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Raymond Smullyan on Self Reference.

By: Fitting, Melvin.
Contributor(s): Rayman, Brian.
Material type: TextTextSeries: eBooks on Demand.Outstanding Contributions to Logic Ser: Publisher: Cham : Springer, 2018Copyright date: ©2017Description: 1 online resource (200 pages).Content type: text Media type: computer Carrier type: online resourceISBN: 9783319687322.Subject(s): Logic, Symbolic and mathematical | Smullyan, Raymond MGenre/Form: Electronic books.Additional physical formats: Print version:: Raymond Smullyan on Self ReferenceDDC classification: 510.92 LOC classification: BC1-199QA8.9-10.3QA7Online resources: Click here to view this ebook.
Contents:
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 The Broad Background -- 1.2 Self-Reference, the Mathematical Side -- 1.3 Self-Reference, the Popular Side -- 1.4 What Must Be Said -- 1.5 Bibliography -- 1.6 Papers in This Volume -- 1.7 Biographies of Authors and Editors -- References -- 2 Formal Systems, Logics, and Programs -- 2.1 Introduction -- 2.2 Constructive Type Theory Background -- 2.2.1 Implemented Type Theories -- 2.3 Validating Hoare Logic using Partial Types -- 2.3.1 Hoare Logic for Programs -- 2.4 Formalizing a Theorem of Smullyan from First-Order Logic -- 2.4.1 Uniform Universal Quantification -- 2.4.2 Rules for forall[x2mu-:6muplus1muT]. P(x) -- 2.4.3 A Uniform Complete Induction Principle -- 2.4.4 Constructing Smullyan's Valuations -- References -- 3 Adaptive Fault Diagnosis using Self-Referential Reasoning -- 3.1 Introduction -- 3.2 Nelson Goodman Principle (NGP) -- 3.3 A Unified Approach -- 3.4 Finding a Reliable Individual -- 3.5 Finding All the Reliables -- 3.6 Is Anyone Really ``Normal'' -- References -- 4 Russell's Paradox, Gödel's Theorem -- 4.1 Introduction -- 4.2 Gödel Numbering and Everyday Life -- 4.3 Really Basic Set Theory -- 4.4 The Machinery of Logic -- 4.5 What Can LS Say? -- 4.6 Logic Is Mathematics Too -- 4.7 Where Are We Now? -- 4.8 Russell's Paradox -- 4.9 Tarski's Theorem and Gödel's Theorem -- 4.10 Final Comments -- References -- 5 Dance of the Starlings -- 5.1 Introduction -- 5.2 Normalization -- 5.3 Automata Methods -- 5.4 Periodic Terms and Reductions -- 5.5 The Order of S-Terms -- 5.6 S-terms in Lambda Calculus -- A A Refresher of Finitary and Infinitary Rewriting -- A.1 Introduction -- A.2 Finitary Combinatory Logic -- A.3 Finitary λ-calculus -- A.4 Head Reduction and Root Reduction -- A.5 Infinitary Rewriting -- A.6 Infinite Normal Forms, Böhm Trees and Berarducci Trees -- References.
6 Some Tweets About Mockingbirds -- 6.1 Introduction -- 6.2 Mimids -- 6.3 Isochrony -- References -- 7 Knights, Knaves, Truth, Truthfulness, Grounding, Tethering, Aboutness, and Paradox -- 7.1 Knights and Knaves -- 7.2 Russell and Moore -- 7.3 Moore Be(k)nighted -- 7.4 The Problem -- 7.5 Kripke and Dependence Trees -- 7.6 Immodesty -- 7.7 TRUTH and Grounding -- 7.8 TRUTH and Tethering -- 7.9 Fixed Points -- 7.10 TRUTH in Fixed Points -- 7.11 True to the FACTS -- 7.12 Conclusion -- References -- 8 What I Tell You Three Times Is True -- References -- 9 Gödel, Lucas, and the Soul-Searching Selfie -- 9.1 Gödel's ``Subjective Mathematics'' -- 9.2 Lucas's Dialectical Argument -- 9.3 The Self-Knowledge Objection -- 9.4 The Soul-Searching Selfie -- 9.5 The Overconfidence Objection -- 9.6 Consistency and Reflection -- 9.7 The Inexpressibilty of Provability -- References -- 10 An Island Tale for Young Anthropologists -- 10.1 In Which We Meet Professor Sune -- 10.2 In Which Professor Sune Shows Her Resourcefulness in the Face of Adversity -- 10.3 In Which Professor Sune Learns Something Surprising About the Island's Recent History -- 10.4 In Which Professor Sune Visits the Other Bay -- 10.5 In Which Sune Talks About Exploding God-Heads -- 10.6 In Which Professor Sune Recounts Another Adventure0pt -- 10.7 Professor Usely Arrives -- 10.8 Wrap-Up, Open Questions -- References -- 11 Making The `Hardest Logic Puzzle Ever' a Bit Harder -- 11.1 Harder and Harder Puzzles -- 11.2 Gods Reasoning with Enhanced Logic -- 11.3 Closing -- References -- 12 Bibliography of Raymond Smullyan -- 12.1 Raymond Smullyan's Books and Papers -- Technical Books.
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Item type Current location Call number URL Status Date due Barcode
Electronic Book UT Tyler Online
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BC1-199QA8.9-10.3QA7 (Browse shelf) https://ebookcentral.proquest.com/lib/uttyler/detail.action?docID=5219545 Available EBC5219545

Intro -- Preface -- Contents -- 1 Introduction -- 1.1 The Broad Background -- 1.2 Self-Reference, the Mathematical Side -- 1.3 Self-Reference, the Popular Side -- 1.4 What Must Be Said -- 1.5 Bibliography -- 1.6 Papers in This Volume -- 1.7 Biographies of Authors and Editors -- References -- 2 Formal Systems, Logics, and Programs -- 2.1 Introduction -- 2.2 Constructive Type Theory Background -- 2.2.1 Implemented Type Theories -- 2.3 Validating Hoare Logic using Partial Types -- 2.3.1 Hoare Logic for Programs -- 2.4 Formalizing a Theorem of Smullyan from First-Order Logic -- 2.4.1 Uniform Universal Quantification -- 2.4.2 Rules for forall[x2mu-:6muplus1muT]. P(x) -- 2.4.3 A Uniform Complete Induction Principle -- 2.4.4 Constructing Smullyan's Valuations -- References -- 3 Adaptive Fault Diagnosis using Self-Referential Reasoning -- 3.1 Introduction -- 3.2 Nelson Goodman Principle (NGP) -- 3.3 A Unified Approach -- 3.4 Finding a Reliable Individual -- 3.5 Finding All the Reliables -- 3.6 Is Anyone Really ``Normal'' -- References -- 4 Russell's Paradox, Gödel's Theorem -- 4.1 Introduction -- 4.2 Gödel Numbering and Everyday Life -- 4.3 Really Basic Set Theory -- 4.4 The Machinery of Logic -- 4.5 What Can LS Say? -- 4.6 Logic Is Mathematics Too -- 4.7 Where Are We Now? -- 4.8 Russell's Paradox -- 4.9 Tarski's Theorem and Gödel's Theorem -- 4.10 Final Comments -- References -- 5 Dance of the Starlings -- 5.1 Introduction -- 5.2 Normalization -- 5.3 Automata Methods -- 5.4 Periodic Terms and Reductions -- 5.5 The Order of S-Terms -- 5.6 S-terms in Lambda Calculus -- A A Refresher of Finitary and Infinitary Rewriting -- A.1 Introduction -- A.2 Finitary Combinatory Logic -- A.3 Finitary λ-calculus -- A.4 Head Reduction and Root Reduction -- A.5 Infinitary Rewriting -- A.6 Infinite Normal Forms, Böhm Trees and Berarducci Trees -- References.

6 Some Tweets About Mockingbirds -- 6.1 Introduction -- 6.2 Mimids -- 6.3 Isochrony -- References -- 7 Knights, Knaves, Truth, Truthfulness, Grounding, Tethering, Aboutness, and Paradox -- 7.1 Knights and Knaves -- 7.2 Russell and Moore -- 7.3 Moore Be(k)nighted -- 7.4 The Problem -- 7.5 Kripke and Dependence Trees -- 7.6 Immodesty -- 7.7 TRUTH and Grounding -- 7.8 TRUTH and Tethering -- 7.9 Fixed Points -- 7.10 TRUTH in Fixed Points -- 7.11 True to the FACTS -- 7.12 Conclusion -- References -- 8 What I Tell You Three Times Is True -- References -- 9 Gödel, Lucas, and the Soul-Searching Selfie -- 9.1 Gödel's ``Subjective Mathematics'' -- 9.2 Lucas's Dialectical Argument -- 9.3 The Self-Knowledge Objection -- 9.4 The Soul-Searching Selfie -- 9.5 The Overconfidence Objection -- 9.6 Consistency and Reflection -- 9.7 The Inexpressibilty of Provability -- References -- 10 An Island Tale for Young Anthropologists -- 10.1 In Which We Meet Professor Sune -- 10.2 In Which Professor Sune Shows Her Resourcefulness in the Face of Adversity -- 10.3 In Which Professor Sune Learns Something Surprising About the Island's Recent History -- 10.4 In Which Professor Sune Visits the Other Bay -- 10.5 In Which Sune Talks About Exploding God-Heads -- 10.6 In Which Professor Sune Recounts Another Adventure0pt -- 10.7 Professor Usely Arrives -- 10.8 Wrap-Up, Open Questions -- References -- 11 Making The `Hardest Logic Puzzle Ever' a Bit Harder -- 11.1 Harder and Harder Puzzles -- 11.2 Gods Reasoning with Enhanced Logic -- 11.3 Closing -- References -- 12 Bibliography of Raymond Smullyan -- 12.1 Raymond Smullyan's Books and Papers -- Technical Books.

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