Andrew Boucher (1997) argues that ``parallel computation is fundamentally different from sequential computation'' (p. 543), and that this fact provides reason to be skeptical about whether AI can produce a genuinely intelligent machine. But parallelism, as I prove herein, is irrelevant. What Boucher has inadvertently glimpsed is one small part of a mathematical tapestry portraying the simple but undeniable fact that physical computation can be fundamentally different from ordinary, ``textbook'' computation (whether parallel or sequential). This tapestry does indeed immediately imply (...) that human cognition may be uncomputable. (shrink)

The dominant scientific and philosophical view of the mind – according to which, put starkly, cognition is computation – is refuted herein, via specification and defense of the following new argument: Computation is reversible; cognition isn't; ergo, cognition isn't computation. After presenting a sustained dialectic arising from this defense, we conclude with a brief preview of the view we would put in place of the cognition-is-computation doctrine.

Covers first-order language in method appropriate for first and second courses in logic. CD-ROM consists of a new book, 3 programs,and an Internet-based grading service.

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.

We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. Everyset. for example, is decidable by such machines, and the semi-decidable sets form a portion of thesets. Our oracle concept leads to a notion of relative computability for sets of reals and a rich degree structure, stratified by two natural jump operators.

When Ken Malone investigates a case of something causing mental static across the United States, he is teleported to a world that doesn't exist.

Modal logic, developed as an extension of classical propositional logic and first-order quantification theory, integrates the notions of possibility and necessity and necessary implication. Arguments whose understanding depends on some fundamental knowledge of modal logic have always been important in philosophy of religion, metaphysics, and epistemology. Moreover, modal logic has become increasingly important with the use of the concept of "possible worlds" in these areas. Introductory Modal Logic fills the need for a basic text on modal logic, accessible to students (...) of elementary symbolic logic. Kenneth Konyndyk presents a natural deduction treatment of propositional modal logic and quantified modal logic, historical information about its development, and discussions of the philosophical issues raised by modal logic. Characterized by clear and concrete explanations, appropriate examples, and varied and challenging exercises, Introductory Modal Logic makes both modal logic and the possible-worlds metaphysics readily available to the introductory level student. (shrink)

NOW IN PAPERBACK"€"Starting from a collection of simple computer experiments"€"illustrated in the book by striking computer graphics"€"Stephen Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe.

Determinism is a perennial topic of philosophical discussion. Very little acquaintance with the philosophical literature is needed to reveal the Tower of ...

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an (...) up-to-date and reliable guide essential for the student. (shrink)

This paper is written from the perspective of a computer scientist and addressed to theoretical physicists. As a consequence it may seem somewhat unusual, but rest assured, everything is really quite simple! The point of this paper is that the study of certain phenomena from computer science suggests that there are computer systems (cellular automata) that may be appropriate as models for microscopic physical phenomena. Cellular automata are now being used to model varied physical phenomena normally modelled by wave equations, (...) fluid dynamics, Ising models, etc. We hypothesize that there will be found a single cellular automaton rule that models all of microscopic physics; and models it exactly. We call this field DM, for digital mechanics. (shrink)