The old evidence problem affects any probabilistic confirmation measure based on comparing pr(H/E) and pr(H). The article argues for the following points: (1) measures based on likelihood ratios also suffer old evidence difficulties; (2) the less-discussed synchronic old evidence problem is, in an important sense, the most acute; (3) prominent attempts to solve or dissolve the synchronic problem fail; (4) a little-discussed variant of the standard measure avoids the problem, in an appealing way; and (5) this measure nevertheless reveals (...) a different problem for probabilistic confirmation measures, a problem that is unlikely to lend itself to formal solution. (shrink)

Confirmation and falsification are different strategies for testing theories and characterizing the outcomes of those tests. Roughly speaking, confirmation is the act of using evidence or reason to verify or certify that a statement is true, definite, or approximately true, whereas falsification is the act of classifying a statement as false in the light of observation reports. After expounding the intellectual history behind confirmation and falsificationism, reaching back to Plato and Aristotle, I survey some of the main (...) controversial issues and arguments that pertain to the choice between these strategies: the Raven Paradox, the Duhem/Quine problem and the Grue Paradox. Finally, I outline an evolutionary criticism of inductive Bayesian approaches based on my assumption of doxastic involuntarism. (shrink)

Alongside science and law, argumentation is also of central importance in everyday life. But what characterizes a good argument? This question has occupied philosophers and psychologists for centuries. The theory of Bayesian argumentation is particularly suitable for clarifying it, because it allows us to take into account in a natural way the role of uncertainty, which is central to much argumentation. Moreover, it offers the possibility of measuring the strength of an argument in probabilistic terms. One way to do this, (...) implicit in much work, is to identify the strength of an argument with the degree to which the premises of the argument confirm the conclusion. We criticize this prima facie plausible proposal and suggest instead that the strength of an argument has something to do with how much the premises and the conclusion of the argument cohere with each other. This leads to a new probabilistic measure whose properties we examine in more detail. (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)

Confirmation theory is intended to codify the evidential bearing of observations on hypotheses, characterizing relations of inductive “support” and “counter­support” in full generality. The central task is to understand what it means to say that datum E confirms or supports a hypothesis H when E does not logically entail H.

Two types of idealization in theory construction are distinguished, and the distinction is used to give a critique of Ron Laymon's account of confirming idealized theories and his argument for scientific realism.

We argue that a particular approach to satisfying the broad predictive ambitions of the sciences demands law confirmation. On this approach we confirm non-nomic generalizations by confirming there are no actually realized ways of causing disconfirming cases. This gives causal generalizations a crucial role in prediction. We then show how rational judgements of relevant causal similarity can be used to confirm that causal generalizations themselves have no actual disconfirmers, providing a distinctive and clearly viable methodology for inductively confirming them. (...) Finally, we argue that for agents in our epistemic position using this methodology to confirm causal generalizations of adequate breadth will commonly demand law confirmation. We make a prima facie assessment of the methodology’s fit with scientific practice and briefly consider the prospects for an associated analysis of laws. (shrink)

Confirmation theory is the study of the logic by which scientific hypotheses may be confirmed or disconfirmed, or even refuted by evidence. A specific theory of confirmation is a proposal for such a logic. Presumably the epistemic evaluation of scientific hypotheses should largely depend on their empirical content – on what they say the evidentially accessible parts of the world are like, and on the extent to which they turn out to be right about that. Thus, all theories (...) of confirmation rely on measures of how well various alternative hypotheses account for the evidence.1 Most contemporary confirmation theories employ probability functions to provide such a measure. They measure how well the evidence fits what the hypothesis says about the world in terms of how likely it is that the evidence should occur were the hypothesis true. Such hypothesis-based probabilities of evidence claims are called likelihoods. Clearly, when the evidence is more likely according to one hypothesis than according to an alternative, that should redound to the credit of the former hypothesis and the discredit of the later. But various theories of confirmation diverge on precisely how this credit is to be measured? (shrink)

It is well known that the probabilistic relation of confirmation is not transitive in that even if E confirms H1 and H1 confirms H2, E may not confirm H2. In this paper we distinguish four senses of confirmation and examine additional conditions under which confirmation in different senses becomes transitive. We conduct this examination both in the general case where H1 confirms H2 and in the special case where H1 also logically entails H2. Based on these analyses, (...) we argue that the Screening-Off Condition is the most important condition for transitivity in confirmation because of its generality and ease of application. We illustrate our point with the example of Moore’s “proof” of the existence of a material world, where H1 logically entails H2, the Screening-Off Condition holds, and confirmation in all four senses turns out to be transitive. (shrink)

Long before skeptical theism was called “skeptical theism,” Stephen Wykstra (1984) defended a version of it based on an epistemological principle he called CORNEA. In this paper, I use elementary confirmation theory to analyze CORNEA’s core. This enables me to show precisely what is right about Wykstra’s very influential defense of skeptical theism and, perhaps more importantly, precisely what is wrong with it. A key premise of that defense is that, on the assumption that God exists, we wouldn’t expect (...) to know what God’s reasons for allowing certain evils are. I show that, while that premise together with CORNEA’s core shows that our inability to adequately explain the existence of those evils in terms of theism is not strong evidence against theism, it fails to show that the evils themselves are not strong evidence against theism. (shrink)

The tendency to test outcomes that are predicted by our current theory (the confirmation bias) is one of the best-known biases of human decision making. We prove that the confirmation bias is an optimal strategy for testing hypotheses when those hypotheses are deterministic, each making a single prediction about the next event in a sequence. Our proof applies for two normative standards commonly used for evaluating hypothesis testing: maximizing expected information gain and maximizing the probability of falsifying the (...) current hypothesis. This analysis rests on two assumptions: (a) that people predict the next event in a sequence in a way that is consistent with Bayesian inference; and (b) when testing hypotheses, people test the hypothesis to which they assign highest posterior probability. We present four behavioral experiments that support these assumptions, showing that a simple Bayesian model can capture people's predictions about numerical sequences (Experiments 1 and 2), and that we can alter the hypotheses that people choose to test by manipulating the prior probability of those hypotheses (Experiments 3 and 4). (shrink)

Confirmation bias has been widely studied for its role in failures of reasoning. Individuals exhibiting confirmation bias fail to engage with information that contradicts their current beliefs, and, as a result, can fail to abandon inaccurate beliefs. But although most investigations of confirmation bias focus on individual learning, human knowledge is typically developed within a social structure. How does the presence of confirmation bias influence learning and the development of consensus within a group? In this paper, (...) we use network models to study this question. We find, perhaps surprisingly, that moderate confirmation bias often improves group learning. This is because confirmation bias leads the group to entertain a wider variety of theories for a longer time, and prevents them from prematurely settling on a suboptimal theory. There is a downside, however, which is that a stronger form of confirmation bias can cause persistent polarization, and hurt the knowledge producing capacity of the community. We discuss implications of these results for epistemic communities, including scientific ones. (shrink)

An experiment is reported which tests for positive confirmation bias in a setting in which individuals choose what information to buy, prior to making a decision. The design – an adaptation of Wason's selection task – reveals the use that subjects make of information after buying it. Strong evidence of positive confirmation bias, in both information acquisition and information use, is found; and this bias is found to be robust to experience. It is suggested that the bias results (...) from a pattern of reasoning which, although producing sub-optimal decisions, is internally coherent and which is self-reinforcing. (shrink)

We provide a novel Bayesian justification of inference to the best explanation. More specifically, we present conditions under which explanatory considerations can provide a significant confirmatory boost for hypotheses that provide the best explanation of the relevant evidence. Furthermore, we show that the proposed Bayesian model of IBE is able to deal naturally with the best known criticisms of IBE such as van Fraassen?s?bad lot? argument.

So far no known measure of confirmation of a hypothesis by evidence has satisfied a minimal requirement concerning thresholds of acceptance. In contrast, Shogenji’s new measure of justification (Shogenji, Synthese, this number 2009) does the trick. As we show, it is ordinally equivalent to the most general measure which satisfies this requirement. We further demonstrate that this general measure resolves the problem of the irrelevant conjunction. Finally, we spell out some implications of the general measure for the Conjunction Effect; (...) in particular we give an example in which the effect occurs in a larger domain, according to Shogenji justification, than Carnap’s measure of confirmation would have led one to expect. (shrink)

Confirmation in evolutionary biology depends on what biologists take to be the genuine rivals. Investigating what constrains the scope of biological possibility provides part of the story: explaining how possible helps determine what counts as a genuine rival and thus informs confirmation. To clarify the criteria for genuine rivalry I distinguish between global and local constraints on biological possibility, and offer an account of how-possibly explanation. To sharpen the connection between confirmation and explaining how possible I discuss (...) the view that formal inquiry can provide a kind of confirmation-theoretic support for evolutionary models, and offer an example of how-possibly explanation interacting with testing practice. (shrink)

Certain hypotheses cannot be directly confirmed for theoretical, practical, or moral reasons. For some of these hypotheses, however, there might be a workaround: confirmation based on analogical reasoning. In this paper we take up Dardashti, Hartmann, Thébault, and Winsberg’s (in press) idea of analyzing confirmation based on analogical inference Baysian style. We identify three types of confirmation by analogy and show that Dardashti et al.’s approach can cover two of them. We then highlight possible problems with their (...) model as a general approach to analogical inference and argue that these problems can be avoided by supplementing Bayesian update with Jeffrey conditionalization. (shrink)

It is well known that the probabilistic relation of confirmation is not transitive in that even if E confirms H1 and H1 confirms H2, E may not confirm H2. In this paper we distinguish four senses of confirmation and examine additional conditions under which confirmation in different senses becomes transitive. We conduct this examination both in the general case where H1 confirms H2 and in the special case where H1 also logically entails H2. Based on these analyses, (...) we argue that the Screening-Off Condition is the most important condition for transitivity in confirmation because of its generality and ease of application. We illustrate our point with the example of Moore’s ‘‘proof’’ of the existence of a material world, where H1 logically entails H2, the Screening-Off Condition holds, and confirmation in all four senses turns out to be transitive. (shrink)

There is a plethora of confirmation measures in the literature. Zalabardo considers four such measures: PD, PR, LD, and LR. He argues for LR and against each of PD, PR, and LD. First, he argues that PR is the better of the two probability measures. Next, he argues that LR is the better of the two likelihood measures. Finally, he argues that LR is superior to PR. I set aside LD and focus on the trio of PD, PR, and (...) LR. The question I address is whether Zalabardo succeeds in showing that LR is superior to each of PD and PR. I argue that the answer is negative. I also argue, though, that measures such as PD and PR, on one hand, and measures such as LR, on the other hand, are naturally understood as explications of distinct senses of confirmation. (shrink)

Confirmation in evolutionary biology depends on what biologists take to be the genuine rivals. Investigating what constrains the scope of biological possibility provides part of the story: explaining how possible helps determine what counts as a genuine rival and thus informs confirmation. To clarify the criteria for genuine rivalry I distinguish between global and local constraints on biological possibility, and offer an account of how-possibly explanation. To sharpen the connection between confirmation and explaining how possible I discuss (...) the view that formal inquiry can provide a kind of confirmation-theoretic support for evolutionary models, and offer an example of how-possibly explanation interacting with testing practice. (shrink)

Theo AF Kuipers THE THREEFOLD EVALUATION OF THEORIES A SYNOPSIS OF FROM INSTRUMENTALISM TO CONSTRUCTIVE REALISM. ON SOME RELATIONS BETWEEN CONFIRMATION, EMPIRICAL PROGRESS, AND TRUTH APPROXIMATION (2000) ABSTRACT.

In this article we argue for the existence of ‘analogue simulation’ as a novel form of scientific inference with the potential to be confirmatory. This notion is distinct from the modes of analogical reasoning detailed in the literature, and draws inspiration from fluid dynamical ‘dumb hole’ analogues to gravitational black holes. For that case, which is considered in detail, we defend the claim that the phenomena of gravitational Hawking radiation could be confirmed in the case that its counterpart is detected (...) within experiments conducted on diverse realizations of the analogue model. A prospectus is given for further potential cases of analogue simulation in contemporary science. 1 Introduction2 Physical Background2.1 Hawking radiation in semi-classical gravity2.2 Modelling sound in fluids2.3 The acoustic analogue model of Hawking radiation3 Simulation and Analogy in Physical Theory3.1 Analogical reasoning and analogue simulation3.2 Confirmation via analogue simulation3.3 Recapitulation4 The Sound of Silence: Analogical Insights into Gravity4.1 Experimental realization of analogue models4.2 Universality and the Hawking effect4.3 Confirmation of gravitational Hawking radiation5 Prospectus. (shrink)

The attempt to explicate the intuitive notions of confirmation and inductive support through use of the formal calculus of probability received its canonical formulation in Carnap's The Logical Foundations of Probability. It is a central part of modern Bayesianism as developed recently, for instance, by Paul Horwich and John Earman. Carnap places much emphasis on the identification of confirmation with the notion of probabilistic favorable relevance. Notoriously, the notion of confirmation as probabilistic favorable relevance violates the intuitive (...) transmittability condition that if e confirms h and h' is part of the content of h then e confirms h'. This suggests that, pace Carnap, it cannot capture our intuitive notions of confirmation and inductive support. Without transmittability confirmation losses much of its intrinsic interest. If e, say a report of past observations, can confirm h, say a law-like generalization, without that confirmation being transmitted to those parts of h dealing with the as yet unobserved, then it is not clear why we should be interested in whether h is confirmed or not. The following paper rehearses these difficulties and then proposes a new probabilistic account of confirmation that does not violate the transmittability condition. (shrink)

Scientific realism driven by inference to the best explanation (IBE) takes empirically confirmed objects to exist, independent, pace empiricism, of whether those objects are observable or not. This kind of realism, it has been claimed, does not need probabilistic reasoning to justify the claim that these objects exist. But I show that there are scientific contexts in which a non-probabilistic IBE-driven realism leads to a puzzle. Since IBE can be applied in scientific contexts in which empirical confirmation has not (...) yet been reached, realists will in these contexts be committed to the existence of empirically unconfirmed objects. As a consequence of such commitments, because they lack probabilistic features, the possible empirical confirmation of those objects is epistemically redundant with respect to realism. (shrink)

In this paper I distinguish various ways in which empirical claims about evolutionary and ecological models can be supported by data. I describe three basic factors bearing on confirmation of empirical claims: fit of the model to data; independent testing of various aspects of the model, and variety of evident. A brief description of the kinds of confirmation is followed by examples of each kind, drawn from a range of evolutionary and ecological theories. I conclude that the greater (...) complexity and precision of my approach, as compared to, for instance, a Popperian approach, can facilitate detailed analysis and comparison of empirical claims. (shrink)

In this chapter probability and confirmation theory are used to investigate the problem of evil, concentrating on whether a theist should consider our ignorance of a good reason for God to permit evil to support a non-religious alternative over a typical theist's beliefs. It is argued that according to Likelihoodism, our ignorance of a good reason does not favor a competing hypothesis over the religious view that there is an incomprehensible good reason for God to permit evil. Bayesian accounts (...) of comparative confirmation, which are alternatives to Likelihoodism, have the same result. Furthermore, according to both Likelihoodism and Bayesian accounts of contrastive confirmation, our ignorance of a good reason for God to permit evil may actually support typical religious beliefs over the alternative hypotheses. (shrink)

Like other epistemic activities, inquiry seems to be governed by norms. Some have argued that one such norm forbids us from believing the answer to a question and inquiring into it at the same time. But another, hither-to neglected norm seems to permit just this sort of cognitive arrangement when we seek to confirm what we currently believe. In this paper, I suggest that both norms are plausible and that the conflict between them constitutes a puzzle. Drawing on the felicity (...) conditions of confirmation requests and the biased interrogatives used to perform them, I argue that the puzzle is genuine. I conclude by considering a response to the puzzle that has implications for the debate regarding the relationship between credences and beliefs. (shrink)

I defend the prospect of good science in the social sciences by looking at the obstacles to social laws. I criticize traditional approaches, which rule for or against social laws on primarily conceptual grounds, and argue that only a close analysis of actual empirical research can decide the issue. To that end, I focus on problems caused by the ceteris paribus nature of social generalizations, outline a variety of ways those problems might be handled, and then examine in detail the (...) work of Paige on agrarian revolutions. Paige's work, I argue, handles its problems roughly as well as does some of the best work in evolutionary biology. The upshot is that some social laws can be relatively well confirmed. (shrink)

Robustness may increase the degree to which the robust result is indirectly confirmed if it is shown to depend on confirmed rather than disconfirmed assumptions. Although increasing the weight with which existing evidence indirectly confirms it in such a case, robustness may also be irrelevant for confirmation, or may even disconfirm. Whether or not it confirms depends on the available data and on what other results have already been established.

The aim of this paper is to apply inductive logic to the field that, presumably, Carnap never expected: legal causation. Legal causation is expressible in the form of singular causal statements; but it is distinguished from the customary concept of scientific causation, because it is subjective. We try to express this subjectivity within the system of inductive logic. Further, by semantic complement, we compensate a defect found in our application, to be concrete, the impossibility of two-place predicates (for causal relationship) (...) in inductive logic. (shrink)

The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. Despite extensive inquiry, however, the attempt to provide a satisfactory account of the phenomenon has proved challenging. Here we elaborate the suggestion (first discussed by Sides, Osherson, Bonini, & Viale, 2002) that in standard conjunction problems the fallacious probability judgements observed experimentally are typically guided by sound assessments of _confirmation_ relations, meant in terms of contemporary Bayesian confirmation theory. Our main (...) formal result is a confirmation-theoretic account of the conjunction fallacy, which is proven _robust_ (i.e., not depending on various alternative ways of measuring degrees of confirmation). The proposed analysis is shown distinct from contentions that the conjunction effect is in fact not a fallacy, and is compared with major competing explanations of the phenomenon, including earlier references to a confirmation-theoretic account. (shrink)

This brief annotated bibliography is intended to help students get started with their research. It is not a substitute for personal investigation of the literature, and it is not a comprehensive bibliography on the subject. For those just beginning to study probabilistic confirmation theory and Bayesian reasoning, I suggest the starred items as good places to start your reading.

Much contemporary epistemology is informed by a kind of confirmational holism, and a consequent rejection of the assumption that all confirmation rests on experiential certainties. Another prominent theme is that belief comes in degrees, and that rationality requires apportioning one's degrees of belief reasonably. Bayesian confirmation models based on Jeffrey Conditionalization attempt to bring together these two appealing strands. I argue, however, that these models cannot account for a certain aspect of confirmation that would be accounted for (...) in any adequate holistic confirmation theory. I then survey the prospects for constructing a formal epistemology that better accommodates holistic insights. (shrink)

According to Bayesian confirmation theory, evidence E (incrementally) confirms (or supports) a hypothesis H (roughly) just in case E and H are positively probabilistically correlated (under an appropriate probability function Pr). There are many logically equivalent ways of saying that E and H are correlated under Pr. Surprisingly, this leads to a plethora of non-equivalent quantitative measures of the degree to which E confirms H (under Pr). In fact, many non-equivalent Bayesian measures of the degree to which E confirms (...) (or supports) H have been proposed and defended in the literature on inductive logic. I provide a thorough historical survey of the various proposals, and a detailed discussion of the philosophical ramifications of the differences between them. I argue that the set of candidate measures can be narrowed drastically by just a few intuitive and simple desiderata. In the end, I provide some novel and compelling reasons to think that the correct measure of degree of evidential support (within a Bayesian framework) is the (log) likelihood ratio. The central analyses of this research have had some useful and interesting byproducts, including: (i ) a new Bayesian account of (confirmationally) independent evidence, which has applications to several important problems in con- firmation theory, including the problem of the (confirmational) value of evidential diversity, and (ii ) novel resolutions of several problems in Bayesian confirmation theory, motivated by the use of the (log) likelihood ratio measure, including a reply to the Popper-Miller critique of probabilistic induction, and a new analysis and resolution of the problem of irrelevant conjunction (a.k.a., the tacking problem). (shrink)

Any theory of confirmation must answer the following question: what is the purpose of its conception of confirmation for scientific inquiry? In this article, we argue that no Bayesian conception of confirmation can be used for its primary intended purpose, which we take to be making a claim about how worthy of belief various hypotheses are. Then we consider a different use to which Bayesian confirmation might be put, namely, determining the epistemic value of experimental outcomes, (...) and thus to decide which experiments to carry out. Interestingly, Bayesian confirmation theorists rule out that confirmation be used for this purpose. We conclude that Bayesian confirmation is a means with no end. 1 Introduction2 Bayesian Confirmation Theory3 Bayesian Confirmation and Belief4 Confirmation and the Value of Experiments5 Conclusion. (shrink)

This paper proposes a framework for representing in Bayesian terms the idea that analogical arguments of various degrees of strength may provide inductive support to yet untested scientific hypotheses. On this account, contextual information plays a crucial role in determining whether, and to what extent, a given similarity or dissimilarity between source and target may confirm an empirical hypothesis over a rival one. In addition to showing confirmation by analogy compatible with the adoption of a Bayesian standpoint, the proposal (...) outlined in this paper reveals a close agreement between the fulfillment of Hesse’s (Models and analogies in science, University of Notre Dame Press, 1963) criteria for analogical arguments capable of inductive support and the attribution of confirmatory power by the lights of Bayesian confirmation theory. In this sense, the Bayesian representation not only enriches a framework, Hesse’s, of enduring relevance for understanding scientific activity, but may offer something akin to a proof of concept of it. (shrink)

The extra value of novel confirmation over accommodation is explained based on an analysis of the underdetermination of scientific theory building. Novel confirmation can provide information on the number of possible scientific alternatives to a predictively successful theory. This information, in turn, can raise the probability that the given theory is true or will be empirically viable in the future.

Nelson Goodman suggests that a generalization of the form “all A’s are B” is confirmable by an observed instance only if the generalization is law-like. Jackson and Pargetter deny this and give examples of how accidental generalizations can be confirmed. A possible response from Goodman appears to make these accidental generalizations look law-like, but I show it’s defective. And Jackson and Pargetter's substitute nomological condition fares no better than Goodman’s. Because of the multiplicity of possible background assumptions, I doubt that (...) there is a single “nomological condition” that each and every act of confirmation must obey. (shrink)

As inductive logic and the philosophy of probability theory have become of wider interest, it has become clear that a book of readings in these and related topics would be useful for courses since most of the important articles are scattered and inaccessible. The editors have fashioned an extensive collection of papers in four main areas: the meaning of probability, confirmation theory, simplicity of theories and structures, the justification of induction. Each chapter is preceded by an introduction which sets (...) out the basic problems of the topic under consideration. There are thirty-six papers in all, two-thirds of them in the first and last chapters. The first chapter includes articles by Ramsey, Carnap, Nagel, and Reichenbach. The second chapter is dominated by the work of Hempel, Oppenheim, and Kemeny; the third chapter features a long article by D. J. Hillman which takes as its basis the work of Goodman, and there are other papers by Bunge, Quine, and Barker. The discussion of induction and its justification contains articles by Hume and Mill, but the bulk of the papers are contemporary. There is a bibliography for each chapter at the end of the book.—P. J. M. (shrink)

Existing accounts of hypothetico-deductive confirmation are able to circumvent the classical objections, but the confirmation of conjunctions of hypotheses brings them into trouble. Therefore this paper develops a new, falsificationist account of qualitative confirmation by means of Ken Gemes ' theory of content parts. The new approach combines the hypothetico-deductive view with falsificationist and instance confirmation principles. It is considerably simpler than the previous suggestions and gives a better treatment of conjunctive hypotheses while solving the tacking (...) problems equally well. (shrink)

This paper aims to show how Whewell's notions of consilience and unification-explicated in more modern probabilistic terms provide a satisfying treatment of cases of scientific discovery Which require the postulatioin component causes to explain complex events. The results of this analysis support the received view that the increased unification and generality of theories leads to greater testability, and confirmation if the observations are favorable. This solves a puzzle raised by Cartwright in How the Laws of Physics Lie about the (...) nature of explanation by the composition of causes. (shrink)

Various scientific theories stand in a reductive relation to each other. In a recent article, we have argued that a generalized version of the Nagel-Schaffner model (GNS) is the right account of this relation. In this article, we present a Bayesian analysis of how GNS impacts on confirmation. We formalize the relation between the reducing and the reduced theory before and after the reduction using Bayesian networks, and thereby show that, post-reduction, the two theories are confirmatory of each other. (...) We then ask when a purported reduction should be accepted on epistemic grounds. To do so, we compare the prior and posterior probabilities of the conjunction of both theories before and after the reduction and ask how well each is confirmed by the available evidence. (shrink)

Bayesian models of human learning are becoming increasingly popular in cognitive science. We argue that their purported confirmation largely relies on a methodology that depends on premises that are inconsistent with the claim that people are Bayesian about learning and inference. Bayesian models in cognitive science derive their appeal from their normative claim that the modeled inference is in some sense rational. Standard accounts of the rationality of Bayesian inference imply predictions that an agent selects the option that maximizes (...) the posterior expected utility. Experimental confirmation of the models, however, has been claimed because of groups of agents that probability match the posterior. Probability matching only constitutes support for the Bayesian claim if additional unobvious and untested (but testable) assumptions are invoked. The alternative strategy of weakening the underlying notion of rationality no longer distinguishes the Bayesian model uniquely. A new account of rationality—either for inference or for decision-making—is required to successfully confirm Bayesian models in cognitive science. (shrink)