Paul Horwich has formulated a paradox which he believes to be even more virulent than the related Hempel paradox. I show that Horwich's paradox, as orginally formulated, has a purely logical solution, hence that it has no bearing on the theory of confirmation. On the other hand, it illuminates some undesirable traits of classical predicate logic. A revised formulation of the paradox is then dealt with in a way that implies a modest revision of Nicod's criterion.

The confirmation of scientific hypotheses has a quantitative and qualitative aspect. No empirical hypothesis can be confirmed conclusively, so philosophers of science have used the theory of probability to elucidate the quantitative component, which determines a degree of confirmation ‐ that is, the extent to which the hypothesis is supported by the evidence (see probability and evidence and confirmation). By contrast, the qualitative feature of confirmation concerns the prior question of the nature of the relation between (...) the hypothesis and the evidence if the hypothesis is to be confirmed by its instances. If a hypothesis is to be supported by a body of evidence, it must be related to the evidence in an appropriate way. The paradoxes of confirmation arise in the attempt to characterize in first‐order logic the qualitative relation between hypothesis and evidence. (shrink)

Exhumation and study of the 1945 paradox of confirmation brings out the defect of its formulation. In the context of quantifier conditional-probability logic it is shown that a repair can be accomplished if the truth-functional conditional used in the statement of the paradox is replaced with a connective that is appropriate to the probabilistic context. Description of the quantifier probability logic involved in the resolution of the paradox is presented in stages. Careful distinction is maintained between a formal logic (...) language and its semantics, as the same language may be outfitted with different semantics. An acquaintance with sections 1? 5 of Hailperin (2006) covering the sentential aspects of probability logic is assumed as background information for quantifier probability logic. (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)

THE PARADOXES OF CONFIRMATION ARE CONSTITUTED BY THE CONTRADICTIONS ARISING FROM THE CONJUNCTION OF THREE PRINCIPLES OF CONFIRMATION - NICOD’S CRITERION, THE EQUIVALENCE CONDITION, AND WHAT THE PAPER CALLS THE SCIENTIFIC LAWS CONDITION. THE PAPER DISCUSSES IN DETAIL THE VARIOUS SOLUTIONS PROVIDED BY ABANDONING ONE OF THE PRINCIPLES. IN THE END IT FINDS NICOD’S CRITERION FALSE, BUT FINDS THE EXPLANATIONS GIVEN BY H.G. ALEXANDER AND OTHERS OF WHY NICOD’S CRITERION IS FALSE THEMSELVES UNSATISFACTORY. IT THEN PROVIDES A (...) MORE ADEQUATE ACCOUNT OF THE CIRCUMSTANCES IN WHICH "RA.BA" CONFIRMS "ALL R’S ARE B". (shrink)

I present a puzzle which seems simple, but is found to have interesting implications for confirmation. Its dissolution also helps us to throw light on the relationship between first- and second-order probabilities construed as rational degrees of belief.

It is shown that the paradoxes of confirmation are closely linked to the paradoxes of material implication and that they can be avoided by formulating natural laws in terms of a genuine if-Connective rather than the material conditional. However, Natural laws so expressed are not confirmed by simple conjunctions. The question then is whether the common assumption that simple conjunctions do confirm universal generalizations is correct. The answer given is that it is not. In particular, A confirming (...) proposition of the form 'this is a black raven' is not equivalent to 'this is a raven and this is black'. (shrink)

Hempel’s Converse Consequence Condition (CCC), Entailment Condition (EC), and Special Consequence Condition (SCC) have some prima facie plausibility when taken individually. Hempel, though, shows that they have no plausibility when taken together, for together they entail that E confirms H for any propositions E and H. This is “Hempel’s paradox”. It turns out that Hempel’s argument would fail if one or more of CCC, EC, and SCC were modified in terms of explanation. This opens up the possibility that Hempel’s paradox (...) can be solved by modifying one or more of CCC, EC, and SCC in terms of explanation. I explore this possibility by modifying CCC and SCC in terms of explanation and considering whether CCC and SCC so modified are correct. I also relate that possibility to Inference to the Best Explanation. (shrink)

ABSTRACTIn this paper, I review some recent treatments of Simpson's Paradox, and I propose a new rationalizing explanation of its paradoxicality.

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)

In From Instrumentalism to Constructive Realism Theo Kuipers presents a theory of qualitative confirmation that is supposed to not assume the existence of quantitative probabilities. He claims that this theory is able to resolve some paradoxes in confirmation theory, including the ravens paradox. This paper shows that there are flaws in Kuipers' qualitative confirmation theory and in his application of it to the ravens paradox.

Hempel's paradox of the ravens has to do with the question of what constitutes confirmation from a logical point of view; Wason 's selection task has been used extensively to investigate how people go about attempting to confirm or disconfirm conditional claims. This paper presents an argument that the paradox is resolved, and that people's typical performance in the selection task can be explained, by consideration of what constitutes an effective strategy for seeking evidence of the tenability of universal (...) or conditional claims in everyday life. (shrink)

We often want to say that inductive evidence supports some conclusion more or less strongly. This is often put as a matter of "e confirms h", where confirmation comes in degrees.

A distinction is made between the internal paradox (inconsistency of our intuitions) and the external one (no explicatum captures all our intuitions). seemingly counterintuitive aspects of carnap's inductive logic (external paradox) are shown to be sound. considering the purpose of formulating an hypothesis, and its intended competitors, it is explained why nicod's criterion seems plausible (internal paradox). incidentally baumer's theory (bjps, 15) is proved to violate the equivalence condition.

Some of the concerns which motivate attempts to provide a philosophical reduction of nomological necessity are briefly introduced in I. In II, Hempel's treatment of the paradoxes is contrasted with a position which holds that nomological necessity is a pragmatic dimension of laws of nature, and that this pragmatic dimension is of such a type that it prevents laws of nature from contraposing. Such a position is, however, untenable unless (i) the sense of 'pragmatics' at issue is specified, and (...) the possibility of pragmatic differences resulting in differences in confirmation is defended, and (ii) a relevant pragmatic difference between contrapositives is indicated. III attempts to satisfy condition (i) by developing a new sense of pure pragmatics and argues that some remarks by Goodman and Scheffler together with work on the logic of explanation by Dr. Rescher and myself suggest that nomological contrapositives are not pragmatically equivalent (i.e. substitutable salva veritate in the pure pragmatics of an ideal scientific language). If such is the case, condition (ii) is also satisfied. (shrink)