In this influential study of central issues in the philosophy of science, Paul Horwich elaborates on an important conception of probability, diagnosing the failure of previous attempts to resolve these issues as stemming from a too-rigid conception of belief. Adopting a Bayesian strategy, he argues for a probabilistic approach, yielding a more complete understanding of the characteristics of scientific reasoning and methodology. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Colin Howson, illuminating its (...) enduring importance and relevance to philosophical enquiry, this engaging work has been revived for a new generation of readers. (shrink)

Probabilistic methods are providing new explanatory approaches to fundamental cognitive science questions of how humans structure, process and acquire language. This review examines probabilistic models defined over traditional symbolic structures. Language comprehension and production involve probabilistic inference in such models; and acquisition involves choosing the best model, given innate constraints and linguistic and other input. Probabilistic models can account for the learning and processing of language, while maintaining the sophistication of symbolic models. A recent burgeoning of theoretical developments and online (...) corpus creation has enabled large models to be tested, revealing probabilistic constraints in processing, undermining acquisition arguments based on a perceived poverty of the stimulus, and suggesting fruitful links with probabilistic theories of categorization and ambiguity resolution in perception. (shrink)

We show that as a chain of confirmation becomes longer, confirmation dwindles under screening-off. For example, if E confirms H1, H1 confirms H2, and H1 screens off E from H2, then the degree to which E confirms H2 is less than the degree to which E confirms H1. Although there are many measures of confirmation, our result holds on any measure that satisfies the Weak Law of Likelihood. We apply our result to testimony cases, relate it to the Data-Processing Inequality (...) in information theory, and extend it in two respects so that it covers a broader range of cases. (shrink)

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use of optimality assumptions. Through (...) these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

A familiar adage in the philosophy of science is that general hypotheses are better supported by varied evidence than by uniform evidence. Several studies suggest that young children do not respect this principle, and thus suffer from a defect in their inductive methodology. We argue that the diversity principle does not have the normative status that psychologists attribute to it, and should be replaced by a simple rule of probability. We then report experiments designed to detect conformity to the latter (...) rule in children's inductive judgment. The results suggest that young children in both the United States and Taiwan are sensitive to the constraints imposed by the rule on judgments of probability and evidential strength. We conclude with a suggested reinterpretation of the thesis that children's inductive methodology qualifies them as “little scientists.”. (shrink)

If Bayesian Fundamentalism existed, Jones & Love's (J&L's) arguments would provide a necessary corrective. But it does not. Bayesian cognitive science is deeply concerned with characterizing algorithms and representations, and, ultimately, implementations in neural circuits; it pays close attention to environmental structure and the constraints of behavioral data, when available; and it rigorously compares multiple models, both within and across papers. J&L's recommendation of Bayesian Enlightenment corresponds to past, present, and, we hope, future practice in Bayesian cognitive science.

Probability ratio and likelihood ratio measures of inductive support and related notions have appeared as theoretical tools for probabilistic approaches in the philosophy of science, the psychology of reasoning, and artificial intelligence. In an effort of conceptual clarification, several authors have pursued axiomatic foundations for these two families of measures. Such results have been criticized, however, as relying on unduly demanding or poorly motivated mathematical assumptions. We provide two novel theorems showing that probability ratio and likelihood ratio measures can be (...) axiomatized in a way that overcomes these difficulties. (shrink)

Are people rational? This question was central to Greek thought and has been at the heart of psychology and philosophy for millennia. This book provides a radical and controversial reappraisal of conventional wisdom in the psychology of reasoning, proposing that the Western conception of the mind as a logical system is flawed at the very outset. It argues that cognition should be understood in terms of probability theory, the calculus of uncertain reasoning, rather than in terms of logic, the calculus (...) of certain reasoning. (shrink)

We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem recapitulates insights achieved by other investigators, and clarifi es the connection of coherence and proper scoring rules to Bregman divergence.

Crupi et al. (Think Reason 14:182–199, 2008) have recently advocated and partially worked out an account of the conjunction fallacy phenomenon based on the Bayesian notion of confirmation. In response, Schupbach (2009) presented a critical discussion as following from some novel experimental results. After providing a brief restatement and clarification of the meaning and scope of our original proposal, we will outline Schupbach’s results and discuss his interpretation thereof arguing that they do not actually undermine our point of view if (...) properly construed. Finally, we will foster such a claim by means of some novel data. (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 prequel, 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 the prequel, we made this norm mathematically precise; in this paper, we derive its consequences. We show that the two core tenets of Bayesianism (...) follow from the norm, while the characteristic claim of the Objectivist Bayesian follows from the norm along with an extra assumption. Finally, we consider Richard Jeffrey’s proposed generalization of conditionalization. We show not only that his rule cannot be derived from the norm, unless the requirement of Rigidity is imposed from the start, but further that the norm reveals it to be illegitimate. We end by deriving an alternative updating rule for those cases in which Jeffrey’s is usually supposed to apply. (shrink)

APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...) (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

In a seminal work, Tversky and Kahneman showed that in some contexts people tend to believe that a conjunction of events (e.g., Linda is a bank teller and is active in the feminist movement) is more likely to occur than one of the conjuncts (e.g., Linda is a bank teller). This belief violates the conjunction rule in probability theory. Tversky and Kahneman called this phenomenon the “conjunction fallacy”. Since the discovery of the phenomenon in 1983, researchers in psychology and philosophy (...) have engaged in important controversies around the conjunction fallacy. The goal of this paper is to explore the most important of these controversies, namely, the controversy about the nature of the conjunction fallacy. Is the conjunction fallacy mainly due to a misunderstanding of the problem by participants (misunderstanding hypothesis) or is it mainly due to a genuine reasoning bias (reasoning bias hypothesis)? A substantial portion of research on the topic has been directed to test the misunderstanding hypothesis. I review this literature and argue that a stronger case can be made against the misunderstanding hypothesis. Thus, I indirectly provide support for the reasoning bias hypothesis. (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)

Plausibly, when we adopt a probabilistic standpoint any measure Cb of the degree to which evidence e confirms hypothesis h relative to background knowledge b should meet these five desiderata: Cb > 0 when P > P < 0 when P < P; Cb = 0 when P = P. Cb is some function of the values P and P assume on the at most sixteen truth-functional combinations of e and h. If P < P and P = P then (...) Cb ≤ Cb; if P = P and P < P then Cb ≥ Cb. Cb – Cb is fully determined by Cb and Cbe – Cbe; if Cb = 0 then Cb + Cbe = 0. If P = P then Cb = Cb. (shrink)

We wish to give a precise formulation of the intuitive concept: The degree to which the known facts support a given hypothesis.

Epistemologists and philosophers of science have often attempted to express formally the impact of a piece of evidence on the credibility of a hypothesis. In this paper we will focus on the Bayesian approach to evidential support. We will propose a new formal treatment of the notion of degree of confirmation and we will argue that it overcomes some limitations of the currently available approaches on two grounds: (i) a theoretical analysis of the confirmation relation seen as an extension of (...) logical deduction and (ii) an empirical comparison of competing measures in an experimental inquiry concerning inductive reasoning in a probabilistic setting. (shrink)

The thirty-five chapters in this book describe various judgmental heuristics and the biases they produce, not only in laboratory experiments but in important...

It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X‐and‐Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners' interpretation of the expressions “probability” and “and.” We report two experiments designed to clarify the normative status of typical responses to conjunction problems.

Fitelson (1999) demonstrates that the validity of various arguments within Bayesian confirmation theory depends on which confirmation measure is adopted. The present paper adds to the results set out in Fitelson (1999), expanding on them in two principal respects. First, it considers more confirmation measures. Second, it shows that there are important arguments within Bayesian confirmation theory and that there is no confirmation measure that renders them all valid. Finally, the paper reviews the ramifications that this "strengthened problem of measure (...) sensitivity" has for Bayesian confirmation theory and discusses whether it points at pluralism about notions of confirmation. (shrink)

Confirmation of a hypothesis by evidence can be measured by one of the so far known incremental measures of confirmation. As we show, incremental measures can be formally defined as the measures of confirmation satisfying a certain small set of basic conditions. Moreover, several kinds of incremental measure may be characterized on the basis of appropriate structural properties. In particular, we focus on the so-called Matthew properties: we introduce a family of six Matthew properties including the reverse Matthew effect; we (...) further prove that incremental measures endowed with reverse Matthew effect are possible; finally, we shortly consider the problem of the plausibility of Matthew properties. (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)

It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X-and-Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners’ interpretation of the expressions “probability” and “and.” We report two experiments designed to clarify the normative status of typical responses to conjunction problems. © 2004 Cognitive Science Society, Inc. All rights reserved.

Several forms of symmetry in degrees of evidential support areconsidered. Some of these symmetries are shown not to hold in general. This has implications for the adequacy of many measures of degree ofevidential support that have been proposed and defended in the philosophical literature.