Bayesianism and Scientific Reasoning

Description

This Element explores the Bayesian approach to the logic and epistemology of scientific reasoning. Section 1 introduces the probability calculus as an appealing generalization of classical logic for uncertain reasoning. Section 2 explores some of the vast terrain of Bayesian epistemology. Three epistemological postulates suggested by Thomas Bayes in his seminal work guide the exploration. This section discusses modern developments and defenses of these postulates as well as some important criticisms and complications that lie in wait for the Bayesian epistemologist. Section 3 applies the formal tools and principles of the first two sections to a handful of topics in the epistemology of scientific reasoning: confirmation, explanatory reasoning, evidential diversity and robustness analysis, hypothesis competition, and Ockham's Razor. Cover Title Page Copyright Page Bayesianism and Scientific Reasoning Contents Introduction 1 Probability Theory, a Logic of Consistency 1.1 Logic and Uncertainty 1.2 From Deductive Logic to Probability Theory 1.3 A Primer on Probability 1.3.1 Dartboard Representations 1.3.2 Revisiting the Basic Rules 1.3.3 Other Rules of Probability 1.4 A Logic of Confidences 1.4.1 A Subject with No Object? 1.4.2 Consistency of Confidences 1.4.3 Toward a Positive Defense 2 Bayesian Epistemology 2.1 Bayes and Bayesian Epistemology 2.2 Bayes’s Rule 2.2.1 Interlude: Updating Imprecise Confidences 2.2.2 Complications and Generalizations 2.2.3 Epistemology and Convergence 2.3 Calibration 2.3.1 Calibration and Relative Frequency 2.3.2 Calibration and Objective Chance 2.3.3 Discussion 2.4 Insufficient Reason 2.4.1 Bertrand’s Paradox 2.4.2 Invariance 2.5 MAXENT 3 Scientific Reasoning 3.1 Confirmation 3.2 Explanatory Reasoning 3.2.1 Peirce and Power 3.2.2 Measuring Explanatory Power 3.2.3 Inference to the Best (i.e., Most Powerful) Explanation 3.3 Robustness Analysis 3.3.1 RA-Diversity and Explanatory Discrimination 3.3.2 Interlude: Hypothesis Competition and Defeat 3.3.3 A Bayesian Evaluation of Robustness Analysis Mutually Exclusive Competitors Consistent Epistemic Competitors 3.4 Simplicity and Evidential Fit 3.4.1 A Bayesian Approach to Simplicity and Fit 3.4.2 Striking a Balance 3.4.3 Application References