Abstract
In the Paradox of the Ravens, a set of otherwise intuitive claims about evidence seems to be inconsistent. Most attempts at answering the paradox involve rejecting a member of the set, which seems to require a conflict either with commonsense intuitions or with some of our best confirmation theories. In contrast, I argue that the appearance of an inconsistency is misleading: ‘confirms’ and cognate terms feature a significant ambiguity when applied to universal generalisations. In particular, the claim that some evidence confirms a universal generalisation ordinarily suggests, in part, that the evidence confirms the reliability of predicting that something which satisfies the antecedent will also satisfy the consequent. I distinguish between the familiar relation of confirmation simpliciter and what I shall call ‘predictive confirmation’. I use them to formulate my answer, illustrate it in a very simple probabilistic model, and defend it against objections. I conclude that, once our evidential concepts are sufficiently clarified, there is no sense in which the initial claims are both plausible and inconsistent.
Highlights
In the Paradox of the Ravens (PR) a number of plausible claims about confirmation seem to commit us to an excessively broad analysis of evidence, such that discovering non-black non-ravens confirms the hypothesis that ‘All ravens are black’ whenever it confirms ‘All non-black things are non-ravens’.1 The challenge is either to reject one of these claims or to learn to live with this paradoxical result
While it is plausible that, if we discover that a large sample of white swans deep in the Amazon rainforest, this new information can confirm that ‘All swans are white’ is a reliable rule-of-thumb, it is not clear that there is a sense of ‘evidence’ in which this information can provide evidence for the hypothesis is true
That response is plausible to me, but it highlights the difference between my explication and Carnap’s: I am trying to explicate cases where people say that evidence does or does not provide evidence for a universal generalisation, rather than merely the reliability of the hypothesis as a rule-of-thumb
Summary
In the Paradox of the Ravens (PR) a number of plausible claims about confirmation seem to commit us to an excessively broad analysis of evidence, such that discovering non-black non-ravens (or learning sentences reporting them) confirms the hypothesis that ‘All ravens are black’ whenever it confirms ‘All non-black things are non-ravens’.1 The challenge is either to reject one of these claims or to learn to live with this paradoxical result. I shall argue that both the apparently paradoxical claims and our intuitions are correct, because our intuitions are not about the type of evidential relation that confirmation theorists are explicating. My answer is ‘conciliatory’ in the sense that both those confirmation theorists who accept the ‘paradoxical’ results associated with the PR and those who reject them are both correct, but each group is only correct for one of the two different types of evidential relation. When we discuss positive evidential support for universal generalisations, there is a pragmatic implication that the confirming evidence makes it more reliable to infer that something satisfying the antecedent will satisfy the consequent. When the evidence does so, it provides what I call ‘predictive confirmation’ This type of evidential support comes apart from confirmation simpliciter in the PR and this creates the appearance of paradox.
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