The standard theory of computation excludes computations whose completion requires an infinite number of steps. Malament-Hogarth spacetimes admit observers whose pasts contain entire future-directed, timelike half-curves of infinite proper length. We investigate the physical properties of these spacetimes and ask whether they and other spacetimes allow the observer to know the outcome of a computation with infinitely many steps.

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)

The proper treatment of computationalism, as the thesis that cognition is computable, is presented and defended. Some arguments of James H. Fetzer against computationalism are examined and found wanting, and his positive theory of minds as semiotic systems is shown to be consistent with computationalism. An objection is raised to an argument of Selmer Bringsjord against one strand of computationalism, namely, that Turing-Test± passing artifacts are persons, it is argued that, whether or not this objection holds, such artifacts will inevitably (...) be persons. (shrink)

On the occasion of a first conference on Cognitive Science, it seems appropriate to review the basis of common understanding between the various disciplines. In my estimate, the most fundamental contribution so far of artificial intelligence and computer science to the joint enterprise of cognitive science has been the notion of a physical symbol system, i.e., the concept of a broad class of systems capable of having and manipulating symbols, yet realizable in the physical universe. The notion of symbol so (...) defined is internal to this concept, so it becomes a hypothesis that this notion of symbols includes the symbols that we humans use every day of our lives. In this paper we attempt systematically, but plainly, to lay out the nature of physical symbol systems. Such a review is in ways familiar, but not thereby useless. Restatement of fundamentals is an important exercise. (shrink)

Explaining the mind by building machines with minds runs into the other-minds problem: How can we tell whether any body other than our own has a mind when the only way to know is by being the other body? In practice we all use some form of Turing Test: If it can do everything a body with a mind can do such that we can't tell them apart, we have no basis for doubting it has a mind. But what is (...) "everything" a body with a mind can do? Turing's original "pen-pal" version (the TT) only tested linguistic capacity, but Searle has shown that a mindless symbol-manipulator could pass the TT undetected. The Total Turing Test (TTT) calls for all of our linguistic and robotic capacities; immune to Searle's argument, it suggests how to ground a symbol manipulating system in the capacity to pick out the objects its symbols refer to. No Turing Test, however, can guarantee that a body has a mind. Worse, nothing in the explanation of its successful performance requires a model to have a mind at all. Minds are hence very different from the unobservables of physics (e.g., superstrings); and Turing Testing, though essential for machine-modeling the mind, can really only yield an explanation of the body. (shrink)

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)

Is it true that if zombies---creatures who are behaviorally indistinguishable from us, but no more conscious than a rock-are logically possible, the computational conception of mind is false? Are zombies logically possible? Are they physically possible? This paper is a careful, sustained argument for affirmative answers to these three questions.

Having, as it is generally agreed, failed to destroy the computational conception of mind with the G\"{o}delian attack he articulated in his {\em The Emperor's New Mind}, Penrose has returned, armed with a more elaborate and more fastidious G\"{o}delian case, expressed in and 3 of his {\em Shadows of the Mind}. The core argument in these chapters is enthymematic, and when formalized, a remarkable number of technical glitches come to light. Over and above these defects, the argument, at best, is (...) an instance of either the fallacy of denying the antecedent, the fallacy of {\em petitio principii}, or the fallacy of equivocation. More recently, writing in response to his critics in the electronic journal {\em Psyche}, Penrose has offered a G\"{o}delian case designed to improve on the version presented in {\em SOTM}. But this version is yet again another failure. In falling prey to the errors we uncover, Penrose's new G\"{o}delian case is unmasked as the same confused refrain J.R. Lucas initiated 35 years ago. (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.

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)