A Bayesian mind is, at its core, a rational mind. Bayesianism is thus well-suited to predict and explain mental processes that best exemplify our ability to be rational. However, evidence from belief acquisition and change appears to show that we do not acquire and update information in a Bayesian way. Instead, the principles of belief acquisition and updating seem grounded in maintaining a psychological immune system rather than in approximating a Bayesian processor.

It is often claimed that the greatest value of the Bayesian framework in cognitive science consists in its unifying power. Several Bayesian cognitive scientists assume that unification is obviously linked to explanatory power. But this link is not obvious, as unification in science is a heterogeneous notion, which may have little to do with explanation. While a crucial feature of most adequate explanations in cognitive science is that they reveal aspects of the causal mechanism that produces the phenomenon to be (...) explained, the kind of unification afforded by the Bayesian framework to cognitive science does not necessarily reveal aspects of a mechanism. Bayesian unification, nonetheless, can place fruitful constraints on causal–mechanical explanation. 1 Introduction2 What a Great Many Phenomena Bayesian Decision Theory Can Model3 The Case of Information Integration4 How Do Bayesian Models Unify?5 Bayesian Unification: What Constraints Are There on Mechanistic Explanation?5.1 Unification constrains mechanism discovery5.2 Unification constrains the identification of relevant mechanistic factors5.3 Unification constrains confirmation of competitive mechanistic models6 ConclusionAppendix. (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)

Shepard has argued that a universal law should govern generalization across different domains of perception and cognition, as well as across organisms from different species or even different planets. Starting with some basic assumptions about natural kinds, he derived an exponential decay function as the form of the universal generalization gradient, which accords strikingly well with a wide range of empirical data. However, his original formulation applied only to the ideal case of generalization from a single encountered stimulus to a (...) single novel stimulus, and for stimuli that can be represented as points in a continuous metric psychological space. Here we recast Shepard's theory in a more general Bayesian framework and show how this naturally extends his approach to the more realistic situation of generalizing from multiple consequential stimuli with arbitrary representational structure. Our framework also subsumes a version of Tversky's set-theoretic model of similarity, which is conventionally thought of as the primary alternative to Shepard's continuous metric space model of similarity and generalization. This unification allows us not only to draw deep parallels between the set-theoretic and spatial approaches, but also to significantly advance the explanatory power of set-theoretic models. Key Words: additive clustering; Bayesian inference; categorization; concept learning; contrast model; features; generalization; psychological space; similarity. (shrink)

Remarkable progress in the mathematics and computer science of probability has led to a revolution in the scope of probabilistic models. In particular, ‘sophisticated’ probabilistic methods apply to structured relational systems such as graphs and grammars, of immediate relevance to the cognitive sciences. This Special Issue outlines progress in this rapidly developing field, which provides a potentially unifying perspective across a wide range of domains and levels of explanation. Here, we introduce the historical and conceptual foundations of the approach, explore (...) how the approach relates to studies of explicit probabilistic reasoning, and give a brief overview of the field as it stands today. (shrink)

Several philosophers and psychologists have characterized belief in conspiracy theories as a product of irrational reasoning. Proponents of conspiracy theories apparently resist revising their beliefs given disconfirming evidence and tend to believe in more than one conspiracy, even when the relevant beliefs are mutually inconsistent. In this paper, we bring leading views on conspiracy theoretic beliefs closer together by exploring their rationality under a probabilistic framework. We question the claim that the irrationality of conspiracy theoretic beliefs stems from an inadequate (...) response to disconfirming evidence and internal incoherence. Drawing analogies to Lakatosian research programs, we argue that maintaining a core conspiracy belief can be Bayes-rational when it is embedded in a network of auxiliary beliefs, which can be revised to protect the more central belief from disconfirmation. We propose that the (ir)rationality associated with conspiracy belief lies not in a flawed updating method, but in their failure to converge toward well-confirmed, stable belief networks in the long run. This approach not only reconciles previously disjointed views, but also points toward more specific hypotheses explaining why some agents may be prone to adopting beliefs in conspiracy theories. (shrink)

A theory of conceptual development must specify the innate representational primitives, must characterize the ways in which the initial state differs from the adult state, and must characterize the processes through which one is transformed into the other. The Origin of Concepts (henceforth TOOC) defends three theses. With respect to the initial state, the innate stock of primitives is not limited to sensory, perceptual, or sensorimotor representations; rather, there are also innate conceptual representations. With respect to developmental change, conceptual development (...) consists of episodes of qualitative change, resulting in systems of representation that are more powerful than, and sometimes incommensurable with, those from which they are built. With respect to a learning mechanism that achieves conceptual discontinuity, I offer Quinian bootstrapping. TOOC concludes with a discussion of how an understanding of conceptual development constrains a theory of concepts. (shrink)

This article proposes a new model of human concept learning that provides a rational analysis of learning feature‐based concepts. This model is built upon Bayesian inference for a grammatically structured hypothesis space—a concept language of logical rules. This article compares the model predictions to human generalization judgments in several well‐known category learning experiments, and finds good agreement for both average and individual participant generalizations. This article further investigates judgments for a broad set of 7‐feature concepts—a more natural setting in several (...) ways—and again finds that the model explains human performance. (shrink)

We derive a probabilistic account of the vagueness and context-sensitivity of scalar adjectives from a Bayesian approach to communication and interpretation. We describe an iterated-reasoning architecture for pragmatic interpretation and illustrate it with a simple scalar implicature example. We then show how to enrich the apparatus to handle pragmatic reasoning about the values of free variables, explore its predictions about the interpretation of scalar adjectives, and show how this model implements Edgington’s Vagueness: a reader, 1997) account of the sorites paradox, (...) with variations. The Bayesian approach has a number of explanatory virtues: in particular, it does not require any special-purpose machinery for handling vagueness, and it is integrated with a promising new approach to pragmatics and other areas of cognitive science. (shrink)

Symbols enable people to organize and communicate about the world. However, the ways in which symbolic knowledge is learned and then represented in the mind are poorly understood. We present a formal analysis of symbolic learning—in particular, word learning—in terms of prediction and cue competition, and we consider two possible ways in which symbols might be learned: by learning to predict a label from the features of objects and events in the world, and by learning to predict features from a (...) label. This analysis predicts significant differences in symbolic learning depending on the sequencing of objects and labels. We report a computational simulation and two human experiments that confirm these differences, revealing the existence of Feature-Label-Ordering effects in learning. Discrimination learning is facilitated when objects predict labels, but not when labels predict objects. Our results and analysis suggest that the semantic categories people use to understand and communicate about the world can only be learned if labels are predicted from objects. We discuss the implications of this for our understanding of the nature of language and symbolic thought, and in particular, for theories of reference. (shrink)

People draw subtle distinctions in the normative domain. But it remains unclear exactly what gives rise to such distinctions. On one prominent approach, emotion systems trigger non-utilitarian judgments. The main alternative, inspired by Chomskyan linguistics, suggests that moral distinctions derive from an innate moral grammar. In this article, we draw on Bayesian learning theory to develop a rational learning account. We argue that the ‘size principle’, which is implicated in word learning, can also explain how children would use scant and (...) equivocal evidence to interpret candidate rules as applying more narrowly than utilitarian rules. (shrink)

Each of our theories of mental representation provides some insight into how the mind works. However, these insights often seem incompatible, as the debates between symbolic, dynamical, emergentist, sub-symbolic, and grounded approaches to cognition attest. Mental representations—whatever they are—must share many features with each of our theories of representation, and yet there are few hypotheses about how a synthesis could be possible. Here, I develop a theory of the underpinnings of symbolic cognition that shows how sub-symbolic dynamics may give rise (...) to higher-level cognitive representations of structures, systems of knowledge, and algorithmic processes. This theory implements a version of conceptual role semantics by positing an internal universal representation language in which learners may create mental models to capture dynamics they observe in the world. The theory formalizes one account of how truly novel conceptual content may arise, allowing us to explain how even elementary logical and computational operations may be learned from a more primitive basis. I provide an implementation that learns to represent a variety of structures, including logic, number, kinship trees, regular languages, context-free languages, domains of theories like magnetism, dominance hierarchies, list structures, quantification, and computational primitives like repetition, reversal, and recursion. This account is based on simple discrete dynamical processes that could be implemented in a variety of different physical or biological systems. In particular, I describe how the required dynamics can be directly implemented in a connectionist framework. The resulting theory provides an “assembly language” for cognition, where high-level theories of symbolic computation can be implemented in simple dynamics that themselves could be encoded in biologically plausible systems. (shrink)

A central question in human development is how young children gain knowledge so fast. We propose that analogical generalization drives much of this early learning and allows children to generate new abstractions from experience. In this paper, we review evidence for analogical generalization in both children and adults. We discuss how analogical processes interact with the child's changing knowledge base to predict the course of learning, from conservative to domain-general understanding. This line of research leads to challenges to existing assumptions (...) about learning. It shows that it is not enough to consider the distribution of examples given to learners; one must consider the processes learners are applying; contrary to the general assumption, maximizing variability is not always the best route for maximizing generalization and transfer. (shrink)

Cross-situational learning is a mechanism for learning the meaning of words across multiple exposures, despite exposure-by-exposure uncertainty as to the word's true meaning. We present experimental evidence showing that humans learn words effectively using cross-situational learning, even at high levels of referential uncertainty. Both overall success rates and the time taken to learn words are affected by the degree of referential uncertainty, with greater referential uncertainty leading to less reliable, slower learning. Words are also learned less successfully and more slowly (...) if they are presented interleaved with occurrences of other words, although this effect is relatively weak. We present additional analyses of participants’ trial-by-trial behavior showing that participants make use of various cross-situational learning strategies, depending on the difficulty of the word-learning task. When referential uncertainty is low, participants generally apply a rigorous eliminative approach to cross-situational learning. When referential uncertainty is high, or exposures to different words are interleaved, participants apply a frequentist approximation to this eliminative approach. We further suggest that these two ways of exploiting cross-situational information reside on a continuum of learning strategies, underpinned by a single simple associative learning mechanism. (shrink)

Do you know you are not being massively deceived by an evil demon? That is a familiar skeptical challenge. Less familiar is this question: How do you have a conception of knowledge on which the evil demon constitutes a prima facie challenge? Recently several philosophers have suggested that our responses to skeptical scenarios can be explained in terms of heuristics and biases. We offer an alternative explanation, based in learning theory. We argue that, given the evidence available to the learner, (...) it would be rational for the learner to infer an infallibilist conception of knowledge. (shrink)

Surprise—operationalized as looking time—has a long history in developmental research, providing a window into the perception and cognition of infants. Recently, however, a number of developmental researchers have considered infants’ and children's surprise in its own right. This article reviews empirical evidence and computational models of complex statistical inferences underlying surprise, and discusses how these findings relate to the role that surprise appears to play as a catalyst for learning.

Words are the essence of communication: They are the building blocks of any language. Learning the meaning of words is thus one of the most important aspects of language acquisition: Children must first learn words before they can combine them into complex utterances. Many theories have been developed to explain the impressive efficiency of young children in acquiring the vocabulary of their language, as well as the developmental patterns observed in the course of lexical acquisition. A major source of disagreement (...) among the different theories is whether children are equipped with special mechanisms and biases for word learning, or their general cognitive abilities are adequate for the task. We present a novel computational model of early word learning to shed light on the mechanisms that might be at work in this process. The model learns word meanings as probabilistic associations between words and semantic elements, using an incremental and probabilistic learning mechanism, and drawing only on general cognitive abilities. The results presented here demonstrate that much about word meanings can be learned from naturally occurring child-directed utterances (paired with meaning representations), without using any special biases or constraints, and without any explicit developmental changes in the underlying learning mechanism. Furthermore, our model provides explanations for the occasionally contradictory child experimental data, and offers predictions for the behavior of young word learners in novel situations. (shrink)

Unlike behaviorism, cognitive psychology relies on mental concepts to explain behavior. Yet mental processes are not directly observable and multiple explanations are possible, which poses a challenge for finding a useful framework. In this article, I distinguish three new frameworks for explanations that emerged after the cognitive revolution. The first is called tools‐to‐theories: Psychologists' new tools for data analysis, such as computers and statistics, are turned into theories of mind. The second proposes as‐if theories: Expected utility theory and Bayesian statistics (...) are turned into theories of mind, describing an optimal solution of a problem but not its psychological process. The third studies the adaptive toolbox (formal models of heuristics) that describes mental processes in situations of uncertainty where an optimal solution is unknown. Depending on which framework researchers choose, they will model behavior in either situations of risk or of uncertainty, and construct models of cognitive processes or not. The frameworks also determine what questions are asked and what kind of data are generated. What all three frameworks have in common, however, is a clear preference for formal models rather than explanations by general dichotomies or mere verbal concepts. The frameworks have considerable potential to inform each other and to generate points of integration. (shrink)

I consider the role of cognitive modeling in cognitive science. Modeling, and the computers that enable it, are central to the field, but the role of modeling is often misunderstood. Models are not intended to capture fully the processes they attempt to elucidate. Rather, they are explorations of ideas about the nature of cognitive processes. In these explorations, simplification is essential—through simplification, the implications of the central ideas become more transparent. This is not to say that simplification has no downsides; (...) it does, and these are discussed. I then consider several contemporary frameworks for cognitive modeling, stressing the idea that each framework is useful in its own particular ways. Increases in computer power (by a factor of about 4 million) since 1958 have enabled new modeling paradigms to emerge, but these also depend on new ways of thinking. Will new paradigms emerge again with the next 1,000‐fold increase? (shrink)

Things we can say, and the ways in which we can say them, compete with one another. And this has consequences: words we decide not to pronounce have critical effects on the messages we end up conveying. For instance, in saying Chris is a good teacher, we may convey that Chris is not an amazing teacher. How this happens is an unsolvable problem, unless a theory of alternatives indicates what counts, among all the things that have not been pronounced. It (...) is sometimes assumed, explicitly or implicitly, that any word counts, as long as that word could have replaced one that was actually pronounced. We review arguments for going beyond this powerful idea. In doing so, we argue that the level of words is not the right level of analysis for alternatives. Instead, we capitalize on recent conceptual and associated methodological advances within the study of the so-called “language of thought” to reopen the problem from a new perspective. Specifically, we provide theoretical and experimental arguments that the relation between alternatives and words may be indirect, and that alternatives are not merely linguistic objects in the traditional sense. Rather, we propose that competition in language is significantly determined by general reasoning preferences, or thought preferences. We propose that such non-linguistic preferences can be measured and that these measures can be used to explain linguistic competition, non-linguistically, and more in depth. (shrink)

We address the problem of predicting how people will spontaneously divide into groups a set of novel items. This is a process akin to perceptual organization. We therefore employ the simplicity principle from perceptual organization to propose a simplicity model of unconstrained spontaneous grouping. The simplicity model predicts that people would prefer the categories for a set of novel items that provide the simplest encoding of these items. Classification predictions are derived from the model without information either about the number (...) of categories sought or information about the distributional properties of the objects to be classified. These features of the simplicity model distinguish it from other models in unsupervised categorization (where, for example, the number of categories sought is determined via a free parameter), and we discuss how these computational differences are related to differences in modeling objectives. The predictions of the simplicity model are validated in four experiments. We also discuss the significance of simplicity in cognitive modeling more generally. (shrink)

Tenenbaum and Griffiths (2001) have proposed that their Bayesian model of generalisation unifies Shepard’s (1987) and Tversky’s (1977) similarity-based explanations of two distinct patterns of generalisation behaviours by reconciling them under a single coherent task analysis. I argue that this proposal needs refinement: instead of unifying the heterogeneous notion of psychological similarity, the Bayesian approach unifies generalisation by rendering the distinct patterns of behaviours informationally relevant. I suggest that generalisation as a Bayesian inference should be seen as a complement to, (...) instead of a replacement of, similarity-based explanations. Furthermore, I show that the unificatory powers of the Bayesian model of generalisation can contribute to the selection of one of these models of psychological similarity. (shrink)

There has been little investigation to date of the way metacognition is involved in conceptual change. It has been recognised that analytic metacognition is important to the way older children acquire more sophisticated scientific and mathematical concepts at school. But there has been barely any examination of the role of metacognition in earlier stages of concept acquisition, at the ages that have been the major focus of the developmental psychology of concepts. The growing evidence that even young children have a (...) capacity for procedural metacognition raises the question of whether and how these abilities are involved in conceptual development. More specifically, are there developmental changes in metacognitive abilities that have a wholescale effect on the way children acquire new concepts and replace existing concepts? We show that there is already evidence of at least one plausible example of such a link and argue that these connections deserve to be investigated systematically. (shrink)

People are adept at inferring novel causal relations, even from only a few observations. Prior knowledge about the probability of encountering causal relations of various types and the nature of the mechanisms relating causes and effects plays a crucial role in these inferences. We test a formal account of how this knowledge can be used and acquired, based on analyzing causal induction as Bayesian inference. Five studies explored the predictions of this account with adults and 4-year-olds, using tasks in which (...) participants learned about the causal properties of a set of objects. The studies varied the two factors that our Bayesian approach predicted should be relevant to causal induction: the prior probability with which causal relations exist, and the assumption of a deterministic or a probabilistic relation between cause and effect. Adults’ judgments (Experiments 1, 2, and 4) were in close correspondence with the quantitative predictions of the model, and children’s judgments (Experiments 3 and 5) agreed qualitatively with this account. (shrink)

Much research on cognitive development focuses either on early-emerging domain-specific knowledge or domain-general learning mechanisms. However, little research examines how these sources of knowledge interact. Previous research suggests that young infants can make inferences from samples to populations (Xu & Garcia, 2008) and 11- to 12.5-month-old infants can integrate psychological and physical knowledge in probabilistic reasoning (Teglas, Girotto, Gonzalez, & Bonatti, 2007; Xu & Denison, 2009). Here, we ask whether infants can integrate a physical constraint of immobility into a statistical (...) inference mechanism. Results from three experiments suggest that, first, infants were able to use domain-specific knowledge to override statistical information, reasoning that sometimes a physical constraint is more informative than probabilistic information. Second, we provide the first evidence that infants are capable of applying domain-specific knowledge in probabilistic reasoning by using a physical constraint to exclude one set of objects while computing probabilities over the remaining sets. (shrink)

In this prcis we focus on phenomena central to the reaction against similarity-based theories that arose in the 1980s and that subsequently motivated the approach to semantic knowledge. Specifically, we consider (1) how concepts differentiate in early development, (2) why some groupings of items seem to form or coherent categories while others do not, (3) why different properties seem central or important to different concepts, (4) why children and adults sometimes attest to beliefs that seem to contradict their direct experience, (...) (5) how concepts reorganize between the ages of 4 and 10, and (6) the relationship between causal knowledge and semantic knowledge. The explanations our theory offers for these phenomena are illustrated with reference to a simple feed-forward connectionist model. The relationships between this simple model, the broader theory, and more general issues in cognitive science are discussed. (shrink)

Inductive generalization, where people go beyond the data provided, is a basic cognitive capability, and it underpins theoretical accounts of learning, categorization, and decision making. To complete the inductive leap needed for generalization, people must make a key ‘‘sampling’’ assumption about how the available data were generated. Previous models have considered two extreme possibilities, known as strong and weak sampling. In strong sampling, data are assumed to have been deliberately generated as positive examples of a concept, whereas in weak sampling, (...) data are assumed to have been generated without any restrictions. We develop a more general account of sampling that allows for an intermediate mixture of these two extremes, and we test its usefulness. In two experiments, we show that most people complete simple one-dimensional generalization tasks in a way that is consistent with their believing in some mixture of strong and weak sampling, but that there are large individual differences in the relative emphasis different people give to each type of sampling. We also show experimentally that the relative emphasis of the mixture is influenced by the structure of the available information. We discuss the psychological meaning of mixing strong and weak sampling, and possible extensions of our modeling approach to richer problems of inductive generalization. (shrink)

Tenenbaum and Griffiths (Behavioral and Brain Sciences 24(4):629–640, 2001) have proposed that their Bayesian model of generalisation unifies Shepard’s (Science 237(4820): 1317–1323, 1987) and Tversky’s (Psychological Review 84(4): 327–352, 1977) similarity-based explanations of two distinct patterns of generalisation behaviours by reconciling them under a single coherent task analysis. I argue that this proposal needs refinement: instead of unifying the heterogeneous notion of psychological similarity, the Bayesian approach unifies generalisation by rendering the distinct patterns of behaviours informationally relevant. I suggest that (...) generalisation as a Bayesian inference should be seen as a complement to, instead of a replacement of, similarity-based explanations. Furthermore, I show that the unificatory powers of the Bayesian model of generalisation can contribute to the selection of one of these models of psychological similarity. (shrink)

Words refer to objects in the world, but this correspondence is not one-to-one: Each word has a range of referents that share features on some dimensions but differ on others. This property of language is called underspecification. Parts of the lexicon have characteristic patterns of underspecification; for example, artifact nouns tend to specify shape, but not color, whereas substance nouns specify material but not shape. These regularities in the lexicon enable learners to generalize new words appropriately. How does the lexicon (...) come to have these helpful regularities? We test the hypothesis that systematic backgrounding of some dimensions during learning and use causes language to gradually change, over repeated episodes of transmission, to produce a lexicon with strong patterns of underspecification across these less salient dimensions. This offers a cultural evolutionary mechanism linking individual word learning and generalization to the origin of regularities in the lexicon that help learners generalize words appropriately. (shrink)