Reichenbach's Paradise : Constructing the Realm of Probabilstic Common Causes.
- 1 online resource (125 pages)
Intro -- Acknowledgments -- Relation with papers in print or previously published -- Introduction -- 1 The Principle of the Common Cause: Its Shapes and Content -- 1.1 Probability: the Basics -- 1.1.1 Screening Off -- 1.1.2 Observing Probabilities and Correlations -- 1.2 The Plurality of the Principles -- 1.3 What Reichenbach Wrote -- 1.3.1 Reichenbach's Argument for the Principle -- 1.3.2 Other Problems with Reichenbach's Approach -- 1.4 The PCC After Reichenbach -- 1.4.1 The Argument from Conservation Principles -- 1.4.2 The ``Sea Levels vs. Bread Prices'' Argument -- 1.4.3 Which Correlations Demand Explanation? -- 1.5 An Epistemic Position -- 2 Screening Off and Explanation: Formal Properties -- 2.1 The ``Deductive'' Explanatory Feature -- 2.2 In Search for Common Causes, Screening Off Is Enough -- 2.3 ``Common Common'' Constructs -- 2.4 Explanation via Screeners-the General Picture -- 2.4.1 Weakening the Screening Off Condition -- 2.4.2 Introducing Deductive Explanantes -- 3 The Principle of the Common Cause and the Bell Inequalities -- 3.1 Towards the Derivations of the Inequalities -- 3.1.1 Introduction -- 3.1.2 The Big Space Approach and the Many Spaces Approach -- 3.1.3 Deriving the Bell Inequalities -- 3.1.4 The Bell Inequalities via a Non-empirical Joint Measure -- 3.1.5 A Bell-CH Inequality from Weakened Screening Off -- 3.1.6 Connection with the PCC -- 3.2 Separate Common Causal Explanations -- 3.2.1 Separate Common Causes-Contra and Pro -- 3.2.2 Towards a Separate-common-cause Model of EPR Correlations -- 3.2.3 Bell Inequalities as Proof of Nonexistence -- 3.3 Exploiting the Detection Loophole -- 3.4 Common Causes as Hypersurfaces -- 3.5 Summary -- 4 The Principle of the Common Cause and the Causal Markov Condition -- 4.1 DAGs-an Introduction -- 4.2 The Causal Markov Condition -- 4.3 Conclusions -- 5 Causal Closedness. 5.1 A Preliminary Formal Remark -- 5.2 Causal (up-to-n-)closedness -- 5.2.1 Introduction -- 5.2.2 Preliminary Definitions -- 5.2.3 Summary of the Results of this Chapter -- 5.3 Proofs -- 5.3.1 Some Useful Parameters -- 5.3.2 Proof of Theorem 3 -- 5.3.3 Proof of Lemmas 10-12 -- 5.4 The ``Proper'' / ``Improper'' Common Cause Distinction and the Relations of Logical Independence -- 5.5 Other Independence Relations -- 5.6 A Slight Generalization -- 5.6.1 Examples -- 5.7 Application for Constructing Bayesian Networks-a Negative Opinion -- 5.8 The Existence of Deductive Explanantes -- 5.9 Conclusions and Problems -- 5.10 Causal Closedness of Atomless Spaces -- 6 Causal Completability -- 6.1 Causal Completability the Easy Way-``Splitting the Atom'' -- 6.2 Causal Completability of Classical Probability Spaces-the General Case -- 6.3 Some Remarks on Causal Completability of Non-classical Probability Spaces -- 6.4 The Impact of the Results -- Conclusion -- Bibliography -- Index.
Since its first introduction by Hans Reichenbach, many philosophers have claimed to refute the common cause principle. The situation is not so straightforward, though: validity of the principle remains an open question. The book traces different formulations of the principle, and provides proofs of a few pertinent theorems, settling the relevant questions in various probability spaces. It offers both philosophical insight and mathematical rigor.
9783110372717
Logic. Physics -- Philosophy. Reichenbach, Hans, 1891-1953.