This article described three heuristics that are employed in making judgements under uncertainty: representativeness, which is usually employed when people are asked to judge the probability that an object or event A belongs to class or process B; availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development; and adjustment from an anchor, which is usually employed in numerical prediction when a relevant value (...) is available. These heuristics are highly economical and usually effective, but they lead to systematic and predictable errors. A better understanding of these heuristics and of the biases to which they lead could improve judgements and decisions in situations of uncertainty. (shrink)

Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. Ian Hacking presents a philosophical critique of early ideas about probability, induction, and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth, and seventeenth centuries. Hacking invokes a wide intellectual framework involving the growth of science, economics, and the theology of the period. He argues that the (...) transformations that made it possible for probability concepts to emerge have constrained all subsequent development of probability theory and determine the space within which philosophical debate on the subject is still conducted. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends. Ian Hacking is the winner of the Holberg International Memorial Prize 2009. (shrink)

As Aristotle stated, scientific explanation is based on deductive argument--yet, Wesley C. Salmon points out, not all deductive arguments are qualified explanations. The validity of the explanation must itself be examined. _Four Decades of Scientific Explanation_ provides a comprehensive account of the developments in scientific explanation that transpired in the last four decades of the twentieth century. It continues to stand as the most comprehensive treatment of the writings on the subject during these years. Building on the historic 1948 essay (...) by Carl G. Hempel and Paul Oppenheim, "Studies in the Logic of Explanation,” which introduced the deductive-nomological model on which most work on scientific explanation was based for the following four decades, Salmon goes beyond this model's inherent basis of describing empirical knowledge to tells us “not only _what,_ but also _why_.” Salmon examines the predominant models in chronological order and describes their development, refinement, and criticism or rejection. _Four Decades of Scientific Explanation_ underscores the need for a consensus of approach and ongoing evaluations of methodology in scientific explanation, with the goal of providing a better understanding of natural phenomena. (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)

Brains, it has recently been argued, are essentially prediction machines. They are bundles of cells that support perception and action by constantly attempting to match incoming sensory inputs with top-down expectations or predictions. This is achieved using a hierarchical generative model that aims to minimize prediction error within a bidirectional cascade of cortical processing. Such accounts offer a unifying model of perception and action, illuminate the functional role of attention, and may neatly capture the special contribution of cortical processing to (...) adaptive success. This target article critically examines this approach, concluding that it offers the best clue yet to the shape of a unified science of mind and action. Sections 1 and 2 lay out the key elements and implications of the approach. Section 3 explores a variety of pitfalls and challenges, spanning the evidential, the methodological, and the more properly conceptual. The paper ends (sections 4 and 5) by asking how such approaches might impact our more general vision of mind, experience, and agency. (shrink)

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

The received view of dynamical explanation is that dynamical cognitive science seeks to provide covering law explanations of cognitive phenomena. By analyzing three prominent examples of dynamicist research, I show that the received view is misleading: some dynamical explanations are mechanistic explanations, and in this way resemble computational and connectionist explanations. Interestingly, these dynamical explanations invoke the mathematical framework of dynamical systems theory to describe mechanisms far more complex and distributed than the ones typically considered by philosophers. Therefore, contemporary dynamicist (...) research reveals the need for a more sophisticated account of mechanistic explanation. (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)

Continuing his exploration of the organization of complexity and the science of design, this new edition of Herbert Simon's classic work on artificial ...

Oaksford & Chater (O&C) aim to provide teleological explanations of behavior by giving an appropriate normative standard: Bayesian inference. We argue that there is no uncontroversial independent justification for the normativity of Bayesian inference, and that O&C fail to satisfy a necessary condition for teleological explanations: demonstration that the normative prescription played a causal role in the behavior's existence.

the _algorithmic_, and the _implementational_; Zenon Pylyshyn (1984) calls them the _semantic_, the _syntactic_, and the _physical_; and textbooks in cognitive psychology sometimes call them the levels of _content_, _form_, and _medium_ (e.g. Glass, Holyoak, and Santa 1979).

In exploring the nature of psychological explanation, this book looks at how psychologists theorize about the human ability to calculate, to speak a language and the like. It shows how good theorizing explains or tries to explain such abilities as perception and cognition. It recasts the familiar explanations of "intelligence" and "cognitive capacity" as put forward by philosophers such as Fodor, Dennett, and others in terms of a theory of explanation that makes established doctrine more intelligible to professionals and their (...) students.In particular, the book shows that vestigial adherence to the positivists' D-N model has distorted the view of philosophers of science about what psychologists (and biologists) do and has masked the real nature of explanation. Major sections in the book cover Analysis and Subsumption; Functional Analysis; Understanding Cognitive Capacities; and Historical Reflections.Robert Cummins is Associate Professor of Philosophy at the University of Illinois, Chicago Circle. A Bradford Book. (shrink)

Through the use of such "folk" concepts as belief, desire, intention, and expectation, Daniel Dennett asserts in this first full scale presentation of...

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)

I discuss whether there are some lessons for philosophical inquiry over the nature of simulation to be learnt from the practical methodology of reengineering. I will argue that reengineering serves a similar purpose as simulations in theoretical science such as computational neuroscience or neurorobotics, and that the procedures and heuristics of reengineering help to develop solutions to outstanding problems of simulation.

Can the output of human cognition be predicted from the assumption that it is an optimal response to the information-processing demands of the environment? A methodology called rational analysis is described for deriving predictions about cognitive phenomena using optimization assumptions. The predictions flow from the statistical structure of the environment and not the assumed structure of the mind. Bayesian inference is used, assuming that people start with a weak prior model of the world which they integrate with experience to develop (...) stronger models of specific aspects of the world. Cognitive performance maximizes the difference between the expected gain and cost of mental effort. Memory performance can be predicted on the assumption that retrieval seeks a maximal trade-off between the probability of finding the relevant memories and the effort required to do so; in categorization performance there is a similar trade-off between accuracy in predicting object features and the cost of hypothesis formation; in casual inference the trade-off is between accuracy in predicting future events and the cost of hypothesis formation; and in problem solving it is between the probability of achieving goals and the cost of both external and mental problem-solving search. The implemention of these rational prescriptions in neurally plausible architecture is also discussed. (shrink)

One of the most lasting contributions of Marr's posthumous book is his articulation of the different “levels of analysis” that are needed to understand vision. Although a variety of work has examined how these different levels are related, there is comparatively little examination of the assumptions on which his proposed levels rest, or the plausibility of the approach Marr articulated given those assumptions. Marr placed particular significance on computational level theory, which specifies the “goal” of a computation, its appropriateness for (...) solving a particular problem, and the logic by which it can be carried out. The structure of computational level theory is inherently teleological: What the brain does is described in terms of its purpose. I argue that computational level theory, and the reverse-engineering approach it inspires, requires understanding the historical trajectory that gave rise to functional capacities that can be meaningfully attributed with some sense of purpose or goal, that is, a reconstruction of the fitness function on which natural selection acted in shaping our visual abilities. I argue that this reconstruction is required to distinguish abilities shaped by natural selection—“natural tasks” —from evolutionary “by-products”, rather than merely demonstrating that computational goals can be embedded in a Bayesian model that renders a particular behavior or process rational. (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.

In many learning or inference tasks human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and standard assumptions about optimality: People often appear to make decisions based on just one or a few samples from the appropriate posterior probability distribution, rather than using the full distribution. Although sampling-based approximations are a common way to implement Bayesian (...) inference, the very limited numbers of samples often used by humans seem insufficient to approximate the required probability distributions very accurately. Here, we consider this discrepancy in the broader framework of statistical decision theory, and ask: If people are making decisions based on samples—but as samples are costly—how many samples should people use to optimize their total expected or worst-case reward over a large number of decisions? We find that under reasonable assumptions about the time costs of sampling, making many quick but locally suboptimal decisions based on very few samples may be the globally optimal strategy over long periods. These results help to reconcile a large body of work showing sampling-based or probability matching behavior with the hypothesis that human cognition can be understood in Bayesian terms, and they suggest promising future directions for studies of resource-constrained cognition. (shrink)

In the book, I argue that the mind can be explained computationally because it is itself computational—whether it engages in mental arithmetic, parses natural language, or processes the auditory signals that allow us to experience music. All these capacities arise from complex information-processing operations of the mind. By analyzing the state of the art in cognitive science, I develop an account of computational explanation used to explain the capacities in question.

According to a growing trend in theoretical neuroscience, the human perceptual system is akin to a Bayesian machine. The aim of this article is to clearly articulate the claims that perception can be considered Bayesian inference and that the brain can be considered a Bayesian machine, some of the epistemological challenges to these claims; and some of the implications of these claims. We address two questions: (i) How are Bayesian models used in theoretical neuroscience? (ii) From the use of Bayesian (...) models in theoretical neuroscience, have we learned or can we hope to learn that perception is Bayesian inference or that the brain is a Bayesian machine? From actual practice in theoretical neuroscience, we argue for three claims. First, currently Bayesian models do not provide mechanistic explanations; instead they are useful devices for predicting and systematizing observational statements about people's performances in a variety of perceptual tasks. That is, currently we should have an instrumentalist attitude towards Bayesian models in neuroscience. Second, the inference typically drawn from Bayesian behavioural performance in a variety of perceptual tasks to underlying Bayesian mechanisms should be understood within the three-level framework laid out by David Marr ( [1982] ). Third, we can hope to learn that perception is Bayesian inference or that the brain is a Bayesian machine to the extent that Bayesian models will prove successful in yielding secure and informative predictions of both subjects' perceptual performance and features of the underlying neural mechanisms. (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)

According to Marr, a computational-level theory consists of two elements, the what and the why . This article highlights the distinct role of the Why element in the computational analysis of vision. Three theses are advanced: ( a ) that the Why element plays an explanatory role in computational-level theories, ( b ) that its goal is to explain why the computed function (specified by the What element) is appropriate for a given visual task, and ( c ) that the (...) explanation consists in showing that the functional relations between the representing cells are similar to the “external” mathematical relations between the entities that these cells represent. *Received September 2009; revised January 2010. †To contact the author, please write to: Departments of Philosophy and Cognitive Science, The Hebrew University, Jerusalem 91905, Israel; e-mail: [email protected]. (shrink)

A recent development in the cognitive science of reasoning has been the emergence of a probabilistic approach to the behaviour observed on ostensibly logical tasks. According to this approach the errors and biases documented on these tasks occur because people import their everyday uncertain reasoning strategies into the laboratory. Consequently participants' apparently irrational behaviour is the result of comparing it with an inappropriate logical standard. In this article, we contrast the probabilistic approach with other approaches to explaining rationality, and then (...) show how it has been applied to three main areas of logical reasoning: conditional inference, Wason's selection task and syllogistic reasoning. (shrink)

Every scientist chooses a preferred level of analysis and this choice shapes the research program, even determining what counts as evidence. This contribution revisits Marr's three levels of analysis and evaluates the prospect of making progress at each individual level. After reviewing limitations of theorizing within a level, two strategies for integration across levels are considered. One is top–down in that it attempts to build a bridge from the computational to algorithmic level. Limitations of this approach include insufficient theoretical constraint (...) at the computation level to provide a foundation for integration, and that people are suboptimal for reasons other than capacity limitations. Instead, an inside-out approach is forwarded in which all three levels of analysis are integrated via the algorithmic level. This approach maximally leverages mutual data constraints at all levels. For example, algorithmic models can be used to interpret brain imaging data, and brain imaging data can be used to select among competing models. Examples of this approach to integration are provided. This merging of levels raises questions about the relevance of Marr's tripartite view. (shrink)

Marr's levels of analysis—computational, algorithmic, and implementation—have served cognitive science well over the last 30 years. But the recent increase in the popularity of the computational level raises a new challenge: How do we begin to relate models at different levels of analysis? We propose that it is possible to define levels of analysis that lie between the computational and the algorithmic, providing a way to build a bridge between computational- and algorithmic-level models. The key idea is to push the (...) notion of rationality, often used in defining computational-level models, deeper toward the algorithmic level. We offer a simple recipe for reverse-engineering the mind's cognitive strategies by deriving optimal algorithms for a series of increasingly more realistic abstract computational architectures, which we call “resource-rational analysis.”. (shrink)

We consider approaches to explanation within the cognitive sciences that begin with Marr's computational level or Marr's implementational level and argue that each is subject to fundamental limitations which impair their ability to provide adequate explanations of cognitive phenomena. For this reason, it is argued, explanation cannot proceed at either level without tight coupling to the algorithmic and representation level. Even at this level, however, we argue that additional constraints relating to the decomposition of the cognitive system into a set (...) of interacting subfunctions are required. Integrated cognitive architectures that permit abstract specification of the functions of components and that make contact with the neural level provide a powerful bridge for linking the algorithmic and representational level to both the computational level and the implementational level. (shrink)

The vivid terms, "Top-down" and "Bottom-up" have become popular in several different contexts in cognitive science. My task today is to sort out some different meanings and comment on the relations between them, and their implications for cognitive science.