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)

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)

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)

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.

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)

1. Confirmation Theory One, which we shall construct, when applied to the Raven Hypothesis yields the following results: Any black raven confirms the Raven Hypothesis.Any black non-raven confirms the Raven Hypothesis.Any non-black raven disconfirms the Raven Hypothesis.Any non-black non-raven is neutral to the Raven Hypothesis.Theory One consists of two parts: six basic concepts from confirmation theory proper, and the underlying logic.

In order to confirm any statement of the form A are B we consider a sufficiently large number of A in order to check them for having or failing to have property B. But logic leads us to believe that A are B is equivalent to non-B are non-A. If this is so then it seems reasonable to suppose that we confirm and in the same way. Whatever set of things we consider for confirming one must be the same set (...) that we consider for the other. Yet in confirming the set considered seems to be the set of A, while in confirming the set considered seems to be the set of non-B. How can two logically equivalent statements be confirmable in different ways? (shrink)

To solve the highly counterintuitive paradox of confirmation represented by the statement, “A pair of red shoes confirms that all ravens are black,” Hempel employed a strategy that retained the equivalence condition but abandoned Nicod’s irrelevance condition. However, his use of the equivalence condition is fairly ad hoc, raising doubts about its applicability to this problem. Furthermore, applying the irrelevance condition from Nicod’s criterion does not necessarily lead to paradoxes, nor does discarding it prevent the emergence of paradoxes. (...) Hempel’s approach fails to adequately resolve the paradox. (shrink)

Hempel‘s paradox of the ravens, and his take on it, are meant to be understood as being restricted to situations where we have no additional background information. According to him, in the absence of any such information, observations of FGs confirm the hypothesis that all Fs are G. In this paper I argue against this principle by way of considering two other paradoxes of confirmation, Goodman‘s 'grue‘ paradox and the 'tacking‘ (or 'irrelevant conjunct‘) paradox. What these (...) paradoxes reveal, I argue, is that a presumption of causal realism is required to ground any confirmation; but once we grant causal realism, we have no reason to accept the central principles giving rise to the paradoxes. (shrink)

Bayesians regard their solution to the paradox of confirmation as grounds for preferring their theory of confirmation to Hempel’s. They point out that, unlike Hempel, they can at least say that a black raven confirms “All ravens are black” more than a white shoe. However, I argue that this alleged advantage is cancelled out by the fact that Bayesians are equally committed to the view that a white shoe confirms “All non-black things are non-ravens” less than a (...) black raven. In light of this, I reexamine the dialectic between Hempel and the Bayesians. (shrink)

The (recent, Bayesian) cognitive science literature on the Wason Task (WT) has been modeled largely after the (not-so-recent, Bayesian) philosophy of science literature on the Paradox of Confirmation (POC). In this paper, we apply some insights from more recent Bayesian approaches to the (POC) to analogous models of (WT). This involves, first, retracing the history of the (POC), and, then, re-examining the (WT) with these historico-philosophical insights in mind.

The (recent, Bayesian) cognitive science literature on The Wason Task (WT) has been modeled largely after the (not-so-recent, Bayesian) philosophy of science literature on The Paradox of Confirmation (POC). In this paper, we apply some insights from more recent Bayesian approaches to the (POC) to analogous models of (WT). This involves, first, retracing the history of the (POC), and, then, reexamining the (WT) with these historico-philosophical insights in mind.

Several authors, e.g. Patrick Suppes and I. J. Good, have recently argued that the paradox of confirmation can be resolved within the developing subjective Bayesian account of inductive reasoning. The aim of this paper is to show that the paradox can also be resolved by the rival orthodox account of hypothesis testing currently employed by most statisticians and scientists. The key to the orthodox statistical resolution is the rejection of a generalized version of Hempel's instantiation condition, namely, (...) the condition that a PQ is inductively relevant to the hypothesis $(x)(Px\supset Qx)$ even in the absence of all further information. Though their reasons differ, it turns out that Bayesian and orthodox statisticians agree that this condition lies at the heart of the paradox. (shrink)

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)

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)

To undermine much of what we ordinarily claim to know, sceptics have often appealed to a principle (known as the principle of closure) according to which knowledge (justification) is closed under known entailment. In this paper after expounding the views of Stein, Klein and others, I shall argue that they all fail to take note of different contexts in which the principle of closure is applied. The relevance of the principle of closure for scepticism is then analyzed in the light (...) of, what I call, the infectious' character of epistemic contexts. I shall also highlight the similarities in the behavior of the concepts of justification and confirmation and appeal to certain solutions to the paradoxes of confirmation to provide a comprehensive account of the different instances of the principle of closure. (shrink)