The Paradox of the Ravens (a.k.a,, The Paradox of Confirmation) is indeed an old chestnut. A great many things have been written and said about this paradox and its implications for the logic of evidential support. The first part of this paper will provide a brief survey of the early history of the paradox. This will include the original formulation of the paradox and the early responses of Hempel, Goodman, and Quine. The second part of the paper will describe attempts (...) to resolve the paradox within a Bayesian framework, and show how to improve upon them. This part begins with a discussion of how probabilistic methods can help to clarify the statement of the paradox itself. And it describes some of the early responses to probabilistic explications. We then inspect the assumptions employed by traditional (canonical) Bayesian approaches to the paradox. These assumptions may appear to be overly strong. So, drawing on weaker assumptions, we formulate a new-and-improved Bayesian confirmation-theoretic resolution of the Paradox of the Ravens. (shrink)

Hempel first introduced the paradox of confirmation in (Hempel 1937). Since then, a very extensive literature on the paradox has evolved (Vranas 2004). Much of this literature can be seen as responding to Hempel’s subsequent discussions and analyses of the paradox in (Hempel 1945). Recently, it was noted that Hempel’s intuitive (and plausible) resolution of the paradox was inconsistent with his official theory of confirmation (Fitelson & Hawthorne 2006). In this article, we will try to explain how this inconsistency affects (...) the historical dialectic about the paradox and how it illuminates the nature of confirmation. In the end, we will argue that Hempel’s intuitions about the paradox of confirmation were (basically) correct, and that it is his theory that should be rejected, in favor of a (broadly) Bayesian account of confirmation. (shrink)

Vagueness is epistemic, according to some. Vagueness is ontological, according to others. This article deploys what I take to be a compromise position. Predicates are coined in specific contexts for specific purposes, but these limited practices do not automatically fix the extensions of predicates over the domain of all objects. The linguistic community using the predicate has rarely considered, much less decided, all questions that might arise about the predicate’s extension. To this extent, the ontological view is correct. But a (...) predicate that applies in some contexts can be reasonably extended to other contexts where it is initially vague. This process of development approximates the cognitive remedy for vagueness that the epistemic view prescribes. The process is piecemeal and inductive, akin to what von Wright described as the molding of concepts. Vagueness cannot be understood apart from the backdrop of classification, for vagueness is classification gone awry. Hence these pages explore the classification of particulars, both its clear successes and vague failures. How we classify unique particulars is the theme of Sections 2 and 3, which are primarily descriptive. Section 2 identifies a way of classifying particulars that pervades discourse of all sorts, and Section 3 illustrates its use in a field notorious for vagueness: ethics. Why a certain particular should (or should not) be classified in a certain way is a normative question, however, and it occupies Sections 4 and 5. Section 4 proposes a norm for strong arguments by analogy, and Section 5 illustrates how the norm might resolve vagueness in one kind of ethical dispute. This norm, which has a strong probabilistic component, is one way of affirming that probability is a guide to life. (shrink)

This volume recreates the received notion of reflective equilibrium. It reconfigures reflective equilibrium as both a cognitive ideal and a method for approximating this ideal. The ideal of reflective equilibrium is restructured using the concept of discursive strata, which are formed by sentences and differentiated by function. Sentences that perform the same kind of linguistic function constitute a stratum. The book shows how moral discourse can be analyzed into phenomenal, instrumental, and teleological strata, and the ideal of reflective equilibrium reworked (...) in these terms. In addition, the work strengthens the method of reflective equilibrium by harnessing the resources of decision theory and inductive logic. It launches a comparative version of decision theory and employs this framework as a guide to moral theory choice. It also recruits quantitative inductive logic to inform a standard of inductive cogency. When used in tandem with comparative decision theory, this standard can aid in the effort to turn the undesirable condition of reflective disequilibrium into reflective equilibrium. (shrink)

To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...

The discussion about the Raven Paradox is ever-renewing: after nearly 70 years, many authors propose from time to time new solutions, and many authors state that these solutions are unsatisfactory. It is worthy to be carefully noted that though most arguments in favor or against the paradox are based on the notion of “probability” and on the application of Bayes’ law, not one of them makes use of the Kolmogorov axiomatic theory of probability and on the subsequent notion of “random (...) variable”. This seems to be due to a preference for the purely logical interpretation of the notion of “probability” which makes it possible to assign a probability value to propositions expressing natural (universal) laws. This paper aims at presenting an attempt to contribute a solution to the paradox by the proposal of a different way to express universal natural laws and by the use of a language which does not allow one to apply probability to universal statements. (shrink)