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)

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)

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)

Begin discussing various forms of G1 put into the form: If a first order theory satisfies one or more adequacy conditions then it has one or more wildness properties. We continue with the new ‘no interpretation’ forms of G2, which are fundamentally model theoretic formulations. We also give corresponding model theoretic characterizations of the consistency statement Con(T) for finitely axiomatized T. We present the known proof of the 1-Con form by G2 by transparent diagonalization and discuss attempts to do so (...) for G2. (shrink)

Lorenzen's article has immediately been recognised as a landmark in the history of infinitary proof theory. We propose a translation and this introduction in order to publicise its approach and method of proof, without any ordinal assignment. It is best known for providing a constructive proof of consistency for ramified type theory without axiom of reducibility by showing that it is a part of a trivially consistent ‘inductive calculus’ that describes our knowledge of arithmetic without detour; the proof resorts only (...) to the inductive definition of formulas and theorems. It proposes a definition of semilattices, of distributive lattices, of pseudocomplemented semilattices, and of countably complete boolean algebras as deductive calculi, and constructs conservatively the respective free objects over a given preordered set. It illustrates that lattice theory is a bridge between algebra and logic: the construction of an element corresponds to a step in a proof. The fruitfulness of its use of the ω-rule is immediately recognised by Schütte. It triggers the analysis by Ackermann (1951) of the infinitary inductive definition of the accessibility predicate with the goal of proving transfinite induction up to ordinal terms beyond ϵ0. (shrink)

The philosophy of computer science is concerned with issues that arise from reflection upon the nature and practice of the discipline of computer science. This book presents an approach to the subject that is centered upon the notion of computational artefact. It provides an analysis of the things of computer science as technical artefacts. Seeing them in this way enables the application of the analytical tools and concepts from the philosophy of technology to the technical artefacts of (...) computer science. With this conceptual framework the author examines some of the central philosophical concerns of computer science including the foundations of semantics, the logical role of specification, the nature of correctness, computational ontology and abstraction, formal methods, computational epistemology and explanation, the methodology of computer science, and the nature of computation. The book will be of value to philosophers and computer scientists. (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)

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)

Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions ...

Searle’s celebrated Chinese room thought experiment was devised as an attempted refutation of the view that appropriately programmed digital computers literally are the possessors of genuine mental states. A standard reply to Searle, known as the “robot reply” (which, I argue, reflects the dominant approach to the problem of content in contemporary philosophy of mind), consists of the claim that the problem he raises can be solved by supplementing the computational device with some “appropriate” environmental hookups. I argue that not (...) only does Searle himself casts doubt on the adequacy of this idea by applying to it a slightly revised version of his original argument, but that the weakness of this encoding-based approach to the problem of intentionality can also be exposed from a somewhat different angle. Capitalizing on the work of several authors and, in particular, on that of psychologist Mark Bickhard, I argue that the existence of symbol-world correspondence is not a property that the cognitive system itself can appreciate, from its own perspective, by interacting with the symbol and therefore, not a property that can constitute intrinsic content. The foundational crisis to which Searle alluded is, I conclude, very much alive. (shrink)

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.

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.

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)

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)

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

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)

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)

In this paper we show that for any set X ⊆ ω there exists a structure [MATHEMATICAL SCRIPT CAPITAL A] that has no presentation computable in X such that [MATHEMATICAL SCRIPT CAPITAL A]2 has a computable presentation. We also show that there exists a structure [MATHEMATICAL SCRIPT CAPITAL A] with infinitely many computable isomorphism types such that [MATHEMATICAL SCRIPT CAPITAL A]2 has exactly one computable isomorphism type.

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)

Molecular models are typical topics of chemical research depending on the technical standards of observation, computation, and representation. Mathematically, molecular structures have been represented by means of graph theory, topology, differential equations, and numerical procedures. With the increasing capabilities of computer networks, computational models and computer-assisted visualization become an essential part of chemical research. Object-oriented programming languages create a virtual reality of chemical structures opening new avenues of exploration and collaboration in chemistry. From an epistemic point of view, (...) virtual reality is a new computer-assisted tool of human imagination and recognition. (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)

A distinction between the use of computational models in cognitive science and a philosophically inspired reductivist thesis is developed. PF is found questionable for phenomenal states, and, by analogy, dubious for the nonphenomenal introspectible mental states of common sense. PF is also shown to be threatened for the sub-cognitive theoretical states of cognitive science by the work of the so-called New Connectionists. CMM is shown to be less vulnerable to these criticisms.

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)

Computer simulations may allow us to understand the earth’s fickle climate and how it is affected by detours of the great ocean currents. These detours cause abrupt coolings -- the average global temperature can drop dramatically in just a few years, with droughts that set up El-Niño-like forest fires even in the tropics. While volcanic eruptions and Antarctic ice shelf collapses can also abruptly cool things, what we’re talking about here is a flip-flop: a few centuries later, there’s an (...) equally abrupt rewarming. This cycle has repeated every few thousand years (though it has been 12,000 years since the most recent one). (shrink)

~Et moi,.... si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and (...) non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics...'; 'One service logic has rendered com­ puter science...'; 'One service category theory has rendered mathematics...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. (shrink)

Let R be a real closed field. An integer part I for R is a discretely ordered subring such that for every \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r \in R}$$\end{document}, there exists an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${i \in I}$$\end{document} so that i ≤ r < i + 1. Mourgues and Ressayre (J Symb Logic 58:641–647, 1993) showed that every real closed field has an integer part. The procedure of Mourgues and (...) Ressayre appears to be quite complicated. We would like to know whether there is a simple procedure, yielding an integer part that is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^0_2(R)}$$\end{document} —limit computable relative to R. We show that there is a maximal Z-ring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${I \subseteq R}$$\end{document} which is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^0_2(R)}$$\end{document}. However, this I may not be an integer part for R. By a result of Wilkie (Logic Colloquium ’77), any Z-ring can be extended to an integer part for some real closed field. Using Wilkie’s ideas, we produce a real closed field R with a Z-ring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${I \subseteq R}$$\end{document} such that I does not extend to an integer part for R. For a computable real closed field, we do not know whether there must be an integer part in the class \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^0_2}$$\end{document}. We know that certain subclasses of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^0_2}$$\end{document} are not sufficient. We show that for each \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n \in \omega}$$\end{document}, there is a computable real closed field with no n-c.e. integer part. In fact, there is a computable real closed field with no n-c.e. integer part for any n. (shrink)

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)

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)

Ubiquitous Computing bezeichnet keine konkrete Technologie, sondern eine informatische Vision allgegenwärtiger Datenverarbeitung und Nutzung informatischer Systeme, bei der es weder nennenswerte Bedienungsanforderungen noch Hardwarebelastungen für den Nutzer gibt. Ubiquitäre Systeme agieren quasi unsichtbar im Hintergrund unseres Handlungsfeldes. Die bisherigen Realisierungen sind in unterschiedlichen informatischen und nachrichtentechnischen Technologien konkretisiert.

Since the cognitive revolution, it has become commonplace that cognition involves both computation and information processing. Is this one claim or two? Is computation the same as information processing? The two terms are often used interchangeably, but this usage masks important differences. In this paper, we distinguish information processing from computation and examine some of their mutual relations, shedding light on the role each can play in a theory of cognition. We recommend that theorists of cognition be explicit and careful (...) in choosing notions of computation and information and connecting them together.Keywords: Computation; Information processing; Computationalism; Computational theory of mind; Cognitivism. (shrink)

This paper has three dimensions, historical, theoretical and social. The historical dimension is to show how the Ciceronian system of dialectical argumentation served as a precursor to computational models of argumentation schemes such as Araucaria and Carneades. The theoretical dimension is to show concretely how these argumentation schemes reveal the interdependency of rhetoric and logic, and so the interdependency of the normative with the empirical. It does this by identifying points of disagreement in a dialectical format through using argumentation schemes (...) and critical questions. The social dimension is to show how the Ciceronian dialectical viewpoint integrates with the use of computational tools that can be used to support the principle of reason-based deliberation and facilitate deliberative democracy. (shrink)

The Computational Theory of Mind (CTM) holds that cognitive processes are essentially computational, and hence computation provides the scientific key to explaining mentality. The Representational Theory of Mind (RTM) holds that representational content is the key feature in distinguishing mental from non-mental systems. I argue that there is a deep incompatibility between these two theoretical frameworks, and that the acceptance of CTM provides strong grounds for rejecting RTM. The focal point of the incompatibility is the fact that representational content is (...) extrinsic to formal procedures as such, and the intended interpretation of syntax makes no difference to the execution of an algorithm. So the unique 'content' postulated by RTM is superfluous to the formal procedures of CTM. And once these procedures are implemented in a physical mechanism, it is exclusively the causal properties of the physical mechanism that are responsible for all aspects of the system's behaviour. So once again, postulated content is rendered superfluous. To the extent that semantic content may appear to play a role in behaviour, it must be syntactically encoded within the system, and just as in a standard computational artefact, so too with the human mind/brain - it's pure syntax all the way down to the level of physical implementation. Hence 'content' is at most a convenient meta-level gloss, projected from the outside by human theorists, which itself can play no role in cognitive processing. (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)

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)

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.

This chapter contains sections titled: Introduction The ACL2 System A Modeling Problem Case Studies.

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)

Only computational explanations of a content‐involving sort can answer certain ‘how’‐questions; can support content‐involving counterfactuals; and have the generality characteristic of psychological explanations. Purely formal characteriza‐tions of computations have none of these properties, and do not determine content. These points apply not only to psychological explanation, but to Turing machines themselves. Computational explanations which involve content are not opposed to naturalism. They are also required if we are to explain the content‐involving properties of mental states.

The computational mind paradigm proposes that the mind is an information-processing system equivalent to a Turing machine. Some proponents of this view hope to emulate the mind using methods such as symbolism, connectionism or more biological models. In the present work, the following question is posed: is a computational mind capable of deciding (yes or no) whether a proposed emulation of the mind is indeed an emulation of the mind? It is argued that this is not possible. Intuitively, the reason (...) a computational mind cannot recognize an emulation of itself is for much the same reason that a set of scales cannot weigh itself. In this article, a formal argument for this stance is given by noticing the following: for a computational mind to recognize an emulation of itself, it must be capable of deciding whether two Turing Machines (namely, itself and the proposed emulation) are functionally equivalent. This task is uncomputable, and thus there cannot exist a computational procedure in the mind that is capable of recognizing an emulation of itself. (shrink)

This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book 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. John Burgess has now enhanced the book by adding a selection of problems at the end of each chapter, and by reorganising and rewriting chapters to make them more independent of each other and thus to increase the range of options available to instructors as to what to cover and what to defer. (shrink)

In an attempt to determine the epistemic status of computer simulation results, philosophers of science have recently explored the similarities and differences between computer simulations and experiments. One question that arises is whether and, if so, when, simulation results constitute novel empirical data. It is often supposed that computer simulation results could never be empirical or novel because simulations never interact with their targets, and cannot go beyond their programming. This paper argues against this position by examining (...) whether, and under what conditions, the features of empiricality and novelty could be displayed by computer simulation data. I show that, to the extent that certain familiar measurement results have these features, so can some computer simulation results. (shrink)

The title of the article was inspired by the novel by John Steinbeck “Of Mice and Men” (1937) and the poem by Robet Burns about the deception of human plans. Even the best of them often lead astray, or their far-reaching negative effects are revealed. As it seems, nowadays nature (“mice”) and men (people) are in a breakthrough period – in the geological sense between the old and the new era, the Holocene and the Anthropocene, in the cultural sense – (...) between the analogue and digital era that can be – and it should actually be called a digit. Levi-Strauss in his essay “Raw and cooked” points to the groundbreaking for the emergence of human culture the use of fire in the preparation of food, and therefore the transition from nature to culture, and its foundation – the kitchen [12]. At present, this new phase of transition can be seen in the digitization of interpersonal communication and its current correlation – cross-linking. It was announced by the famous Turing machine (1936), a computer design and layout, which was realized in the 1940s and 1950s, and enter in mass production at its end, networked on a global scale in the 1990s and make mobile in the second decade of the 21st century in the form of a smartphone. (shrink)