Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of Bayesian confirmation-theoretic enthymemes, and a brief analysis of some recent attempts to resolve the problem of measure sensitivity.

Abstract. The "conjunction fallacy" has been a key topic in discussions and debates on the rationality of human reasoning and its limitations. Yet the attempt of providing a satisfactory account of the phenomenon has proven challenging. Here we propose a new analysis. We suggest that in standard conjunction problems the fallacious probability judgments experimentally observed are typically guided by sound assessments of confirmation relations, meant in terms of contemporary Bayesian confirmation theory. The proposed analysis is shown robust (i.e., not depending on various alternative ways of measuring degrees of confirmation), consistent with available data, and prompting further empirical investigations. The present approach emphasizes the relevance of the notion of confirmation in the assessments of the relationships between the normative and descriptive study of inductive reasoning.

A Bayesian account of independent evidential support is outlined. This account is partly inspired by the work of C.S. Peirce. I show that a large class of quantitative Bayesian measures of confirmation satisfy some basic desiderata suggested by Peirce for adequate accounts of independent evidence. I argue that, by considering further natural constraints on a probabilistic account of independent evidence, all but a very small class of Bayesian measures of confirmation can be ruled out. In closing, another application of my account to the problem of evidential diversity is also discussed.

Likelihoodists and Bayesians seem to have a fundamental disagreement about the proper probabilistic explication of relational (or contrastive) conceptions of evidential support (or confirmation). In this paper, I will survey some recent arguments and results in this area, with an eye toward pinpointing the nexus of the dispute. This will lead, first, to an important shift in the way the debate has been couched, and, second, to an alternative explication of relational support, which is in some sense a "middle way" between Likelihoodism and Bayesianism. In the process, I will propose some new work for an old probability puzzle: the "Monty Hall" problem.

Carnap's inductive logic (or confirmation) project is revisited from an "increase in firmness" (or probabilistic relevance) point of view. It is argued that Carnap's main desiderata can be satisfied in this setting, without the need for a theory of "logical probability". The emphasis here will be on explaining how Carnap's epistemological desiderata for inductive logic will need to be modified in this new setting. The key move is to abandon Carnap's goal of bridging confirmation and credence, in favor of bridging confirmation and evidential support. * Department of Philosophy, University of California-Berkeley, 314 Moses Hall #2390, Berkeley, CA 94720-2390 † I would like to thank audiences at the University of California-Berkeley, the University of Michigan, the University of Oklahoma, and the PSA 2004 symposium at which this paper was presented for useful comments and discussion (there are too many members of these audiences who have made valuable suggestions to name each one individually). Setting the Stage: Three Carnapian DesiderataIn the second edition of Logical Foundations of Probability (LFP), Carnap (1962, xvi) distinguished two kinds of inductive-logical confirmation relations: confirmation as firmness, which he informally characterized as "How probable the hypothesis H is on the basis of the evidence E", and confirmation as increase in firmness, which he informally characterized as "How much the probability of H is increased when new evidence E is acquired (in addition to the prior evidence which, for simplicity, we shall take here as tautological)." Carnap devotes almost all of LFP to the task of explicating the former. Presently, I will discuss Carnap's approach to the former, and sketch my own approach to the latter. My discussion will focus, ultimately, on the relation between inductive logic (the confirmation as increase in firmness relation), and epistemology (the relation of incremental evidential support).I begin with some quotes from LFP to set the stage. The first gives a general sense of the very idea of inductive logic, as a quantitative analogue (or generalization) of deductive logic:Deductive logic may be regarded as the theory of the relation of logical consequence [ ], and inductive logic as the theory of another concept [c] which is likewise objective and logical . . . degree of confirmation.The next two quotes give Carnap's (1962, 200) informal characterizations of the terms "logical" and "objective" as they apply to the relations and c:The principal common characteristic of the statements in both fields is their independence of the contingency of facts. This characteristic justifies the application of the common term 'logic' to both fields.That c is an objective concept means this: if a certain c value holds for a certain hypothesis with respect to a certain evidence, then this value is entirely independent of what any person may happen to think about these sentences.It is clear that Carnap, at least, intends here to be saying that statements of confirmation theory shou...