Unterhuber Possible Worlds Semantics for Indicative and Counterfactual Conditionals?

A Formal Philosophical Inquiry into Chellas-Segerberg Semantics
1. Auflage 2013
ISBN: 978-3-11-032366-5
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 21, 348 Seiten

Reihe: LogosISSN

Conditional structures lie at the heart of the sciences, humanities, and everyday reasoning. This is why conditional logics – logics specifically designed to account for natural language conditionals – are an active, interdisciplinary area. Discussing a wide range of topics, this book gives a formal and a philosophical account of indicative and counterfactual conditionals in terms of Chellas-Segerberg semantics.

Zielgruppe

Philosophers, Libraries, Institutes

Autoren/Hrsg.

Unterhuber, Matthias

Fachgebiete

• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Geisteswissenschaften Philosophie Sprachphilosophie
• Geisteswissenschaften Sprachwissenschaft Sprachwissenschaften Sprachphilosophie

Inhaltsverzeichnis

1;Preface;11
2;I Foundational Issues ;1
2.1;Arguments for Conditional Logics;17
2.1.1;The Framework of My Investigation;18
2.1.2;Indicative Conditionals;18
2.1.3;Counterfactual Conditionals;24
2.1.4;Normic Conditionals;26
2.1.4.1;The Generic Case;27
2.1.4.2;The Qualification Problem;29
2.1.4.3;The Propositional Case;33
2.1.4.4;The Role of Normic Conditionals;35
2.1.5;Conversational Implicatures;36
2.2;The Conditional Logic Project in an Interdisciplinary Context and Default Logics;41
2.2.1;The Conditional Logic Project in an Interdisciplinary Context;41
2.2.1.1;The Conditional Logic Project;43
2.2.1.2;The Linguistics of Conditionals Project;43
2.2.1.3;The Philosophy of Conditionals Project;44
2.2.1.4;The Psychology of Reasoning Project;45
2.2.1.5;The Non-Monotonic Logic Project;47
2.2.2;Non-Monotonic Logics, Defaults Logics, and Conditional Logics;48
2.2.2.1;A Motivation for the Study of Non-Monotonic Logics;48
2.2.2.2;Reiter Defaults;50
2.2.2.3;Default Logics, Non-Monotonic Rules, and Inductive Inferences ;52
2.2.2.4;Types of Non-Derivability Conditions and the Rule of Substitution;58
2.2.2.5;Model Theory, Proof Theory, and Axiomatization of Default Logics;61
2.2.2.6;Conditional Logics and Default Logics;62
2.3;Possible Worlds Semantics and Probabilistic Semantics for Indicative Conditionals: a Survey and a Defense of Possible Worlds Semantics;67
2.3.1;Outline of My Defense of Possible Worlds Semantics for Indicative Conditionals and the Core Idea of Chellas-Segerberg Semantics;69
2.3.2;Possible Worlds Ordering Semantics for Conditionals: D. Lewis' and Kraus et al.'s Semantics and Related Approaches;72
2.3.3;The Ramsey Test, Stalnaker Semantics, and a General Ramsey Test Requirement;84
2.3.3.1;Ramsey's Original Proposal;85
2.3.3.2;Stalnaker's Version of the Ramsey Test;87
2.3.3.3;Stalnaker Models;88
2.3.3.4;Stalnaker Semantics, Set Selection Semantics, and Chellas-Segerberg Semantics ;91
2.3.3.5;Contrasting Ramsey Test Interpretations of Conditionals and Ordering Semantics;93
2.3.3.6;Stalnaker Semantics, Conditional Consistency Criteria, and the Principle of Conditional Excluded Middle;96
2.3.3.7;Bennett's Version of the Ramsey Test;102
2.3.3.8;A General Ramsey Test Requirement;103
2.3.4;Indicative and Counterfactual Conditionals and Conditional Logics;105
2.3.4.1;Criteria for Distinguishing Indicative and Counterfactual Conditionals;106
2.3.4.2;Bridge Principles and Logics for Indicative and Counterfactual Conditionals;110
2.3.4.3;Subjective and Objective Interpretations of Indicative and Counterfactual Conditionals and the Ramsey Test;114
2.3.5;Fundamental Issues of Probabilistic Approaches to Conditional Logic;117
2.3.5.1;Subjective and Objective Probabilistic Semantics and the Principle of Total Evidence;118
2.3.5.2;The Stalnaker Thesis, the Ramsey Test, and Conditional or Non-Conditional Probabilities as Primitive;120
2.3.5.3;Languages of a Probabilistic Conditional Logic;123
2.3.5.4;Further Reasons for the Restriction of Languages of Probabilistic Conditional Logics;125
2.3.5.5;Propositions, NTV (``No Truth Value''), and Conditional Logic Languages;127
2.3.6;Adams' Probabilistic P Systems;131
2.3.6.1;The P Systems: Systems P, P*, and P+;132
2.3.6.2;Threshold Semantics;139
2.3.6.3;Adams' System P and Schurz's Modification;139
2.3.6.4;Possible Worlds Semantics for (Indicative) Conditionals and Quasi Truth Value Assignments in Adams' Probabilistic Semantics;148
2.3.7;D. Lewis' Triviality Result and Logics for Indicative Conditionals;155
2.3.7.1;D. Lewis' Triviality Result;156
2.3.7.2;Triviality due to Iterations (and Nestings) of Conditional Formulas;161
2.3.7.3;D. Lewis' Triviality Result, Restrictions of Languages, and Truth Value Accounts of Indicative Conditionals;163
2.3.7.4;Conclusion;166
2.3.8;Bennett's Gibbardian Stand-Off Argument;166
2.3.8.1;Bennett's Extended Gibbardian Stand-Off Argument;167
2.3.8.2;A Criticism of Bennett's Gibbardian Stand-Off Argument;171
2.3.8.3;Summary;174
2.3.9;Conclusion;175
3;II Formal Results for Chellas-Segerberg Semantics;175
3.1;Formal Framework;179
3.1.1;Why Chellas-Segerberg Semantics?;179
3.1.2;Proof-Theoretic Notions;180
3.1.2.1;Languages LCL, LCL-, LrCL, LrCL*, and LrrCL;180
3.1.2.2;Logics;188
3.1.2.3;Non-Monotonicity;189
3.1.2.4;Consistency and Maximality;190
3.1.2.5;A Propositional Basis for Conditional Logics;190
3.1.2.6;System CK;191
3.1.2.7;A Further Axiomatization of System CK;193
3.1.3;Model-Theoretic Notions;195
3.1.3.1;Chellas Frames and Chellas Models;196
3.1.3.2;Chellas Models and Frames and Kripke Semantics;198
3.1.3.3;Segerberg Frames and Segerberg Models;202
3.1.3.4;Validity, Logical Consequence, and Satisfiability;204
3.1.3.5;Notions of Frame Correspondence;207
3.1.3.6;Standard and Non-Standard Chellas Models and Segerberg Frames;209
3.1.3.7;Notions of Soundness and Completeness;210
3.2;Frame Correspondence for a Lattice of Conditional Logics;219
3.2.1;Non-Trivial Frame Conditions for a Lattice of Conditional Logics;221
3.2.2;The Notions of Trivial and Non-Trivial Frame Conditions;227
3.2.2.1;A Translation Procedure from Axiom Schemata to Trivial Frame Conditions;228
3.2.2.2;A Non-Triviality Criterion;231
3.2.3;Chellas Frame Correspondence Proofs;233
3.2.3.1;System P;233
3.2.3.2;Extensions of System P;236
3.2.3.3;Weak Probability Logic (Threshold Logic);237
3.2.3.4;Monotonic Principles;239
3.2.3.5;Bridge Principles;241
3.2.3.6;Collapse Conditions Material Implication;243
3.2.3.7;Traditional Extensions;244
3.2.3.8;Iteration Principles;246
3.3;Soundness and Completeness for a Lattice of Conditional Logics;249
3.3.1;General Overview;249
3.3.1.1;Focus of the Completeness Proofs;249
3.3.1.2;Proofs for Segerberg Frame Completeness and Chellas Frames Completeness;251
3.3.2;Singleton Frames for CS Semantics;255
3.3.3;Soundness w.r.t. Classes of Chellas Frames;257
3.3.4;Standard Segerberg Frame Completeness;258
3.3.4.1;General Principles;258
3.3.4.2;Canonical Models;259
3.3.4.3;Canonicity Proofs for Individual Principles;262
3.4;Chellas-Segerberg Semantics for Indicative and Counterfactual Conditionals;273
3.4.1;The Basic Chellas-Segerberg Systems (Systems CK and CKR);276
3.4.1.1;Objective and Subjective Interpretations of Chellas-Segerberg Semantics;277
3.4.1.2;Alternative Axiomatizations of System CKR;285
3.4.2;Conditional Logics without Bridge Principles;287
3.4.2.1;System C;287
3.4.2.2;System CL;295
3.4.2.3;System P;295
3.4.2.4;System R;303
3.4.2.5;D. Lewis' System V;306
3.4.2.6;Monotonic Systems without Bridge Principles (Systems CM and M);314
3.4.3;Conditional Logics with Bridge Principles;322
3.4.3.1;Adams' System P*;322
3.4.3.2;D. Lewis' System VC;328
3.4.3.3;Stalnaker's System S;329
3.4.3.4;The Material Collapse System MC;331
3.4.4;Summary;336
3.5;Concluding Remarks;339
3.6;References;343

Über Autor(innen)

Matthias Unterhuber, University of Düsseldorf, Germany.