Completeness 3.1. Strength of inductive support3.2. Explicit definition3.3. Implicit definition Strength of inductive support Explicit definition Implicit definition The Symmetry Theorem 4.1. An illustration4.2. The general case An illustration The general case Asymptotic Stability 5.1. Illustrations5.2. The general condition Illustrations The general condition The No-Go Result 6.1. Illustration: the principle of indifference6.2. The result Illustration: the principle of indifference The result Incompleteness Unsuccessful Escapes 8.1. Enriching the deductive logic8.2. Enrich the inductive logic8.3. Preferred refinements and preferred languages8.4. The subjective turn Enriching the deductive logic Enrich the inductive logic Preferred refinements and preferred languages The subjective turn Conclusions Appendices