Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part II supplements (...) the material covered in Part I and introduces some of the newer ideas and the more profound results of logical research in the twentieth century. Subsequent chapters introduce the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Godel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Godel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. Unabridged republication of the edition published by John Wiley & Sons, Inc. New York, 1967. Preface. Bibliography. Theorem and Lemma Numbers: Pages. List of Postulates. Symbols and Notations. Index. (shrink)

Cognitive Science is a single-source undergraduate text that broadly surveys the theories and empirical results of cognitive science within a consistent computational perspective. In addition to covering the individual contributions of psychology, philosophy, linguistics, and artificial intelligence to cognitive science, the book has been revised to introduce the connectionist approach as well as the classical symbolic approach and adds a new chapter on cognitively related advances in neuroscience. Cognitive science is a rapidly evolving field that is characterized by considerable contention (...) among different views and approaches. Cognitive Science presents these in a relatively neutral manner. It covers many new orientations theories and findings, embedding them in an integrated computational perspective and establishing a sense of continuity and contrast with more traditional work in cognitive science. The text assumes no prerequisite knowledge, introducing all topics in a uniform, accessible style. Many topics, such as natural language processing and vision, however, are developed in considerable depth, which allows the book to be used with more advanced undergraduates or even in beginning graduate settings. A Bradford Book. (shrink)

Semantic Engines: An Introduction to Mind Design, John C. Haugeland; Computer Science as Empirical Inquiry: Symbols and Search, Alan Newell and Herbert A. Simon; Complexity and the Study of Artificial and Human Intelligence, Zenon Pylyshyn; A Framework for Representing Knowledge, Marvin Minsky; Artificial Intelligence---A Personal View, David Marr; Artificial Intelligence Meets Natural Stupidity, Drew McDermott; From Micro-Worlds to Knowledge Representation: AI at an Impasse, Hubert L. Dreyfus; Reductionism and the Nature of Psychology, Hilary Putnam; Intentional Systems, Daniel C. Dennett; The (...) Nature and Plausibility of Cognitivism, John C. Haugeland; Minds, Brains, and Programs, John R. Searle; MethodologicalSolipsism Considered as a Research Strategy in Cognitive Psychology, Jerry A. Fodor; The Material Mind, Donald Davidson. (shrink)

The title of The Rediscovery of the Mind suggests the question "When was the mind lost?" Since most people may not be aware that it ever was lost, we must also then ask "Who lost it?" It was lost, of course, only by philosophers, by certain philosophers. This passed unnoticed by society at large. The "rediscovery" is also likely to pass unnoticed. But has the mind been rediscovered by the same philosophers who "lost" it? Probably not. John Searle is an (...) analytic philosopher, with some of the same notions as the positivists and behaviorists who rejected consciousness and "lost" the mind in the first place, but he also does not sound like the kind of reductionist who would have joined that crowd. His views, indeed, are sensible enough, and some of his insights so important, that it is a shame to find his thought profoundly limited by some of the same mistakes and prejudices that ruined philosophy, and not just philosophy of mind, under the influence of those positivists and behaviorists. There is enough of genuine value in his treatment, that it can easily be taken up and, with relatively slight modification, added to what is of permanent value in the history of philosophy. (shrink)

This paper explores Church's Thesis and related claims madeby Turing. Church's Thesis concerns computable numerical functions, whileTuring's claims concern both procedures for manipulating uninterpreted marksand machines that generate the results that these procedures would yield. Itis argued that Turing's claims are true, and that they support (the truth of)Church's Thesis. It is further argued that the truth of Turing's and Church'sTheses has no interesting consequences for human cognition or cognitiveabilities. The Theses don't even mean that computers can do as much (...) as peoplecan when it comes to carrying out effective procedures. For carrying out aprocedure is a purposive, intentional activity. No actual machine does, orcan do, as much. (shrink)

This paper explores Church's Thesis and related claims madeby Turing. Church's Thesis concerns computable numerical functions, whileTuring's claims concern both procedures for manipulating uninterpreted marksand machines that generate the results that these procedures would yield. Itis argued that Turing's claims are true, and that they support (the truth of)Church's Thesis. It is further argued that the truth of Turing's and Church'sTheses has no interesting consequences for human cognition or cognitiveabilities. The Theses don't even mean that computers can do as much (...) as peoplecan when it comes to carrying out effective procedures. For carrying out aprocedure is a purposive, intentional activity. No actual machine does, orcan do, as much. (shrink)

We critically discuss Cleland''s analysis of effective procedures as mundane effective procedures. She argues that Turing machines cannot carry out mundane procedures, since Turing machines are abstract entities and therefore cannot generate the causal processes that are generated by mundane procedures. We argue that if Turing machines cannot enter the physical world, then it is hard to see how Cleland''s mundane procedures can enter the world of numbers. Hence her arguments against versions of the Church-Turing thesis for number theoretic functions (...) miss the mark. (shrink)

The idea that human thought requires the execution of mental algorithms provides a foundation for research programs in cognitive science, which are largely based upon the computational conception of language and mentality. Consideration is given to recent work by Penrose, Searle, and Cleland, who supply various grounds for disputing computationalism. These grounds in turn qualify as reasons for preferring a non-computational, semiotic approach, which can account for them as predictable manifestations of a more adquate conception. Thinking does not ordinarily require (...) the execution of mental algorithms, which appears to be at best no more than one rather special kind of thinking. (shrink)

The idea that human thought requires the execution of mental algorithms provides a foundation for research programs in cognitive science, which are largely based upon the computational conception of language and mentality. Consideration is given to recent work by Penrose, Searle, and Cleland, who supply various grounds for disputing computationalism. These grounds in turn qualify as reasons for preferring a non-computational, semiotic approach, which can account for them as predictable manifestations of a more adquate conception. Thinking does not ordinarily require (...) the execution of mental algorithms, which appears to be at best no more than one rather special kind of thinking. (shrink)

Little, Brown, 1992 Review by Glenn Branch on Jul 5th 1999 Volume: 3, Number: 27.

The issue of what distinguishes systems which have original intentionalityfrom those which do not has been brought into sharp focus by Saul Kripke inhis discussion of the sceptical paradox he attributes to Wittgenstein.In this paper I defend a sophisticated version of the dispositionalistaccount of meaning against the principal objection raised by Kripke in hisattack on dispositional views. I argue that the objection put by the sceptic,to the effect that the dispositionalist cannot give a satisfactory account ofnormativity and mistake, in fact (...) comprises a number of distinct lines ofargument, all of which can be satisfactorily answered by the dispositionalist. (shrink)

The Church-Turing thesis makes a bold claim about the theoretical limits to computation. It is based upon independent analyses of the general notion of an effective procedure proposed by Alan Turing and Alonzo Church in the 1930''s. As originally construed, the thesis applied only to the number theoretic functions; it amounted to the claim that there were no number theoretic functions which couldn''t be computed by a Turing machine but could be computed by means of some other kind of effective (...) procedure. Since that time, however, other interpretations of the thesis have appeared in the literature. In this paper I identify three domains of application which have been claimed for the thesis: (1) the number theoretic functions; (2) all functions; (3) mental and/or physical phenomena. Subsequently, I provide an analysis of our intuitive concept of a procedure which, unlike Turing''s, is based upon ordinary, everyday procedures such as recipes, directions and methods; I call them mundane procedures. I argue that mundane procedures can be said to be effective in the same sense in which Turing machine procedures can be said to be effective. I also argue that mundane procedures differ from Turing machine procedures in a fundamental way, viz., the former, but not the latter, generate causal processes. I apply my analysis to all three of the above mentioned interpretations of the Church-Turing thesis, arguing that the thesis is (i) clearly false under interpretation (3), (ii) false in at least some possible worlds (perhaps even in the actual world) under interpretation (2), and (iii) very much open to question under interpretation (1). (shrink)

Horsten and Roelants have raised a number of important questions about my analysis of effective procedures and my evaluation of the Church-Turing thesis. They suggest that, on my account, effective procedures cannot enter the mathematical world because they have a built-in component of causality, and, hence, that my arguments against the Church-Turing thesis miss the mark. Unfortunately, however, their reasoning is based upon a number of misunderstandings. Effective mundane procedures do not, on my view, provide an analysis of ourgeneral concept (...) of an effective procedure; mundane procedures and Turing machine procedures are different kinds of procedure. Moreover, the same sequence ofparticular physical action can realize both a mundane procedure and a Turing machine procedure; it is sequences of particular physical actions, not mundane procedures, which enter the world of mathematics. I conclude by discussing whether genuinely continuous physical processes can enter the world of real numbers and compute real-valued functions. I argue that the same kind of correspondence assumptions that are made between non-numerical structures and the natural numbers, in the case of Turing machines and personal computers, can be made in the case of genuinely continuous, physical processes and the real numbers. (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.

1. WHAT IS ARTIFICIAL INTELLIGENCE? One of the fascinating aspects of the field of artificial intelligence (AI) is that the precise nature of its subject ..

The purpose of this paper is to explore three alternative frameworks for understanding the nature of language and mentality, which accent syntactical, semantical, and pragmatical aspects of the phenomena with which they are concerned, respectively. Although the computational conception currently exerts considerable appeal, its defensibility appears to hinge upon an extremely implausible theory of the relation of form to content. Similarly, while the representational approach has much to recommend it, its range is essentially restricted to those units of language that (...) can be understood in terms of undefined units. Thus, the only alternative among these three that can account for the meaning of primitive units of language is one emphasizing the basic role of skills, habits, and tendencies in relating signs and dispositions. (shrink)

This essay considers what it means to understand natural language and whether a computer running an artificial-intelligence program designed to understand natural language does in fact do so. It is argued that a certain kind of semantics is needed to understand natural language, that this kind of semantics is mere symbol manipulation (i.e., syntax), and that, hence, it is available to AI systems. Recent arguments by Searle and Dretske to the effect that computers cannot understand natural language are discussed, and (...) a prototype natural-language-understanding system is presented as an illustration. (shrink)