The Laws of Belief : Ranking Theory and Its Philosophical Applications

Ranking theory will be claimed to deliver the first full account of the dynamics of belief and to be the legitimate sister of probability theory. This entails its deep significance for fundamental issues in epistemology and the philosophy of science. Therefore this book motivates and introduces the basic notion of a ranking function, which provides a new kind of degrees ob belief that at same time accounts for belief simpliciter. It develops ranking theory in ample detail, up to algorithms of inductive reasoning. It provides a measurement theory for ranking functions. It accounts for auto-epistemology in ranking-theoretic terms. It explicates the basic notion of a (deductive or non-deductive) reason, which is the entry to its rich philosophical applications. Among these are: a new account of lawlikeness, an account of ceteris paribus laws, a new perspective on dispositions, a rich and detailed theory of deterministic causation, an understanding of natural modalities as an objectification of epistemic modalities, an account of the experiential basis of belief, and thus a restructuring of the debate on foundationalism and coherentism (and externalism and contextualism), and finally a revival of fundamental a priori principles of reason fathoming the basics of empiricism and the relation between reason and truth and concluding in a proof of a weak principle of causality. All this is accompanied by thorough-going comparative discussions, on a general level as well as within each topic, and in particular with respect to probability theory that proves to be the major guideline of this book. Cover Contents Preface 1. Introduction 1.1 Some Reflections on Skepticism and the Problem of Induction 1.2 The Agenda 2. Belief and its Objects 2.1 The Formal Representation 2.2 Interpretation: The Noncommittal Way 2.3 A More Determinate View 3. The Probabilistic Way 3.1 The Basic Laws of Subjective Probability 3.2 The Dynamics of Subjective Probability 3.3 Probability and Belief 4. The Representation of Belief: Some Standard Moves 4.1 The Basic Laws of Belief 4.2 The Dynamics of Belief 4.3 Equivalent Formulations 4.4 AGM Belief Revision Theory 5. Ranking Functions 5.1 The Problem of Iterated Belief Change 5.2 Ranking Functions 5.3 Conditional Ranks 5.4 The Dynamics of Ranking Functions 5.5 Conditionalization Generalizes AGM Belief Revision and Contraction 5.6 An Appendix on Iterated AGM Belief Revision and Contraction 5.7 A Further Appendix on Multiple Contraction 6. Reasons and Apriority 6.1 Explicating Reasons 6.2 The Formal Structure of Reasons 6.3 The Balance of Reasons 6.4 The Force of Reasons 6.5 Maximal Certainty, Unrevisability, and Apriority 7. Conditional Independence and Ranking Nets 7.1 Independence Among Propositions and Among Variables 7.2 An Example: Mr. Holmes and His Alarm 7.3 Ranking Nets and Bayesian Nets 7.4 Propagation in Local Ranking and Bayesian Nets 7.5 Appendix on Independent Testimonies 8. The Measurement of Ranks 8.1 The Method of Upgradings 8.2 A Difference Measurement of Conditional Ranks 8.3 Measuring Ranks by Iterated Contractions 8.4 The Laws of Iterated Contraction 8.5 Two Further Lines of Justification 9. Supposing, Updating, and Reflection 9.1 Conditional Belief 9.2 Reflection 9.3 Auto-Epistemic Updating 10. Ranks and Probabilities 10.1 Once More: Belief and Probability 10.2 Ways of Formal Unification 10.3 Philosophical Convergences and Divergences 10.4 Appendix on Ranking-Theoretic Decision Theory 11. Comparisons 11.1 Predecessors: Rescher, Cohen, Shackle 11.2 Isaac Levi’s Incomparable Epistemological Picture 11.3 AGM Belief Revision Theory Once More, and the Problematic Force of Examples 11.4 Undefeated Justification Defeated: A Criticism of Lehrer’s Account of Knowledge 11.5 John Pollock’s Theory of Defeasible Reasoning: An Ally? 11.6 On the Nature of Normative Epistemology 11.7 Formal Learning Theory 11.8 Possibility Theory 11.9 Dempster–Shafer Belief Functions 11.10 A Brief Remark on Non-Monotonic Reasoning 12. Laws and their Confirmation 12.1 A Plan for the Next Chapters 12.2 The Problem of Lawlikeness 12.3 Laws, Symmetry, and Instantial Relevance 12.4 Laws and Persistence 12.5 The Confirmation of Laws 12.6 A Priori Lawfulness? 13. Ceteris Paribus Conditions and Dispositions 13.1 Ceteris Paribus Conditions: Hard to Avoid and Hard to Understand 13.2 A Ranking-Theoretic Account of Ceteris Paribus Conditions 13.3 What We Know A Priori about Dispositions 13.4 The Metaphysics and the Epistemology of Dispositions: A Short Comparative Discussion 14. Causation 14.1 The Conceptual Framework 14.2 A Preliminary Discussion 14.3 Causes and Reasons 14.4 Direct Causes 14.5 Some Examples 14.6 The Circumstances of Direct Causes 14.7 Multi-Valued Variables 14.8 Causal Dependence between Variables, Markov Conditions, and the Principle of the Common Cause 14.9 Frame-Relative and Absolute Causal Dependence 14.10 Interactive Forks, Simultaneous Causal Dependence, and Chain Graphs 14.11 Indirect Causes: Conflicting Demands 14.12 Causation and its Transitivity 14.13 Some Further Examples 14.14 Appendix on Explanation 14.15 A Further Appendix on Inference to the Best Explanation and Innocence of the Worst Explanation 15. Objectification 15.1 The Fundamental Problem 15.2 What Could Objectification Mean? 15.3 The Non-Objectifiability of Reasons 15.4 The Objectification of Causation: First Method 15.5 The Objectification of Causation: Second Method 15.6 The Conditional Objectifiability of Laws 15.7 Concluding Reflections 16. Justification, Perception, and Consciousness 16.1 Justification 16.2 Perception 16.3 The Schein–Sein Principle 16.4 Consciousness 17. The A Priori Structure of Reasons 17.1 Once More: Unrevisable and Defeasible Apriority 17.2 Empiricism and Coherence 17.3 Reason, Truth, and Stability 17.4 Principles of Causality Bibliography Name Index A B C D E F G H I J K L M N O P Q R S T U V W Y Z Subject Index A B C D E F G H I J K L M N O P Q R S T U V W "Wolfgang Spohn presents the first full account of the dynamic laws of belief, by means of ranking theory. This book is his long-awaited presentation of ranking theory and its ramifications. He motivates and introduces the basic notion of a ranking function, which recognises degrees of belief and at the same time accounts for belief simpliciter. He provides a measurement theory for ranking functions, accounts for auto-epistemology in ranking-theoretic terms, and explicates the basic notion of a (deductive or non-deductive) reason. The rich philosophical applications of Spohn's theory include: a new account of lawlikeness, an account of ceteris paribus laws, a new perspective on dispositions, a rich and detailed theory of deterministic causation, an understanding of natural modalities as an objectification of epistemic modalities, an account of the experiential basis of belief--and thus a restructuring of the debate on foundationalism and coherentism (and externalism and contextualism)--and, finally, a revival of fundamental a priori principles of reason fathoming the basics of empiricism and the relation between reason and truth, and concluding in a proof of a weak principle of causality. All this is accompanied by thorough comparative discussions, on a general level as well as within each topic, and in particular with respect to probability theory."--Publisher's website Wolfgang Spohn Presents A Full Account Of The Dynamic Laws Of Belief, By Means Of Ranking Theory, A Relative Of Probability Theory Which He Has Pioneered Since The 1980s. He Offers Novel Insights Into The Nature Of Laws, The Theory Of Causation Inductive Reasoning And Its Experiential Base, And A Priori Principles Of Reason. Wolfgang Spohn. Includes Bibliographical References (p. [556]-580) And Indexes.