How Probabilities Reflect Evidence

James M. Joyce
2005 Philosophical Perspectives  
Many philosophers think of Bayesianism as a theory of practical rationality. This is not at all surprising given that the view's most striking successes have come in decision theory. Ramsey (1931 ), Savage (1972 ), and De Finetti (1964 showed how to interpret subjective degrees of belief in terms of betting behavior, and how to derive the central probabilistic requirement of coherence from reflections on the nature of rational choice. This focus on decision-making can obscure the fact that
more » ... ianism is also an epistemology. Indeed, the great statistician Harold Jeffries (1939), who did more than anyone else to further Bayesian methods, paid rather little heed to the work of Ramsey, de Finetti, and Savage. Jeffries, and those who followed him, saw Bayesianism as a theory of inductive evidence, whose primary role was not to help people make wise choices, but to facilitate sound scientific reasoning. 1 This paper seeks to promote a broadly Bayesian approach to epistemology by showing how certain central questions about the nature of evidence can be addressed using the apparatus of subjective probability theory. Epistemic Bayesianism, as understood here, is the view that evidential relationships are best represented probabilistically. It has three central components: Evidential Probability. At any time t, a rational believer's opinions can be faithfully modeled by a family of probability functions C t , hereafter called her credal state, 2 the members of which accurately reflect her total evidence at t. Learning as Bayesian Updating. Learning experiences can be modeled as shifts from one credal state to another that proceed in accordance with Bayes's Rule. Confirmational Relativity. A wide range of questions about evidential relationships can be answered on the basis of information about structural features credal states. The first of these three theses is most fundamental. Much of what Bayesians say about learning and confirmation only makes sense if probabilities in credal
doi:10.1111/j.1520-8583.2005.00058.x fatcat:ko4tfb7jq5cdfj4aitwyttsvti