The final work of a distinguished physicist, this remarkable volume examines the emotive significance of time, the time order of mechanics, the time direction of thermodynamics and microstatistics, the time direction of macrostatistics, and the time of quantum physics. Coherent discussions include accounts of analytic methods of scientific philosophy in the investigation of probability, quantum mechanics, the theory of relativity, and causality. "[Reichenbach’s] best by a good deal."—Physics Today. 1971 ed.

Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...) She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics. (shrink)

This book represents the views of one of the greatest mathematicians of the twentieth century on the analogies between computing machines and the living human brain.

The computational view of mind rests on certain intuitions regarding the fundamental similarity between computation and cognition. We examine some of these intuitions and suggest that they derive from the fact that computers and human organisms are both physical systems whose behavior is correctly described as being governed by rules acting on symbolic representations. Some of the implications of this view are discussed. It is suggested that a fundamental hypothesis of this approach is that there is a natural domain of (...) human functioning that can be addressed exclusively in terms of a formal symbolic or algorithmic vocabulary or level of analysis. Much of the paper elaborates various conditions that need to be met if a literal view of mental activity as computation is to serve as the basis for explanatory theories. The coherence of such a view depends on there being a principled distinction between functions whose explanation requires that we posit internal representations and those that we can appropriately describe as merely instantiating causal physical or biological laws. In this paper the distinction is empirically grounded in a methodological criterion called the " cognitive impenetrability condition." Functions are said to be cognitively impenetrable if they cannot be influenced by such purely cognitive factors as goals, beliefs, inferences, tacit knowledge, and so on. Such a criterion makes it possible to empirically separate the fixed capacities of mind from the particular representations and algorithms used on specific occasions. In order for computational theories to avoid being ad hoc, they must deal effectively with the "degrees of freedom" problem by constraining the extent to which they can be arbitrarily adjusted post hoc to fit some particular set of observations. This in turn requires that the fixed architectural function and the algorithms be independently validated. It is argued that the architectural assumptions implicit in many contemporary models run afoul of the cognitive impenetrability condition, since the required fixed functions are demonstrably sensitive to tacit knowledge and goals. The paper concludes with some tactical suggestions for the development of computational cognitive theories. (shrink)

Looks at accounts by Locke, Fodor, Dretske, and Millikan concerning the nature of mental representation, and discusses connectionism and representation.

First Published in 1995. Routledge is an imprint of Taylor & Francis, an informa company.

We identify two aspects of the problem of maintaining perceptual stability despite an observer's eye movements. The first, visual direction constancy, is the (egocentric) stability of apparent positions of objects in the visual world relative to the perceiver. The second, visual position constancy, is the (exocentric) stability of positions of objects relative to each other. We analyze the constancy of visual direction despite saccadic eye movements.Three information sources have been proposed to enable the visual system to achieve stability: the structure (...) of the visual field, proprioceptive inflow, and a copy of neural efference or outflow to the extraocular muscles. None of these sources by itself provides adequate information to achieve visual direction constancy; present evidence indicates that all three are used.Our final question concerns how information processing operations result in a stable world. The three traditionally suggested means have been elimination, translation, or evaluation. All are rejected. From a review of the physiological and psychological evidence we conclude that no subtraction, compensation, or evaluation need take place. The problem for which these solutions were developed turns out to be a false one. We propose a “calibration” solution: correct spatiotopic positions are calculated anew for each fixation. Inflow, outflow, and retinal sources are used in this calculation: saccadic suppression of displacement bridges the errors between these sources and the actual extent of movement. (shrink)

Hilary Putnam, who may have been the first philosopher to advance the notion that the computer is an apt model for the mind, takes a radically new view of his...

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models. (shrink)

In the first section of the article, we examine some recent criticisms of the connectionist enterprise: first, that connectionist models are fundamentally behaviorist in nature (and, therefore, non-cognitive), and second that connectionist models are fundamentally associationist in nature (and, therefore, cognitively weak). We argue that, for a limited class of connectionist models (feed-forward, pattern-associator models), the first criticism is unavoidable. With respect to the second criticism, we propose that connectionist modelsare fundamentally associationist but that this is appropriate for building models (...) of human cognition. However, we do accept the point that there are cognitive capacities for which any purely associative model cannot provide a satisfactory account. The implication that we draw from is this is not that associationist models and mechanisms should be scrapped, but rather that they should be enhanced.In the next section of the article, we identify a set of connectionist approaches which are characterized by “active symbols” — recurrent circuits which are the basis of knowledge representation. We claim that such approaches avoid criticisms of behaviorism and are, in principle, capable of supporting full cognition. In the final section of the article, we speculate at some length about what we believe would be the characteristics of a fully realized active symbol system. This includes both potential problems and possible solutions (for example, mechanisms needed to control activity in a complex recurrent network) as well as the promise of such systems (in particular, the emergence of knowledge structures which would constitute genuine internal models). (shrink)

This article addresses the ability of Parallel Distributed Processing (PDP) networks to generate stagewise cognitive development in accordance with Piaget's theory of cognitive epigenesis. We carried out a replication study of the simulation experiments by McClelland (1989) and McClelland and Jenkins (1991) in which a PDP network learns to solve balance scale problems. In objective tests motivated from catastrophe theory, a mathematical theory of transitions in epigenetical systems, no evidence for stage transitions in network performance was found. It is concluded (...) that PDP networks lack the ability to recover the positive outcomes of analogous catastrophe analyses of real cognitive developmental data. In an attempt to further characterize the learning behaviour of PDP networks, we carried out a second simulation study using the discrimination‐shift paradigm. The results thus obtained indicate that PDP learning is compatible with the learning of stimulus‐response relationships, not with the acquisition of mediating rules such as conceived in (neo‐)Piagetian theory. In closing, we speculate about the feasibility of simulating stagewise development with alternative network architectures. (shrink)

It is proposed to conceive of representation as an emergent phenomenon that is supervenient on patterns of activity of coarsely tuned and highly redundant feature detectors. The computational underpinnings of the outlined concept of representation are (1) the properties of collections of overlapping graded receptive fields, as in the biological perceptual systems that exhibit hyperacuity-level performance, and (2) the sufficiency of a set of proximal distances between stimulus representations for the recovery of the corresponding distal contrasts between stimuli, as in (...) multidimensional scaling. The present preliminary study appears to indicate that this concept of representation is computationally viable, and is compatible with psychological and neurobiological data. (shrink)

The calibration solution to the stability of the world despite eye movements depends, according to Bridgeman et al., upon a combination of three factors which presumably all need to operate to achieve the goal of stability. Although the authors admit (sect. 4.3, para. 5) that the relative contributions of retinal and extraretinal factors will depend on the particular viewing situation, Figure 5 (sect. 4.3) makes it clear in its representation that the role of perceptual factors is relatively minor compared to (...) extraretinal ones. It is with this representation that this commentary wishes to take issue, believing that it occurs as a result of some assumptions about terminology that may be ambiguous, as well as some misconceptions about the circumstances in which there is a need for stability. (shrink)