Advocates of the self-corrective thesis argue that scientific method will refute false theories and find closer approximations to the truth in the long run. I discuss a contemporary interpretation of this thesis in terms of frequentist statistics in the context of the behavioral sciences. First, I identify experimental replications and systematic aggregation of evidence (meta-analysis) as the self-corrective mechanism. Then, I present a computer simulation study of scientific communities that implement this mechanism to argue that frequentist statistics may converge (...) upon a correct estimate or not depending on the social structure of the community that uses it. Based on this study, I argue that methodological explanations of the “replicability crisis” in psychology are limited and propose an alternative explanation in terms of biases. Finally, I conclude suggesting that scientific self-correction should be understood as an interaction effect between inference methods and social structures. (shrink)

One recursively enumerable real α dominates another one β if there are nondecreasing recursive sequences of rational numbers (a[n] : n ∈ ω) approximating α and (b[n] : n ∈ ω) approximating β and a positive constant C such that for all n, C(α − a[n]) ≥ (β − b[n]). See [R. M. Solovay, Draft of a Paper (or Series of Papers) on Chaitin’s Work, manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1974, p. 215] and [G. J. (...) Chaitin, IBM J. Res. Develop., 21 (1977), pp. 350–359]. We show that every recursively enumerable random real dominates all other recursively enumerable reals. We conclude that the recursively enumerable random reals are exactly the Ω-numbers [G. J. Chaitin, IBM J. Res. Develop., 21 (1977), pp. 350–359]. Second, we show that the sets in a universal Martin-Lof test for randomness have random measure, and every recursively enumerable random number is the sum of the measures represented in a universal Martin-Lof test. (shrink)

This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its applications and thus (...) presents the state of the art in the area. (shrink)

The problem of intentional identity, as originally offered by Peter Geach, says that there can be an anaphoric link between an indefinite term and a pronoun across a sentential boundary and across propositional attitude contexts, where the actual existence of an individual for the indefinite term is not presupposed. In this paper, a semantic resolution to this elusive puzzle is suggested, based on a new quantified intensional logic and game-theoretic semantics (GTS) of imperfect information. This constellation leads to an expressive (...) intensional language with a property of informational independence, argued to produce a purely semantic explication to intentional identity statements. One consequence is that various extra-logical and pragmatic factors become of secondary concern; it is possible to solve the puzzle by logico-semantic methods, albeit somewhat radically renewed ones. (shrink)

Theory of Mind (ToM), the cognitive capacity to attribute internal mental states to oneself and others, is a crucial component of social skills. Its formal study has become important, witness recent research on reasoning and information update by intelligent agents, and some proposals for its formal modelling have put forward settings based on Epistemic Logic (EL). Still, due to intrinsic idealisations, it is questionable whether EL can be used to model the high-order cognition of ‘real’ agents. This manuscript proposes a (...) framework that takes visibility, memory, perspective and communication as the main factors underpinning mental attributions. This is more in-line with findings in cognitive science and allows us to model well-known False-Belief Tasks that are typically used in testing people's ToM. We discuss some of the framework's technical features, arguing why it does justice to empirical observations. (shrink)

For the computability of subsets of real numbers, several reasonable notions have been suggested in the literature. We compare these notions in a systematic way by relating them to pairs of ‘basic’ ones. They turn out to coincide for full-dimensional convex sets; but on the more general class of regular sets, they reveal rather interesting ‘weaker/stronger’ relations. This is in contrast to single real numbers and vectors where all ‘reasonable’ notions coincide.

Computation is central to the foundations of modern cognitive science, but its role is controversial. Questions about computation abound: What is it for a physical system to implement a computation? Is computation sufficient for thought? What is the role of computation in a theory of cognition? What is the relation between different sorts of computational theory, such as connectionism and symbolic computation? In this paper I develop a systematic framework that addresses all of these questions. Justifying the role of computation (...) requires analysis of implementation, the nexus between abstract computations and concrete physical systems. I give such an analysis, based on the idea that a system implements a computation if the causal structure of the system mirrors the formal structure of the computation. This account can be used to justify the central commitments of artificial intelligence and computational cognitive science: the thesis of computational sufficiency, which holds that the right kind of computational structure suffices for the possession of a mind, and the thesis of computational explanation, which holds that computation provides a general framework for the explanation of cognitive processes. The theses are consequences of the facts that (a) computation can specify general patterns of causal organization, and (b) mentality is an organizational invariant, rooted in such patterns. Along the way I answer various challenges to the computationalist position, such as those put forward by Searle. I close by advocating a kind of minimal computationalism, compatible with a very wide variety of empirical approaches to the mind. This allows computation to serve as a true foundation for cognitive science. (shrink)

When computing is defined as the causal implementation of algorithms and algorithms are defined as effective decision procedures, human thought is mental computation only if it is governed by mental algorithms. An examination of ordinary thinking, however, suggests that most human thought processes are non-algorithmic. Digital machines, moreover, are mark-manipulating or string-processing systems whose marks or strings do not stand for anything for those systems, while minds are semiotic (or “signusing”) systems for which signs stand for other things for those (...) systems. Computing, at best, turns out to be no more than a special kind of thinking. (shrink)

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)

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a (...) simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual. (shrink)

This volume is a collection of selected papers presented at the Second Asia-Pacific Computing and Philsosophy Conference, which was held in Bangkok, Thailand in January 2005. The conference was organized by the Center for Ethics of Science and Technology, Chulalongkorn University on behalf of the International Association of Computing and Philosophy (www.ia-cap.org). Computing have had a long relationship with philosophy, starting from the problem of how symbols being manipulated in computing bear a relation to the outside world, to those of (...) artificial intelligence, robotics, computer simulation, and so on. Moreover, as computer technologies have become thoroughly pervasive in today's environment, there are also issues concerning social and ethical impacts brought about by them. The papers in the volume represent a wide variety of concerns and various dimensions within which computing and philosophy are related. Furthermore, it also represents some of the first attempts to highlight cultural dimensions of computing and philosophy, which became prominent when the conference was held for the first time within the milieu of an Asian culture. (The First Asia-Pacific Computing and Philosophy was held in Canberra, Australia.) Hence, many of the papers in the volume address this added dimension. Apart form the usual problems of how computers and human lives are interconnected, the papers here also discuss how computers are related to human lives as lived in a specific culture. Thus the book breaks a new ground and should be of interest to a wide range of scholars and students who are interested, not only on computing and philosophy generally construed, but also on this exciting new dimension of how the cultures of Asia, the West, and others bear upon the traditional issues in computing and philosophy, and on how this dimension raises some new concerns and agenda. Among the topics discussed in this volume are: political online forums in Saudi Arabia, e-democracy and structural transformation of public sphere, the Buddhist informational person, a glance into the lives of computerized generation in Thailand, technology and journalism in the market, local approaches and global potential (?) of information ethics, computer-enhanced good life, computer teaching ethics, and many others. (shrink)

Gualtiero Piccinini articulates and defends a mechanistic account of concrete, or physical, computation. A physical system is a computing system just in case it is a mechanism one of whose functions is to manipulate vehicles based solely on differences between different portions of the vehicles according to a rule defined over the vehicles. Physical Computation discusses previous accounts of computation and argues that the mechanistic account is better. Many kinds of computation are explicated, such as digital vs. analog, serial vs. (...) parallel, neural network computation, program-controlled computation, and more. Piccinini argues that computation does not entail representation or information processing although information processing entails computation. Pancomputationalism, according to which every physical system is computational, is rejected. A modest version of the physical Church-Turing thesis, according to which any function that is physically computable is computable by Turing machines, is defended. (shrink)

First-ever comprehensive introduction to the major new subject of quantum computing and quantum information.

The unique compendium re-assesses the value of future and emergent computing technologies via artistic and philosophical means. The book encourages scientists to adopt inspiring thinking of artists and philosophers to reuse scientific concepts in their works.The useful reference text consists of non-typical topics, where artistic and philosophical concepts encourage readers to adopt unconventional approaches towards computing and immerse themselves into discoveries of future emerging landscape.

Understanding Computers and Cognition presents an important and controversial new approach to understanding what computers do and how their functioning is related to human language, thought, and action. While it is a book about computers, Understanding Computers and Cognition goes beyond the specific issues of what computers can or can't do. It is a broad-ranging discussion exploring the background of understanding in which the discourse about computers and technology takes place. Understanding Computers and Cognition is written for a wide audience, (...) not just those professionals involved in computer design or artificial intelligence. It represents an important contribution to the ongoing discussion about what it means to be a machine, and what it means to be human. Book jacket. (shrink)

The self‐teaching hypothesis describes how children progress toward skilled sight‐word reading. It proposes that children do this via phonological recoding with assistance from contextual cues, to identify the target pronunciation for a novel letter string, and in so doing create an opportunity to self‐teach new orthographic knowledge. We present a new computational implementation of self‐teaching within the dual‐route cascaded (DRC) model of reading aloud, and we explore how decoding and contextual cues can work together to enable accurate self‐teaching under a (...) variety of circumstances. The new model (ST‐DRC) uses DRC’s sublexical route and the interactivity between the lexical and sublexical routes to simulate phonological recoding. Known spoken words are activated in response to novel printed words, triggering an opportunity for orthographic learning, which is the basis for skilled sight‐word reading. ST‐DRC also includes new computational mechanisms for simulating how contextual information aids word identification, and it demonstrates how partial decoding and ambiguous context interact to achieve irregular‐word learning. Beyond modeling orthographic learning and self‐teaching, ST‐DRC’s performance suggests new avenues for empirical research on how difficult word classes such as homographs and potentiophones are learned. (shrink)

Fluid neural networks can be used as a theoretical framework for a wide range of complex systems as social insects. In this article we show that collective logical gates can be built in such a way that complex computation can be possible by means of the interplay between local interactions and the collective creation of a global field. This is exemplified by a NOR gate. Some general implications for ant societies are outlined. ©.

We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π01 class P is a subshift if and only if there exists a computable function F mapping 2ℕ to 2ℕ such that P is the set of itineraries of elements of 2ℕ. Π01 subshifts are constructed in 2ℕ and in 2ℤ which have no computable elements. We also consider the symbolic dynamics of maps on the unit interval.

A Computable Universe is a collection of papers discussing computation in nature and the nature of computation, a compilation of the views of the pioneers in the contemporary area of intellectual inquiry focused on computational and informational theories of the world. This volume is the definitive source of informational/computational views of the world, and of cutting-edge models of the universe, both digital and quantum, discussed from a philosophical perspective as well as in the greatest technical detail. The book discusses the (...) foundations of computation in relation to nature. It focuses on two main questions: What is computation? How does nature compute? The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and their philosophical implications. The volume provides a state-of-the-art collection of technical papers and non-technical essays representing a field that takes information and computation to be key to understanding and explaining the basic structure underpinning physical reality. It also includes a new edition of Konrad Zuse's "Calculating Space", and a panel discussion transcription on the topic, featuring worldwide experts (including a Nobel prize) in quantum mechanics, physics, cognition, computation and algorithmic complexity.A Computable Universe is a collection of papers discussing computation in nature and the nature of computation, a compilation of the views of the pioneers in the contemporary area of intellectual inquiry focused on computational and informational theories of the world. This volume is the definitive source of informational/computational views of the world, and of cutting-edge models of the universe, both digital and quantum, discussed from a philosophical perspective as well as in the greatest technical detail. The book discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? How does nature compute? The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and their philosophical implications. The volume provides a state-of-the-art collection of technical papers and non-technical essays representing a field that takes information and computation to be key to understanding and explaining the basic structure underpinning physical reality. It also includes a new edition of Konrad Zuse's "Calculating Space", and a panel discussion transcription on the topic, featuring worldwide experts (including a Nobel prize) in quantum mechanics, physics, cognition, computation and algorithmic complexity. (shrink)

A study is described in which the effectiveness of a computer program (Hermes) on improving argumentative writing is tested. One group of students was randomly assigned to a control group and the other was assigned to the experimental group where they are asked to use the Hermes program. All students were asked to write essays on controversial topics to an opposed audience. Their essays were content-analysed for dialectical traits. Based on this analysis, it was concluded that the experimental group (...) wrote more dialectically effective essays than the control group, and the amount of difference between the control and experimental groups was related to the students' intellectual developmental level, as assessed by the Measure of Epistemological Reflection (MER). It is concluded that argumentative writing, operationalized here as dialectical writing, can be improved by computer-assisted instruction, but that attempts to teach such forms of thinking and writing need to take into account students' capacity to benefit from such instruction. Such capacity is defined here as intellectual development. (shrink)

Different characterizations of classes of shift dynamical systems via labeled digraphs, languages, and sets of forbidden words are investigated. The corresponding naming systems are analyzed according to reducibility and particularly with regard to the computability of the topological entropy relative to the presented naming systems. It turns out that all examined natural representations separate into two equivalence classes and that the topological entropy is not computable in general with respect to the defined natural representations. However, if a specific labeled digraph (...) representation - namely primitive, right-resolving labeled digraphs - of some class of shifts is considered, namely the shifts having the specification property, then the topological entropy gets computable. (shrink)

We investigate in the frame of TTE the computability of functions of the measurable sets from an infinite computable measure space such as the measure and the four kinds of set operations. We first present a series of undecidability and incomputability results about measurable sets. Then we construct several examples of computable topological spaces from the abstract infinite computable measure space, and analyze the computability of the considered functions via respectively each of the standard representations of the computable topological spaces (...) constructed. (shrink)

We study the computational complexity of reciprocal sentences with quantified antecedents. We observe a computational dichotomy between different interpretations of reciprocity, and shed some light on the status of the so-called Strong Meaning Hypothesis.

This makes his book especially valuable." -- Yuri Gurevich, Professor of Computer Science, University of Michigan Computability and complexity theory should be of central concern to practitioners as well as theorists.

This systematic investigation of computation and mental phenomena by a noted psychologist and computer scientist argues that cognition is a form of computation, that the semantic contents of mental states are encoded in the same general way as computer representations are encoded. It is a rich and sustained investigation of the assumptions underlying the directions cognitive science research is taking. 1 The Explanatory Vocabulary of Cognition 2 The Explanatory Role of Representations 3 The Relevance of Computation 4 The (...) Psychological Reality of Programs: Strong Equivalence 5 Constraining Functional Architecture 6 The Bridge from Physical to Symbolic: Transduction 7 Functional Architecture and Analogue Processes 8 Mental Imagery and Functional Architecture 9 Epilogue: What is Cognitive Science the Science of? (shrink)

Social choice rules are often evaluated and compared by inquiring whether they satisfy certain desirable criteria such as the Condorcet criterion, which states that an alternative should always be chosen when more than half of the voters prefer it over any other alternative. Many of these criteria can be formulated in terms of choice sets that single out reasonable alternatives based on the preferences of the voters. In this paper, we consider choice sets whose definition merely relies on the pairwise (...) majority relation. These sets include the Copeland set, the Smith set, the Schwartz set, von Neumann-Morgenstern stable sets, the Banks set, and the Slater set. We investigate the relationships between these sets and completely characterize their computational complexity, which allows us to obtain hardness results for entire classes of social choice rules. (shrink)

Provides a comprehensive introduction to ethical frameworks and of many of the modern issues arising in technology ethics including computing, privacy, artificial intelligence, and more.

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts (...) and methods originating from randomness enrich computability theory.The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory. (shrink)

In this paper we give an axiomatisation of the concept of a computability structure with partial sequences on a many‐sorted metric partial algebra, thus extending the axiomatisation given by Pour‐El and Richards in [9] for Banach spaces. We show that every Banach‐Mazur computable partial function from an effectively separable computable metric partial Σ‐algebraAto a computable metric partial Σ‐algebraBmust be continuous, and conversely, that every effectively continuous partial function with semidecidable domain and which preserves the computability of a computably enumerable dense (...) set must be computable. Finally, as an application of these results we give an alternative proof of the first main theorem for Banach spaces first proved by Pour‐El and Richards. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

Continuing the paper [7], in which the Blum-Shub-Smale approach to computability over the reals has been generalized to arbitrary algebraic structures, this paper deals with computability and recognizability over structures of infinite signature. It begins with discussing related properties of the linear and scalar real structures and of their discrete counterparts over the natural numbers. Then the existence of universal functions is shown to be equivalent to the effective encodability of the underlying structure. Such structures even have universal functions satisfying (...) the s-m-n theorem and related features. The real and discrete examples are discussed with respect to effective encodability. Megiddo structures and computational extensions of effectively encodable structures are encodable, too. As further variants of universality, universal functions with enumerable sets of program codes and such ones with constructible codes are investigated. Finally, the existence of m-complete sets is shown to be independent of the effective encodability of structures, and the linear and scalar structures are discussed once more, under this aspect. (shrink)

The theory of inner functions plays an important role in the study of bounded analytic functions. Inner functions are also useful in applied mathematics. Two foundational results in this theory are Frostman's Theorem and the Factorization Theorem. We prove a uniformly computable version of Frostman's Theorem. We then show that the Factorization Theorem is not uniformly computably true. We then show that for an inner function u with infinitely many zeros, the Blaschke sum of u provides the exact amount of (...) information necessary to compute the factorization of u. Along the way, we prove some uniform computability results for Blaschke products; these results play a key role in the analysis of factorization. We also give some computability results concerning zeros and singularities of analytic functions. We use Type-Two Effectivity as our foundation. (shrink)

_Minds, Brains, Computers_ serves as both an historical and interdisciplinary introduction to the foundations of cognitive science.

According to usage‐based approaches to language acquisition, linguistic knowledge is represented in the form of constructions—form‐meaning pairings—at multiple levels of abstraction and complexity. The emergence of syntactic knowledge is assumed to be a result of the gradual abstraction of lexically specific and item‐based linguistic knowledge. In this article, we explore how the gradual emergence of a network consisting of constructions at varying degrees of complexity can be modeled computationally. Linguistic knowledge is learned by observing natural language utterances in an ambiguous (...) context. To determine meanings of constructions starting from ambiguous contexts, we rely on the principle of cross‐situational learning. While this mechanism has been implemented in several computational models, these models typically focus on learning mappings between words and referents. In contrast, in our model, we show how cross‐situational learning can be applied consistently to learn correspondences between form and meaning beyond such simple correspondences. (shrink)

This paper outlines the development of a proof-of-concept workflow using machine learning and computer vision techniques to unlock the data within digitized handwritten US Census forms from the 1950s. The 1950s US Census includes over 6.5 million page images and was only recently made available to the public on April 1, 2022, following a 72-year access restriction period. Our project uses computational treatments to assist researchers in their efforts to recover and preserve the history of the erased Sacramento Japantown. (...) Sacramento once housed the fourth largest Japantown in the United States before experiencing WWII Japanese American Incarceration and the 1950s US Government program of urban renewal. The goal is to augment a researcher’s work in selecting a subset of Census pages for further transcription and analysis. We demonstrate a workflow for extracting demographic information using computer vision for image segmentation, and machine learning for handwritten character recognition. The workflow consists of a computational filtering process for Census records and a user interface for page review. These computational techniques are suitable for other cities, states, and communities, and demonstrate new strategies to unlock vital demographic information. The approach highlights the potential benefits of computational techniques for the analysis of form-based historical records of the twentieth century that can have an impact on social justice. (shrink)

Digital computers play a special role in cognitive science—they may actually be instances of the phenomenon they are being used to model. This paper surveys some of the main issues involved in understanding the relationship between digital computers and cognition. It sketches the role of digital computers within orthodox computational cognitive science, in the light of a recently emerging alternative approach based around dynamical systems.

This book brings together the latest technological research in computational intelligence and fuzzy logic as a way to care for our environment, highlighting current advances and future trends in environmental sustainability using the principles of soft computing.

Since the late 1970s, the field of evolutionary biology has undergone empirical and theoretical developments that have threaten the pillars of evolutionary theory. Some evolutionary biologists have recently argued that evolutionary biology is not experiencing a paradigm shift, but an expansion of the modern synthesis. Philosophers of biology focusing on scientific practices seem to agree with this pluralistic interpretation and have argued that evolutionary theory should rather be seen as an organized network of multiple problem agendas with diverse disciplinary contributors. (...) In this paper, I apply a computational analysis to study the dynamics and conceptual structure of one of the main emerging problem agendas in evolutionary biology: evolvability. I have used CiteSpace, an application for visualizing and analyzing trends and patterns in scientific literature that applies cocitation analysis to identify scientific specialities. I analyze the main clusters of the evolvability cocitation network with the aim to identify the main research lines and the interdisciplinary relationships that structure this research front. I then compare these results with the existing classifications of evolvability concepts, and identify four main conceptual tensions within the definitions of evolvability. Finally, I argue that there is a lot of usefulness in the inconsistency in which the term evolvability is used in biological research. I claim that evolvability research has set up “trading zones” in biology that make possible interdisciplinary exchanges. (shrink)

We begin by distinguishing computationalism from a number of other theses that are sometimes conflated with it. We also distinguish between several important kinds of computation: computation in a generic sense, digital computation, and analog computation. Then, we defend a weak version of computationalism—neural processes are computations in the generic sense. After that, we reject on empirical grounds the common assimilation of neural computation to either analog or digital computation, concluding that neural computation is sui generis. Analog computation requires continuous (...) signals; digital computation requires strings of digits. But current neuroscientific evidence indicates that typical neural signals, such as spike trains, are graded like continuous signals but are constituted by discrete functional elements (spikes); thus, typical neural signals are neither continuous signals nor strings of digits. It follows that neural computation is sui generis. Finally, we highlight three important consequences of a proper understanding of neural computation for the theory of cognition. First, understanding neural computation requires a specially designed mathematical theory (or theories) rather than the mathematical theories of analog or digital computation. Second, several popular views about neural computation turn out to be incorrect. Third, computational theories of cognition that rely on non-neural notions of computation ought to be replaced or reinterpreted in terms of neural computation. (shrink)

Computational methods such as computer simulations, Monte Carlo methods, and agent-based modeling have become the dominant techniques in many areas of science. Extending Ourselves contains the first systematic philosophical account of these new methods, and how they require a different approach to scientific method. Paul Humphreys draws a parallel between the ways in which such computational methods have enhanced our abilities to mathematically model the world, and the more familiar ways in which scientific instruments have expanded our access to (...) the empirical world. This expansion forms the basis for a new kind of empiricism, better suited to the needs of science than the older anthropocentric forms of empiricism. Human abilities are no longer the ultimate standard of epistemological correctness.Humphreys also includes arguments for the primacy of properties rather than objects, the need to consider technological constraints when appraising scientific methods, and a detailed account of how the path from computational template to scientific application is constructed. This last feature allows us to hold a form of selective realism in which anti-realist arguments based on formal reconstructions of theories can be avoided. One important consequence of the rise of computational methods is that the traditional organization of the sciences is being replaced by an organization founded on computational templates.Extending Ourselves will be of interest to philosophers of science, epistemologists, and to anyone interested in the role played by computers in modern science. (shrink)

According to some philosophers, computational explanation is proprietary
to psychology—it does not belong in neuroscience. But neuroscientists routinely offer computational explanations of cognitive phenomena. In fact, computational explanation was initially imported from computability theory into the science of mind by neuroscientists, who justified this move on neurophysiological grounds. Establishing the legitimacy and importance of computational explanation in neuroscience is one thing; shedding light on it is another. I raise some philosophical questions pertaining to computational explanation and outline some promising answers that (...) are being developed by a number of authors. (shrink)

Classic text considersgeneral theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, computable functionals, classification of unsolvable decision problems and more.

What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr (...) Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. The later chapters provide an introduction to more advanced topics such as Gildel's incompleteness theorem, degrees of unsolvability, the Recursion theorems and the theory of complexity of computation. Computability is thus a branch of mathematics which is of relevance also to computer scientists and philosophers. Mathematics students with no prior knowledge of the subject and computer science students who wish to supplement their practical expertise with some theoretical background will find this book of use and interest. (shrink)

This book addresses key conceptual issues relating to the modern scientific and engineering use of computer simulations. It analyses a broad set of questions, from the nature of computer simulations to their epistemological power, including the many scientific, social and ethics implications of using computer simulations. The book is written in an easily accessible narrative, one that weaves together philosophical questions and scientific technicalities. It will thus appeal equally to all academic scientists, engineers, and researchers in industry (...) interested in questions related to the general practice of computer simulations. (shrink)