Inference, Method and Decision

1. Front Matter

   Pages i-xv

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2. Informative Inference

   1. Front Matter

      Pages 1-1

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   2. Information

      • Roger D. Rosenkrantz

      Pages 3-32

   3. The Paradoxes of Confirmation

      • Roger D. Rosenkrantz

      Pages 33-41

   4. Inductivism and Probabilism

      • Roger D. Rosenkrantz

      Pages 42-83

   5. Inductive Generalization

      • Roger D. Rosenkrantz

      Pages 84-90

3. Scientific Method

   1. Front Matter

      Pages 91-91

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   2. Simplicity

      • Roger D. Rosenkrantz

      Pages 93-117

   3. Bayes and Popper

      • Roger D. Rosenkrantz

      Pages 118-134

   4. The Copernican Revelation

      • Roger D. Rosenkrantz

      Pages 135-161

   5. Explanation

      • Roger D. Rosenkrantz

      Pages 162-173

4. Statistical Decision

   1. Front Matter

      Pages 175-175

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   2. Support

      • Roger D. Rosenkrantz

      Pages 177-187

   3. Testing

      • Roger D. Rosenkrantz

      Pages 188-223

   4. Bayes/Orthodox Comparisons

      • Roger D. Rosenkrantz

      Pages 224-241

   5. Cognitive Decisions

      • Roger D. Rosenkrantz

      Pages 242-256

5. Back Matter

   Pages 257-270

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This book grew out of previously published papers of mine composed over a period of years; they have been reworked (sometimes beyond recognition) so as to form a reasonably coherent whole. Part One treats of informative inference. I argue (Chapter 2) that the traditional principle of induction in its clearest formulation (that laws are confirmed by their positive cases) is clearly false. Other formulations in terms of the 'uniformity of nature' or the 'resemblance of the future to the past' seem to me hopelessly unclear. From a Bayesian point of view, 'learning from experience' goes by conditionalization (Bayes' rule). The traditional stum­ bling block for Bayesians has been to fmd objective probability inputs to conditionalize upon. Subjective Bayesians allow any probability inputs that do not violate the usual axioms of probability. Many subjectivists grant that this liberality seems prodigal but own themselves unable to think of additional constraints that might plausibly be imposed. To be sure, if we could agree on the correct probabilistic representation of 'ignorance' (or absence of pertinent data), then all probabilities obtained by applying Bayes' rule to an 'informationless' prior would be objective. But familiar contra­ dictions, like the Bertrand paradox, are thought to vitiate all attempts to objectify 'ignorance'. BuUding on the earlier work of Sir Harold Jeffreys, E. T. Jaynes, and the more recent work ofG. E. P. Box and G. E. Tiao, I have elected to bite this bullet. In Chapter 3, I develop and defend an objectivist Bayesian approach.

• Karl R. Popper
• invariance
• philosophy of science
• probability

• Virginia Polytechnic Institute and State University, Blacksburg, USA

  Roger D. Rosenkrantz

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