M. Oaksford and N. Chater presented a Bayesian analysis of the Wason selection task in which they proposed that people choose cards in order to maximize expected information gain as measured by reduction in uncertainty in the Shannon-Weaver information theory sense. It is argued that the EIG measure is both psychologically implausible and normatively inadequate as a measure of epistemic utility. The article is also concerned with the descriptive account of findings in the selection task literature offered by Oaksford and (...) Chater. First, it is shown that their analysis data reported in the recent article of K. N. Kirby is unsound; second, an EIG analysis is presented of the experiments of P. Pollard and J. St. B. T. Evans that provides a strong empirical disconfirmation of the theory. (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)

I show how scoring rules, interpreted as measuring the inaccuracy of a set of degrees of belief, may be exploited to construct confirmation measures as used in Bayesian confirmation theory. I construct two confirmation measures from two particular standard scoring rules. One of these measures is genuinely new, the second is trivially ordinally equivalent to the difference measure. These two measures are tested against three well-known measures of confirmation in a simple but illuminating case that contains in a natural way (...) the problem of irrelevant conjunction. The genuinely new measure emerges, arguably, as the best. (shrink)

I explore the prospects for modelling epistemic rationality (in the probabilist setting) via an epistemic decision theory, in a consequentialist spirit. Previous work has focused on cases in which the truth-values of the propositions in which the agent is selecting credences do not depend, either causally or merely evidentially, on the agent’s choice of credences. Relaxing that restriction leads to a proliferation of puzzle cases and theories to deal with them, including epistemic analogues of evidential and causal decision theory, and (...) of the Newcomb Problem and ‘Psychopath Button’ Problem. A variant of causal epistemic decision theory deals well with most cases. However, there is a recalcitrant class of problem cases for which no epistemic decision theory seems able to match our intuitive judgements of epistemic rationality. This lends both precision and credence to the view that there is a fundamental mismatch between epistemic consequentialism and the intuitive notion of epistemic rationality; the implications for understanding the latter are briefly discussed. (shrink)

Beliefs come in different strengths. An agent's credence in a proposition is a measure of the strength of her belief in that proposition. Various norms for credences have been proposed. Traditionally, philosophers have tried to argue for these norms by showing that any agent who violates them will be lead by her credences to make bad decisions. In this article, we survey a new strategy for justifying these norms. The strategy begins by identifying an epistemic utility function and a decision-theoretic (...) norm; we then show that the decision-theoretic norm applied to the epistemic utility function yields the norm for credences that we wish to justify. We survey results already obtained using this strategy, and we suggest directions for future research. (shrink)

We propose a critique of normativism, defined as the idea that human thinking reflects a normative system against which it should be measured and judged. We analyze the methodological problems associated with normativism, proposing that it invites the controversial “is-ought” inference, much contested in the philosophical literature. This problem is triggered when there are competing normative accounts (the arbitration problem), as empirical evidence can help arbitrate between descriptive theories, but not between normative systems. Drawing on linguistics as a model, we (...) propose that a clear distinction between normative systems and competence theories is essential, arguing that equating them invites an “is-ought” inference: to wit, supporting normative “ought” theories with empirical “is” evidence. We analyze in detail two research programmes with normativist features – Oaksford and Chater’s rational analysis and Stanovich and West’s individual differences approach – demonstrating how, in each case, equating norm and competence leads to an is-ought inference. Normativism triggers a host of research biases in the psychology of reasoning and decision making: focusing on untrained participants and novel problems, analyzing psychological processes in terms of their normative correlates, and neglecting philosophically significant paradigms when they do not supply clear standards for normative judgement. For example, in a dual-process framework, normativism can lead to a fallacious “ought-is” inference, in which normative responses are taken as diagnostic of analytic reasoning. We propose that little can be gained from normativism that cannot be achieved by descriptivist computational-level analysis, illustrating our position with Hypothetical Thinking Theory and the theory of the suppositional conditional. We conclude that descriptivism is a viable option, and that theories of higher mental processing would be better off freed from normative considerations. (shrink)

One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its sequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In this paper, we make this norm mathematically precise in various ways. We describe three epistemic dilemmas that an agent might face if she attempts (...) to follow Accuracy, and we show that the only inaccuracy measures that do not give rise to such dilemmas are the quadratic inaccuracy measures. In the sequel, we derive the main tenets of Bayesianism from the relevant mathematical versions of Accuracy to which this characterization of the legitimate inaccuracy measures gives rise, but we also show that Jeffrey conditionalization has to be replaced by a different method of update in order for Accuracy to be satisfied. (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)

Oaksford and Chater (1994) proposed to analyse the Wason selection task as an inductive instead of a deductive task. Applying Bayesian statistics, they concluded that the cards that participants tend to select are those with the highest expected information gain. Therefore, their choices seem rational from the perspective of optimal data selection. We tested a central prediction from the theory in three experiments: card selection frequencies should be sensitive to the subjective probability of occurrence for individual cards. In Experiment 1, (...) expected frequencies of the p- and the q-card were manipulated independently by concepts referring to large vs. small sets. Although the manipulation had an effect on card selection frequencies, there was only a weak correlation between the predicted and the observed patterns. In the second experiment, relative frequencies of individual cards were manipulated more directly by explicit frequency information. In addition, participants estimated probabilities for the four logical cases and of the conditional statement itself. The experimental manipulations strongly affected the probability estimates, but were completely unrelated to card selections. This result was replicated in a third experiment. We conclude that our data provide little support for optimal data selection theory. (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.

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)

The pragmatic character of the Dutch book argument makes it unsuitable as an "epistemic" justification for the fundamental probabilist dogma that rational partial beliefs must conform to the axioms of probability. To secure an appropriately epistemic justification for this conclusion, one must explain what it means for a system of partial beliefs to accurately represent the state of the world, and then show that partial beliefs that violate the laws of probability are invariably less accurate than they could be otherwise. (...) The first task can be accomplished once we realize that the accuracy of systems of partial beliefs can be measured on a gradational scale that satisfies a small set of formal constraints, each of which has a sound epistemic motivation. When accuracy is measured in this way it can be shown that any system of degrees of belief that violates the axioms of probability can be replaced by an alternative system that obeys the axioms and yet is more accurate in every possible world. Since epistemically rational agents must strive to hold accurate beliefs, this establishes conformity with the axioms of probability as a norm of epistemic rationality whatever its prudential merits or defects might be. (shrink)

Two different programmes are in the business of explicating accuracy—the truthlikeness programme and the epistemic utility programme. Both assume that truth is the goal of inquiry, and that among inquiries that fall short of realizing the goal some get closer to it than others. Truthlikeness theorists have been searching for an account of the accuracy of propositions. Epistemic utility theorists have been searching for an account of the accuracy of credal states. Both assume we can make cognitive progress in an (...) inquiry even while falling short of the target. I show that the prospects for combining these two programmes are bleak. A core accuracy principle, proximity, that is universally embraced within the truthlikeness programme turns out to be incompatible with a central principle within the epistemic utility programme, namely propriety. 1Truthlikeness and Epistemic Utility 2Inquiries 3Accuracy for Propositions 4Proximity 5Accuracy for Credal States 6Propriety 7Proximity for Credal States 8Extensionality 9Admissible Weightings 10Propriety Violates Proximity 11Possible Responses 11.1Retreat to convexity 11.2Reject boundedness 11.3Reject additivity 12The Upshot. (shrink)

A number of authors have recently put forward arguments pro or contra various rules for scoring probability estimates. In doing so, they have skipped over a potentially important consideration in making such assessments, to wit, that the hypotheses whose probabilities are estimated can approximate the truth to different degrees. Once this is recognized, it becomes apparent that the question of how to assess probability estimates depends heavily on context.

Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people's goal is to reduce uncertainty about possible states of the world. In cognitive science, psychology, and medical decision making, Shannon entropy is the most prominent and most widely used model to formalize probabilistic uncertainty and the (...) reduction thereof. However, a variety of alternative entropy metrics (Hartley, Quadratic, Tsallis, Rényi, and more) are popular in the social and the natural sciences, computer science, and philosophy of science. Particular entropy measures have been predominant in particular research areas, and it is often an open issue whether these divergences emerge from different theoretical and practical goals or are merely due to historical accident. Cutting across disciplinary boundaries, we show that several entropy and entropy reduction measures arise as special cases in a unified formalism, the Sharma–Mittal framework. Using mathematical results, computer simulations, and analyses of published behavioral data, we discuss four key questions: How do various entropy models relate to each other? What insights can be obtained by considering diverse entropy models within a unified framework? What is the psychological plausibility of different entropy models? What new questions and insights for research on human information acquisition follow? Our work provides several new pathways for theoretical and empirical research, reconciling apparently conflicting approaches and empirical findings within a comprehensive and unified information-theoretic formalism. (shrink)

This article proposes a new interpretation of mutual information. We examine three extant interpretations of MI by reduction in doubt, by reduction in uncertainty, and by divergence. We argue that the first two are inconsistent with the epistemic value of information assumed in many applications of MI: the greater is the amount of information we acquire, the better is our epistemic position, other things being equal. The third interpretation is consistent with EVI, but it is faced with the problem of (...) measure sensitivity and fails to justify the use of MI in giving definitive answers to questions of information. We propose a fourth interpretation of MI by reduction in expected inaccuracy, where inaccuracy is measured by a strictly proper monotonic scoring rule. It is shown that the answers to questions of information given by MI are definitive whenever this interpretation is appropriate, and that it is appropriate in a wide range of applications with epistemic implications. _1_ Introduction _2_ Formal Analyses of the Three Interpretations _2.1_ Reduction in doubt _2.2_ Reduction in uncertainty _2.3_ Divergence _3_ Inconsistency with Epistemic Value of Information _4_ Problem of Measure Sensitivity _5_ Reduction in Expected Inaccuracy _6_ Resolution of the Problem of Measure Sensitivity _6.1_ Alternative measures of inaccuracy _6.2_ Resolution by strict propriety _6.3_ Range of applications _7_ Global Scoring Rules _8_ Conclusion. (shrink)

It has been claimed that, in response to certain kinds of evidence, agents ought to adopt imprecise credences: doxastic states that are represented by sets of credence functions rather than single ones. In this paper I argue that, given some plausible constraints on accuracy measures, accuracy-centered epistemologists must reject the requirement to adopt imprecise credences. I then show that even the claim that imprecise credences are permitted is problematic for accuracy-centered epistemology. It follows that if imprecise credal states are permitted (...) or required in the cases that their defenders appeal to, then the requirements of rationality can outstrip what would be warranted by an interest in accuracy. (shrink)

Measures of epistemic utility are used by formal epistemologists to make determinations of epistemic betterness among cognitive states. The Brier rule is the most popular choice among formal epistemologists for such a measure. In this paper, however, we show that the Brier rule is sometimes seriously wrong about whether one cognitive state is epistemically better than another. In particular, there are cases where an agent gets evidence that definitively eliminates a false hypothesis, but where the Brier rule says that things (...) have become epistemically worse. Along the way to this ‘elimination experiment’ counter-example to the Brier rule as a measure of epistemic utility, we identify several useful monotonicity principles for epistemic betterness. We also reply to several potential objections to this counter-example. (shrink)

The current state of inductive logic is puzzling. Survey presentations are recurrently offered and a very rich and extensive handbook was entirely dedicated to the topic just a few years ago [23]. Among the contributions to this very volume, however, one finds forceful arguments to the effect that inductive logic is not needed and that the belief in its existence is itself a misguided illusion , while other distinguished observers have eventually come to see at least the label as “slightly (...) antiquated” .What seems not to have lost any of its currency is the problem which inductive logic is meant to address. Inference from limited ascertained information to uncertain hypotheses is ubiquitous in learning, prediction and discovery. The logical insight that such kind of inference is fallible m .. (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.

The adverse reaction to Hempel's 'ravens paradox' embodied in giving it that description is compared with the usual reaction of experimental subjects to the Wason selection task.

How should rational believers pursue the aim of truth? Epistemic utility theorists have argued that by combining the tools of decision theory with an epistemic form of value—gradational accuracy, proximity to the truth—we can justify various epistemological norms. I argue that deriving these results requires using decision rules that are different in important respects from those used in standard (practical) decision theory. If we use the more familiar decision rules, we can’t justify the epistemic coherence norms that epistemic utility theory (...) had hoped to justify. In short, those of us who are attracted to the project of epistemic utility theory face a dilemma. If we choose “consequentialist” rules, then we can vindicate the idea that rational belief has the aim of accuracy—but at the cost of giving up attractive epistemic norms. (shrink)

We propose a critique ofnormativism, defined as the idea that human thinking reflects a normative system against which it should be measured and judged. We analyze the methodological problems associated with normativism, proposing that it invites the controversial “is-ought” inference, much contested in the philosophical literature. This problem is triggered when there are competing normative accounts (the arbitration problem), as empirical evidence can help arbitrate between descriptive theories, but not between normative systems. Drawing on linguistics as a model, we propose (...) that a clear distinction between normative systems and competence theories is essential, arguing that equating them invites an “is-ought” inference: to wit, supporting normative “ought” theories with empirical “is” evidence. We analyze in detail two research programmes with normativist features – Oaksford and Chater's rational analysis and Stanovich and West's individual differences approach – demonstrating how, in each case, equating norm and competence leads to an is-ought inference. Normativism triggers a host of research biases in the psychology of reasoning and decision making: focusing on untrained participants and novel problems, analyzing psychological processes in terms of their normative correlates, and neglecting philosophically significant paradigms when they do not supply clear standards for normative judgement. For example, in a dual-process framework, normativism can lead to a fallacious “ought-is” inference, in which normative responses are taken as diagnostic of analytic reasoning. We propose that little can be gained from normativism that cannot be achieved by descriptivist computational-level analysis, illustrating our position with Hypothetical Thinking Theory and the theory of the suppositional conditional. We conclude that descriptivism is a viable option, and that theories of higher mental processing would be better off freed from normative considerations. (shrink)

Considerations of accuracy – the epistemic good of having credences close to truth-values – have led to the justification of a host of epistemic norms. These arguments rely on specific ways of measuring accuracy. In particular, the accuracy measure should be strictly proper. However, the main argument for strict propriety supports only weak propriety. But strict propriety follows from weak propriety given strict truth directedness and additivity. So no further argument is necessary.

This paper proposes a new interpretation of mutual information (MI). We examine three extant interpretations of MI by reduction in doubt, by reduction in uncertainty, and by divergence. We argue that the first two are inconsistent with the epistemic value of information (EVI) assumed in many applications of MI: the greater is the amount of information we acquire, the better is our epistemic position, other things being equal. The third interpretation is consistent with EVI, but it is faced with the (...) problem of measure sensitivity and fails to justify the use of MI in giving definitive answers to questions of information. We propose a fourth interpretation of MI by reduction in expected inaccuracy, where inaccuracy is measured by a strictly proper monotonic scoring rule. It is shown that the answers to questions of information given by MI are definitive whenever this interpretation is appropriate, and that it is appropriate in a wide range of applications with epistemic implications. (shrink)

ABSTRACTSuppose that beliefs come in degrees. How should we then measure the accuracy of these degrees of belief? Scoring rules are usually thought to be the mathematical tool appropriate for this job. But there are many scoring rules, which lead to different ordinal accuracy rankings. Recently, Fallis and Lewis [2016] have given an argument that, if sound, rules out many popular scoring rules, including the Brier score, as genuine measures of accuracy. I respond to this argument, in part by noting (...) that the argument fails to account for verisimilitude—that certain false hypotheses might be closer to the truth than other false hypotheses are. Oddie [forthcoming], however, has argued that no member of a very wide class of scoring rules can appropriately handle verisimilitude. I explain how to respond to Oddie's argument, and I recommend a class of weighted scoring rules that, I argue, genuinely measure accuracy while escaping the arguments of Fallis and Lewis as well as Oddie. (shrink)

Are humans rational? Various experiments performed over the last several decades have been interpreted as showing that humans are irrational we make significant and consistent errors in logical reasoning, probabilistic reasoning, similarity judgements, and risk-assessment, to name a few areas. But can these experiments establish human irrationality, or is it a conceptual truth that humans must be rational, as various philosophers have argued? In this book, Edward Stein offers a clear critical account of this debate about rationality in philosophy and (...) cognitive science. He discusses concepts of rationality - the pictures of rationality that the debate centres on - and assesses the empirical evidence used to argue that humans are irrational. He concludes that the question of human rationality must be answered not conceptually but empirically, using the full resources of an advanced cognitive science. Furthermore, he extends this conclusion to argue that empirical considerations are also relevant to the theory of knowedge - in other words, that epistemology should be naturalized. from the reviews: 'Stein has done a great service in bringing together all of the important arguments in the human rationality debate and providing a measured critical assessment of them.... This will be an important book and is essential reading for epistemologists, philosophers of mind, and cognitive and evolutionary psychologists.' Choice 'very considerable value... for professionals' Times Higher Education Supplement. (shrink)

ABSTRACTThe judgment of blame was studied in a group of 28 teenagers, 14 with Asperger syndrome and 14 typically developed. Teenagers in each group were matched by age, cognitive development and academic level. They were presented with 12 short vignettes in which they had to judge an action according to the intent of the actor, the consequences of the action and the seriousness of the situation. Results showed a significant difference in the patterns of judgment of both groups. The AS (...) group judged the action according to the physical consequence of the action more than the intent of the actor; the opposite was observed with the control group. In addition, the AS teenagers were less capable than the control group of grading injury to a person when apportioning blame especially when they were not familiar with the social situations. This result suggests that the judgement of the seriousness of the outcome of the social interactio... (shrink)

Although I agree with Elqayam & Evans' (E&E's) criticisms of is-ought and ought-is fallacies, I criticize their rejection of normativism on two grounds: (1) Contrary to E&E's assumption, not every normative system of reasoning consists of formal rules. (2) E&E assume that norms of reasoning are grounded on intuition or authority, whereas in contemporary epistemology they have to be justified, primarily by their truth-conduciveness.