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)

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)

The mathematical theory of communication.

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)

We distinguish between literal and metaphorical applications of Bayesian models. When intended literally, an isomorphism exists between the elements of representation assumed by the rational analysis and the mechanism that implements the computation. Thus, observation of the implementation can externally validate assumptions underlying the rational analysis. In other applications, no such isomorphism exists, so it is not clear how the assumptions that allow a Bayesian model to fit data can be independently validated.

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)

We propose a framework for including information‐processing bounds in rational analyses. It is an application of bounded optimality (Russell & Subramanian, 1995) to the challenges of developing theories of mechanism and behavior. The framework is based on the idea that behaviors are generated by cognitive mechanisms that are adapted to the structure of not only the environment but also the mind and brain itself. We call the framework computational rationality to emphasize the incorporation of computational mechanism into the definition of (...) rational action. Theories are specified as optimal program problems, defined by an adaptation environment, a bounded machine, and a utility function. Such theories yield different classes of explanation, depending on the extent to which they emphasize adaptation to bounds, and adaptation to some ecology that differs from the immediate local environment. We illustrate this variation with examples from three domains: visual attention in a linguistic task, manual response ordering, and reasoning. We explore the relation of this framework to existing “levels” approaches to explanation, and to other optimality‐based modeling approaches. (shrink)

Two books have been particularly influential in contemporary philosophy of science: Karl R. Popper's Logic of Scientific Discovery, and Thomas S. Kuhn's Structure of Scientific Revolutions. Both agree upon the importance of revolutions in science, but differ about the role of criticism in science's revolutionary growth. This volume arose out of a symposium on Kuhn's work, with Popper in the chair, at an international colloquium held in London in 1965. The book begins with Kuhn's statement of his position followed by (...) seven essays offering criticism and analysis, and finally by Kuhn's reply. The book will interest senior undergraduates and graduate students of the philosophy and history of science, as well as professional philosophers, philosophically inclined scientists, and some psychologists and sociologists. (shrink)

David Marr's (1982) three‐level analysis of computational cognition argues for three distinct levels of cognitive information processing—namely, the computational, representational, and implementational levels. But Marr's levels are—and were meant to be—descriptive, rather than interactive and dynamic. For this reason, we suggest that, had Marr been writing today, he might well have gone even farther in his analysis, including the emergence of structure—in particular, explicit structure at the conceptual level—from lower levels, and the effect of explicit emergent structures on the level (...) (or levels) that gave rise to them. The message is that today's cognitive scientists need not only to understand how emergent structures—in particular, explicit emergent structures at the cognitive level—develop but also to understand how they feed back on the sub‐structures from which they emerged. (shrink)

underpinning of the cognitive sciences. I argue, however, that it often fails to provide adequate explanations, in particular in conjunction with competence theories. This failure originates in the idealizations in competence descriptions, which either ?block? the cascade, or produce a successful cascade which fails to explain cognition.

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)

Chomsky proposes a reformulation of the theory of transformational generative grammar that takes recent developments in the descriptive analysis of particular ...

Computational models will play an important role in our understanding of human higher‐order cognition. How can a model's contribution to this goal be evaluated? This article argues that three important aspects of a model of higher‐order cognition to evaluate are (a) its ability to reason, solve problems, converse, and learn as well as people do; (b) the breadth of situations in which it can do so; and (c) the parsimony of the mechanisms it posits. This article argues that fits of (...) models to quantitative experimental data, although valuable for other reasons, do not address these criteria. Further, using analogies with other sciences, the history of cognitive science, and examples from modern‐day research programs, this article identifies five activities that have been demonstrated to play an important role in our understanding of human higher‐order cognition. These include modeling within a cognitive architecture, conducting artificial intelligence research, measuring and expanding a model's ability, finding mappings between the structure of different domains, and attempting to explain multiple phenomena within a single model. (shrink)

We sketch four applications of Marr's levels-of-analysis methodology to the relations between logic and experimental data in the cognitive neuroscience of language and reasoning. The first part of the paper illustrates the explanatory power of computational level theories based on logic. We show that a Bayesian treatment of the suppression task in reasoning with conditionals is ruled out by EEG data, supporting instead an analysis based on defeasible logic. Further, we describe how results from an EEG study on temporal prepositions (...) can be reanalyzed using formal semantics, addressing a potential confound. The second part of the article demonstrates the predictive power of logical theories drawing on EEG data on processing progressive constructions and on behavioral data on conditional reasoning in people with autism. Logical theories can constrain processing hypotheses all the way down to neurophysiology, and conversely neuroscience data can guide the selection of alternative computational level models of cognition. (shrink)

We sketch four applications of Marr's levels‐of‐analysis methodology to the relations between logic and experimental data in the cognitive neuroscience of language and reasoning. The first part of the paper illustrates the explanatory power of computational level theories based on logic. We show that a Bayesian treatment of the suppression task in reasoning with conditionals is ruled out by EEG data, supporting instead an analysis based on defeasible logic. Further, we describe how results from an EEG study on temporal prepositions (...) can be reanalyzed using formal semantics, addressing a potential confound. The second part of the article demonstrates the predictive power of logical theories drawing on EEG data on processing progressive constructions and on behavioral data on conditional reasoning in people with autism. Logical theories can constrain processing hypotheses all the way down to neurophysiology, and conversely neuroscience data can guide the selection of alternative computational level models of cognition. (shrink)

Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored (...) to issue this commemorative reprinting of a classic. (shrink)

In this book, Newell makes the case for unified theories by setting forth a candidate.

The human cognitive architecture consists of a set of largely independent modules associated with different brain regions. This book discusses in detail how these various modules can combine to produce behaviours as varied as driving a car and solving an algebraic equation.

To understand the mind, we need to draw equally on the fields of cognitive science and neuroscience. But these two fields have very separate intellectual roots, and very different styles. So how can these two be reconciled in order to develop a full understanding of the mind and brain.This is the focus of this landmark new book.

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)