According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction Hempel's (...) paradox, the standard Bayesian solution, and the disputed assumption Attempts to defend the disputed assumption Attempts to refute the disputed assumption A way out for Bayesians Conclusion. (shrink)

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)

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 Relevance Criterion of confirmation gained prominence as the underlying principle of the class-size approach (CSA) to Hempel's paradoxes of confirmation. The CSA, however, yields counter-intuitive results for (c) instances, and this failing cast serious doubt on the acceptability of the Relevance Criterion. In this paper an attempt is made to rescue the Relevance Criterion from this embarrassment. This is done by incorporating that criterion into a new resolution of the paradoxes, a resolution based on a theory of selective confirmation (...) and a distinction between mere confirmation in principle and evaluative confirmation (E-confirmation). (shrink)

Hempel's paradox of the ravens arises from the inconsistency of three prima facie plausible principles of confirmation. This paper uses Carnapian inductive logic to (a) identify which of the principles is false, (b) give insight into why this principle is false, and (c) identify a true principle that is sufficiently similar to the false one that failure to distinguish the two might explain why the false principle is prima facie plausible. This solution to the paradox is compared with a variety (...) of other responses and is shown to differ from all of them. (shrink)

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)

The Raven and the Bayesian. As an essential benefit of their probabilistic account of confirmation, Bayesians state that it provides a twofold solution to the ravens paradox. It is supposed to show that (i) the paradox’s conclusion is tenable because a white shoe only negligibly confirms the hypothesis that all ravens are black, and (ii) the paradox’s first premise is false anyway because a black raven can speak against the hypothesis. I argue that both proposals are not only unable to (...) solve the paradox, but also point to severe difficulties with Bayesianism. The former does not make the conclusion acceptable, and it entails the bizarre consequence that a great amount of non-black non-ravens substantially confirms the ravens hypothesis. The latter does not go far enough because there is a variant of the first premise which follows from Bayesianism and implies a weaker, but nevertheless untenable, variant of the conclusion. (shrink)

It is widely thought that Bayesian confirmation theory has provided a solution to Hempel's Paradox (the Ravens Paradox). I discuss one well‐known example of this approach, by John Mackie, and argue that it is unconvincing. I then suggest an alternative solution, which shows that the Bayesian approach is altogether mistaken. Nicod's Condition should be rejected because a generalisation is not confirmed by any of its instances if it is not law‐like. And even law‐like non‐basic empirical generalisations, which are expressions of (...) assumed underlying causal regularities, are not so confirmed if they are absurd in the light of our causal background knowledge or if their instances are not also possible instances of the relevant causal claim. (shrink)