"All ravens are black" is logically but not confirmationally equivalent with "all non-black things are non-ravens." But this is impossible, given that logical equivalence guarantees confirmational equivalence. In this paper, this paradox is solved.

I argue that the standard Bayesian solution to the ravens paradox— generally accepted as the most successful solution to the paradox—is insufficiently general. I give an instance of the paradox which is not solved by the standard Bayesian solution. I defend a new, more general solution, which is compatible with the Bayesian account of confirmation. As a solution to the paradox, I argue that the ravens hypothesis ought not to be held equivalent to its (...) contrapositive; more interestingly, I argue that how we formally represent hypotheses ought to vary with the context of inquiry. This explains why the paradox is compelling, while dealing with standard objections to holding hypotheses inequivalent to their contrapositives. (shrink)

In this paper, I provide a new argument in support of a concessive response to the Ravens Paradox. The argument I offer stems from Mark Schroeder's Gricean explanation for why existential judgments about normative reasons for action are unreliable. In short, I argue that Schroeder's work suggests that, in the case of the Ravens Paradox, people are running together the issue of what's assertible about evidence with what's true about evidence. Once these issues are pulled apart, (...) we have reason to think that the negative existential judgment about evidence that drives the Ravens Paradox is mistaken, and thus that there is in fact no paradox here at all. (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)

Simple random sampling resolutions of the raven paradox relevantly diverge from scientific practice. We develop a stratified random sampling model, yielding a better fit and apparently rehabilitating simple random sampling as a legitimate idealization. However, neither accommodates a second concern, the objection from potential bias. We develop a third model that crucially invokes causal considerations, yielding a novel resolution that handles both concerns. This approach resembles Inference to the Best Explanation (IBE) and relates the generalization’s confirmation to confirmation of (...) an associated law. We give it an objective Bayesian formalization and discuss the compatibility of Bayesianism and IBE. (shrink)

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)

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)

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.

In this paper I take Hempel’s raven paradox as the claim that statements of the form ‘∼Ru v Bu’, ‘u is not a raven or u is black,’ confirm the hypothesis h ‘(x)(Rx → Bx)’, ‘All ravens are black.’ Although Hempel discusses this using a criterion of confirmation expressed wholly in terms of deductive logic (see 1965, pp. 35-9), it has become more common to articulate criteria of confirmation using concepts of probability and, in particular, to employ the (...) positive relevance criterion of confirmation which says that, given background knowledge k, (i) e confirms h if and only if P(h/e.k)>P(h/k); (ii) e disconfirms h if and only if P(h/e.k)shrink)

Hempel's famous Raven Paradox derives from Nicod's criteria for confirmation and the Equivalence Condition, the unintuitive conclusion that things like white roses, green T-shirts and ice cubes confirm the raven hypothesis ‘All ravens are black.’ By a small rearrangement of the Equivalence Condition, I show that we can also derive the conclusion, which sounds even more intuitively intolerable, that observation of black ravens fails to confirm the raven hypothesis. We are left with the contradictory result that black (...) ravens both confirm and do not confirm the raven hypothesis. (shrink)

The canonical Bayesian solution to the ravens paradox faces a problem: it entails that black non-ravens disconfirm the hypothesis that all ravens are black. I provide a new solution that avoids this problem. On my solution, black ravens confirm that all ravens are black, while non-black non-ravens and black non-ravens are neutral. My approach is grounded in certain relations of epistemic dependence, which, in turn, are grounded in the fact that the kind (...) raven is more natural than the kind black. The solution applies to any generalization “All F’s are G” in which F is more natural than G. (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)

Think of confirmation in the context of the Ravens Paradox this way. The likelihood ratio measure of incremental confirmation gives us, for an observed Black Raven and for an observed non-Black non-Raven, respectively, the following “full” likelihood ratios.

The paradox is that a natural idea of what counts as confirmation implies that a green leaf confirms the hypothesis that all ravens are black. The following brief paper explains this paradox, proposes a resolution in terms of relative frequency, and suggests that this shows a link between confirmation and falsification.

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. (shrink)

Philosophers such as Goodman, Scheffler and Glymour aim to answer the Paradox of the Ravens by distinguishing between confirmation simpliciter and selective confirmation. In the latter concept, the evidence both supports a hypothesis and undermines one of its "rivals". In this article, I argue that while selective confirmation does seem to be an important scientific notion, no attempt to formalise it thus far has managed to solve the Paradox of the Ravens.

According to Hempel’s raven paradox, the observation of one non-black non-raven confirms the hypothesis that all ravens are black. Bayesians such as Howson and Urbach (Scientific reasoning: the Bayesian approach, 2nd edn. Open Court, Chicago, 1993 ) claim that the raven paradox can be solved by spelling out the concept of confirmation in the sense of the relevance criterion. Siebel (J Gen Philos Sci 35:313–329, 2004 ) disputes the adequacy of this Bayesian solution. He claims that spelling (...) out the concept of confirmation in the relevance sense lets the raven paradox reappear as soon as numerous non-black non-ravens are observed. It is shown in this paper that Siebel’s objection to the Bayesian solution is flawed. Nevertheless, the objection made by Siebel may give us an idea of how Bayesians can successfully handle situations in which we observe more than one non-black non-raven. (shrink)

This chapter advances a contextual view of evidence, through a reconsideration of Hempel's paradox of confirmation. The initial view regarding Hempel's paradox is that a non-black non-raven does confirm ‘All ravens are black’, but only in certain contexts. The chapter begins by reformulating the paradox as a puzzle about how the same entity can have variable evidential values for a given proposition. It then offers a three-stage solution to the reformulated paradox. The situation makes better (...) sense when we reach a deeper propositional understanding of evidence, recognising that each entity can be represented in multiple observational propositions. Some anti-contextualist intuitions can be defused by distinguishing two different senses of the word ‘evidence’, one applying to objects or events and the other applying to propositions; only the latter is relevant to inference. A fuller understanding comes from analysing the constitution and use of evidence in terms of epistemic action. These reflections on the ravens paradox suggest a general philosophical framework more suitable for understanding the function of evidence in scientific and everyday practices. (shrink)

The paper takes a novel approach to a classic problem—Hempel’s Raven Paradox. A standard approach to it supposes the solution to consist in bringing our inductive logic into “reflective equilibrium” with our intuitive judgements about which inductive inferences we should license. This approach leaves the intuitions as a kind of black box and takes it on faith that, whatever the structure of the intuitions inside that box might be, it is one for which we can construct an isomorphic formal (...) edifice, a system of inductive logic. By popping open the box we can see whether that faith is misplaced. I aim, therefore, to characterize our pre-theoretical, intuitive understanding of generalizations like “ravens are black” and argue that, intuitively, we take them to mean, for instance: “ravens are black by some indeterminate yet characteristic means.” I motivate and explicate this formulation and bring it to bear on Hempel’s Problem. (shrink)

Paradox Lost covers ten of philosophy’s most fascinating paradoxes, in which seemingly compelling reasoning leads to absurd conclusions. The following paradoxes are included: The Liar Paradox, in which a sentence says of itself that it is false. Is the sentence true or false? The Sorites Paradox, in which we imagine removing grains of sand one at a time from a heap of sand. Is there a particular grain whose removal converts the heap to a non-heap? The Puzzle (...) of the Self-Torturer, in which a series of seemingly rational choices has us accepting a life of excruciating pain, in exchange for millions of dollars. Newcomb’s Problem, in which we seemingly maximize our expected profit by taking an unknown sum of money, rather than taking the same sum plus $1000. The Surprise Quiz Paradox, in which a professor finds that it is impossible to give a surprise quiz on any particular day of the week... but also that if this is so, then a surprise quiz can be given on any day. The Two Envelope Paradox, in which we are asked to choose between two indistinguishable envelopes, and it is seemingly shown that each envelope is preferable to the other. The Ravens Paradox, in which observing a purple shoe provides evidence that all ravens are black. The Shooting Room Paradox, in which a deadly game kills 90% of all who play, yet each individual’s survival turns on the flip of a fair coin. Each paradox is clearly described, common mistakes are explored, and a clear, logical solution offered. Paradox Lost will appeal to professional philosophers, students of philosophy, and all who love intellectual puzzles. (shrink)

This essential guide to paradoxes takes the reader on a lively tour of puzzles that have taxed thinkers from Zeno to Galileo and Lewis Carroll to Bertrand Russell. Michael Clark uncovers an array of conundrums, such as Achilles and the Tortoise, Theseus' Ship, Hempel's Raven, and the Prisoners' Dilemma, taking in subjects as diverse as knowledge, ethics, science, art and politics. Clark discusses each paradox in non-technical terms, considering its significance and looking at likely solutions.

The paper provides a formal proof that efficient estimates of parameters, which vary as as little as possible when measurements are repeated, may be expected to provide more accurate predictions. The definition of predictive accuracy is motivated by the work of Akaike (1973). Surprisingly, the same explanation provides a novel solution for a well known problem for standard theories of scientific confirmation — the Ravens Paradox. This is significant in light of the fact that standard Bayesian analyses of (...) the paradox fail to account for the predictive utility of universal laws like All ravens are black. (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)

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)

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)

The paper presents the logical milieu of the Paradox of ravens, identified by Hempel in his Studies in the Logic of Confirmation. It deals with Hempel’s interpretations of Nicod’s criterion of confirmation as well as with its inadmissible consequences. I, subsequently, suggest an epistemological and semantic specification of empirical properties, i.e., of their identity; then I formulate a criterion of the test of properties expressed by empirical hypothesis. Finally, I propose a procedural conception of confirmation by means of (...) the testing procedure schema. The confirmation is, therefore, conceived as an attribute which can be ascribed to a hypothesis through the process of its testing. The methods of testing are central to the hypothesis’s qualifica-tion as confirmed. (shrink)

Abstract W. E. Johnson argued that by taking into account both the epistemic and constitutive conditions for using arguments in inferences one could dissolve the paradoxes of material implication. This essay argues that the same sort of consideration can be used to dissolve the paradox of ravens in confirmation theory. It is argued in particular, and in agreement with certain points raised by the Popperians, that those instances of a generalization which are verifying but apparently not confirming cannot (...) raise the posterior of that generalization. (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)

Some believe reality is dynamic: time passes, not just in our experience of reality, but objectively, in reality itself. There are many objections to this view. I focus on the rate objection: that time passes only if it passes at the rate of 1 second per second, but that it cannot coherently pass at that rate. Existing replies to this objection do not fully engage with its motivation. My aim is to refute the rate objection. Time can coherently pass at (...) the rate of 1 second per second. This does not conclusively show that time passes, but it removes one of the main obstacles to believing that it does. (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)

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.

This essay focuses on a recently prominent notion of ground which is distinctive for how it links metaphysics to explanation. Ground is supposed to serve both as the common factor in diverse in virtue of questions as well as the structuring relation in the project of explaining how some phenomena are “built” from more fundamental phenomena. My aim is to provide an opinionated synopsis of this notion of ground without engaging with others. Ground, so understood, generally resists illumination by appeal (...) to more familiar models of explanation. Nevertheless, its distinctive explanatory and metaphysical aspects guide us on characterizing its explanatory logic and its metaphysical features. Some issues concerning the meta-question of what grounds ground are explored, as well as some recent skeptical challenges to ground. (shrink)

By modifying the body in meaningful ways, human beings establish their identity and social status. Lip plugs, ear plugs, penis sheaths, cosmetics, ornaments, scarification, body piercings, and genital modifications encode and transmit messages about age, sex, social status, health, and attractiveness from one individual to another. Through sociocultural sexual selection, male genital modification plays an important role as a sociosexual signal in both male competition and female mate choice. The reliability of the signal correlates with the cost of acquiring the (...) trait. Women use a variety of cues to assess male quality. Male genital modification is one way that some women assess their mates. Extreme male genital modifications not only honestly advertise status, sexual potency, and ability to provide sexual satisfaction, they may provide a reliable index of male-female cooperation through the male’s commitment to endure pain and risk. (shrink)

I defend (metaphysical) ground against recent, unanswered objections aiming to dismiss it from serious philosophical inquiry. Interest in ground stems from its role in the venerable metaphysical project of identifying which facts hold in virtue of others. Recent work on ground focuses on regimenting it. But many reject ground itself, seeing regimentation as yet another misguided attempt to regiment a bad idea (like phlogiston or astrology). I defend ground directly against objections that it is confused, incoherent, or fruitless. This vindicates (...) the very attempt to regiment ground. It also refocuses our attention on the genuine open questions about ground and away from the distracting, unpersuasive reasons for dismissing them. (shrink)