As many philosophers agree, the frame problem is concerned with how an agent may efficiently filter out irrelevant information in the process of problem-solving. Hence, how to solve this problem hinges on how to properly handle semantic relevance in cognitive modeling, which is an area of cognitive science that deals with simulating human's cognitive processes in a computerized model. By "semantic relevance", we mean certain inferential relations among acquired beliefs which may facilitate information retrieval and practical reasoning under certain epistemic (...) constraints, e. g., the insufficiency of knowledge, the limitation of time budget, etc. However, traditional approaches to relevance—as for example, relevance logic, the Bayesian approach, as well as Description Logic—have failed to do justice to the foregoing constraints, and in this sense, they are not proper tools for solving the frame problem/relevance problem. As we will argue in this paper, Non-Axiomatic Reasoning System (NARS) can handle the frame problem in a more proper manner, because the resulting solution seriously takes epistemic constraints on cognition as a fundamental theoretical principle. (shrink)

Hypothetico-deductive (H-D) confirmation builds on the idea that confirming evidence consists of successful predictions that deductively follow from the hypothesis under test. This article reviews scope, history and recent development of the venerable H-D account: First, we motivate the approach and clarify its relationship to Bayesian confirmation theory. Second, we explain and discuss the tacking paradoxes which exploit the fact that H-D confirmation gives no account of evidential relevance. Third, we review several recent proposals that aim at a sounder and (...) more comprehensive formulation of H-D confirmation. Finally, we conclude that the reputation of hypothetico-deductive confirmation as outdated and hopeless is undeserved: not only can the technical problems be addressed satisfactorily, the hypothetico-deductive method is also highly relevant for scientific practice. (shrink)

The paper argues that knowledge is not closed under logical inference. The argument proceeds from the openness of evidential support and the dependence of empirical knowledge on evidence, to the conclusion that knowledge is open. Without attempting to provide a full-fledged theory of evidence, we show that on the modest assumption that evidence cannot support both a proposition and its negation, or, alternatively, that information that reduces the probability of a proposition cannot constitute evidence for its truth, the relation of (...) evidential support is not closed under known entailment. Therefore the evidence-for relation is deductively open regardless of whether evidence is probabilistic or not. Given even a weak dependence of empirical knowledge on evidence, we argue that empirical knowledge is also open. On this basis, we also respond to the strongest argument in support of knowledge closure. Finally, we present a number of significant benefits of our position, namely, offering a unified explanation for a range of epistemological puzzles. (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)

In the first chapter of his book Logical Foundations of Probability, Rudolf Carnap introduced and endorsed a philosophical methodology which he called the method of ‘explication’. P.F. Strawson took issue with this methodology, but it is currently undergoing a revival. In a series of articles, Patrick Maher has recently argued that explication is an appropriate method for ‘formal epistemology’, has defended it against Strawson’s objection, and has himself put it to work in the philosophy of science in further clarification of (...) the very concepts on which Carnap originally used it (degree of confirmation, and probability), as well as some concepts to which Carnap did not apply it (such as justified degree of belief). We shall outline Carnap’s original idea, plus Maher’s recent application of such a methodology, and then seek to show that the problem Strawson raised for it has not been dealt with. The method is indeed, we argue, problematic and therefore not obviously superior to the ‘descriptive’ method associated with Strawson. Our targets will not only be Carnapians, though, for what we shall say also bears negatively on a project that Paul Horwich has pursued under the name ‘therapeutic’, or ‘Wittgensteinian’ Bayesianism. Finally, explication, as we shall suggest and as Carnap recognised, is not the only route to philosophical enlightenment. (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)

This research article revisits Hempel’s logic of confirmation in light of recent developments in categorical proof theory. While Hempel advocated several logical conditions in favor of a purely syntactical definition of a general non-quantitative concept of confirmation, we show how these criteria can be associated to specific logical properties of monoidal modal deductive systems. In addition, we show that many problems in confirmation logic, such as the tacked disjunction, the problem of weakening with background knowledge and the problem of irrelevant (...) conjunction, are also associated with specific logical properties and, incidentally, with some of Hempel’s logical conditions of adequacy. We discuss the raven paradox together with further objections against Hempel’s approach, showing how our analysis enables a clear understanding of the relationships between Hempel’s conditions, the problems in confirmation logic, and the properties of deductive systems. (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, reexamining the (WT) with these historico-philosophical insights in mind.

First, a brief historical trace of the developments in confirmation theory leading up to Goodman's infamous "grue" paradox is presented. Then, Goodman's argument is analyzed from both Hempelian and Bayesian perspectives. A guiding analogy is drawn between certain arguments against classical deductive logic, and Goodman's "grue" argument against classical inductive logic. The upshot of this analogy is that the "New Riddle" is not as vexing as many commentators have claimed. Specifically, the analogy reveals an intimate connection between Goodman's problem, and (...) the "problem of old evidence". Several other novel aspects of Goodman's argument are also discussed. (shrink)

In the first paper, I discussed the basic claims of Bayesianism (that degrees of belief are important, that they obey the axioms of probability theory, and that they are rationally updated by either standard or Jeffrey conditionalization) and the arguments that are often used to support them. In this paper, I will discuss some applications these ideas have had in confirmation theory, epistemol- ogy, and statistics, and criticisms of these applications.

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)

Historically, Nelson Goodman’s paradox involving the predicates ‘grue’ and ‘bleen’ has been taken to furnish a serious blow to Carl Hempel’s theory of confirmation in particular and to purely formal theories of confirmation in general. In this paper, I argue that Goodman’s paradox is no more serious of a threat to Hempel’s theory of confirmation than is Hempel’s own paradox of the ravens. I proceed by developing a suggestion from R. D. Rosenkrantz into an argument for the conclusion that these (...) paradoxes are, in fact, equivalent. My argument, if successful, is of both historical and philosophical interest. Goodman himself maintained that Hempel’s theory of confirmation was capable of handling the paradox of the ravens. And Hempel eventually conceded that Goodman’s paradox showed that there could be no adequate, purely syntactical theory of confirmation. The conclusion of my argument entails, by contrast, that Hempel’s theory of confirmation is incapable of handling Goodman’s paradox if and only if it is incapable of handling the paradox of the ravens. It also entails that for any adequate solution to one of these paradoxes, there is a corresponding and equally adequate solution to the other. (shrink)

We use recently developed approaches in argumentation theory in order to revamp the hypothetico-deductive model of confirmation, thus alleviating the well-known paradoxes the H-D account faces. More specifically, we introduce the concept of dialectic confirmation on the background of the so-called theory of dialectical structures (Betz 2010, 2012b). Dialectic confirmation generalises hypothetico-deductive confirmation and mitigates the raven paradox, the grue paradox, the tacking paradox, the paradox from conceptual difference, and the problem of surprising evidence.

Rudolf Carnap introduced and endorsed a philosophical methodology which he called the method of ‘explication’. P.F. Strawson took issue with this methodology, but it is currently undergoing a revival. In a series of articles, Patrick Maher has recently argued that explication is an appropriate method for ‘formal epistemology’, has defended it against Strawson’s objection, and has himself put it to work in the philosophy of science in further clarification of the very concepts on which Carnap originally used it (degree of (...) confirmation, and probability), as well as some concepts to which Carnap did not apply it (such as justified degree of belief. We outline Carnap’s original idea, plus Maher’s recent application of such a methodology, and then seek to show that the problem Strawson raised for it has not been dealt with. The method is indeed, we argue, problematic and therefore not obviously superior to the ‘descriptive’ method associated with Strawson. (shrink)

Handbook of the History of Logic, vol. 10, eds. Dov Gabbay, Stephan Hartmann, and John Woods, forthcoming.