Turing's programme, the idea that intelligence can be modelled computationally, is set in the context of a parallel between certain elements from metamathematics and Popper's schema for the evolution of knowledge. The parallel is developed at both the formal level, where it hinges on the recursive structuring of Popper's schema, and at the contentual level, where a few key issues common to both epistemology and metamathematics are briefly discussed. In light of this connection Popper's principle of transference, akin to (...) Turing's belief in the relevance of the theory of computation for modelling psychological functions, is widened into the extended principle of transference. Thus Turing's programme gains a solid epistemological footing. *I am grateful to Claude Lamontagne and Jean-Pierre Delage for their comments on this paper. (shrink)

In this essay, I examine the notion of a nondeterministic algorithm from both a conceptual and historical point of view. I argue that the intuitions underwriting nondeterminism in the context of contemporary theoretical computer science cannot be reconciled with the intuitions that originally motivated nondeterminism. I identify four different intuitions about nondeterminism: nondeterminism as evidence for the Church Turing thesis; nondeterminism as a natural reflection of the mathematician's behavior; nondeterminism as a formal, mathematical generalization; and nondeterminism as a physical (...) process. I shall argue that there are irreconcilable tensions among these intuitions and, moreover, that these tensions have not been acknowledged in the conceptual development of theoretical computer science. In fact, a careful review of the received history reveals a number of gaps and discontinuities. For instance, I examine the seminal writings of Turing and argue that the formal introduction of the nondeterminism is to be found there and not, as is often supposed, in the research of the late 1950s and early 1960s. I also examine the period after 1960 and argue that even the more recent developments concerning nondeterminism are hard to reconstruct. ;Although I firmly believe that a rigorous philosophical account of nondeterminism is needed, I am not sure that such an account will bring us any closer to a solution to any of the notoriously difficult theoretical problems that turn on the notion of a nondeterministic algorithm. I do believe, however, that a clear conceptual account of nondeterminism will shed light on many long-standing philosophical problems. I conclude by pointing to a number of philosophical questions that resonate with issues raised by the foregoing investigation of nondeterministic algorithms. (shrink)

Harnad and I agree that the Chinese Room Argument deals a knockout blow to Strong AI, but beyond that point we do not agree on much at all. So let's begin by pondering the implications of the Chinese Room. The Chinese Room shows that a system, me for example, could pass the Turing Test for understanding Chinese, for example, and could implement any program you like and still not understand a word of Chinese. Now, why? What does the genuine (...) Chinese speaker have that I in the Chinese Room do not have? The answer is obvious. I, in the Chinese room, am manipulating a bunch of formal symbols; but the Chinese speaker has more than symbols, he knows what they mean. That is, in addition to the syntax of Chinese, the genuine Chinese speaker has a semantics in the form of meaning, understanding, and mental contents generally. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:522 BOOK REVIEWS The Reason of Following: Christology and the Ecstatic I. By ROBERT P. ScHARLEMANN. Chicago: University of Chicago Press, 1992. Pp. 214. $32.50 (cloth). Robert P. Scharlemann is Commonwealth Professor of Religious Studies at the University of Virginia. Writing in the tradition of Bultmann 's observation that speaking of God requires speaking of oneself, he conceives of christology as a distinctive form of reason, a philosophical /theological (...) anthropology in which the logic of discipleship occupies a prominent place. Accordingly, The Reason of Following is a sustained pursuit of " an articulated understanding of the nature and constitution of human being" (p. 1), a theme which Scharlemann sees as a component of christology which has wrongly been eclipsed by other dimensions in more traditional presentations. The goal of Scharlemann's work is to bring into view " the nature of the relation that is implied when it is reported, for example, that Jesus said' Follow me! ' and there were those who 'immediately' followed.... What is the nature of the ' following ' on the part of those who will ' immediately ' follow the summons of one whose name is ' I am '? And who is the ' I ' of the ' I am ' in the person who makes the summons? " (p. 88). Each of the four themes sounded in this cita· tion-the call to discipleship, the immediacy of following, the identification of Jesus as ' I am,' and the designation of the specifics of the disciples' relationship to Jesus as an example, but no more than an ex· ample, of a broader possibility of human existence-is a fundamental element in Scharlemann's conception of christology. Operating on the principle that the traditional definition of a human being as a rational animal can be replaced by the existential definition " ' I ' am here " (cf. p. ix), Scharlemann devotes two lengthy introductory chapters to explicating the significance of this shift from " what " a human being is to " where " and " when " it is. Dr.awing especially on Descartes, Luther, Kierkegaard, Heidegger, and Fichte, his studies of the subjectivity and being of the self accent the import· ance of the I as subject and explore the differences between the I of pure actuality shown in the method of doubt, the I of pure possibility shown in the anticipation of death, and the I of pure freedom shown in the evocation of trust. Against this background, reflections on the na· ture of following envisage an additional possible I, one summoned by the call to be wholly in the world, in finite freedom. Before investigating the christological relation as " a rational form of its own" (p. viii), Scharlemann offers a preliminary analysis of modes of thinking. Distinguishing between thinking ("the openness BOOK REVIEWS 523 of the self to what is other than thinking" [p. 62]) and reason ("the configuration of this openness" [p. 62], i.e., "a definite way in which the self is related to its other through an activity " [p. 103] ), he argues that thinking always appears in one of two basic modes: understanding of being, or faith in God. These two modes-not to he confused with forms of reason-cover the entire field of thinking: " When we trust anyone at all, we are trusting God, just as, when we understand anything at all, we understand being" {p. 76). While aware that his implied definition of faith differs from those of the Christian theological tradition and is not serviceable for purposes of historical theology, Scharlemann opts nonetheless for a terminology which draws " as clearly as possible the parallel between faith and understanding as two modes of thinking whose own object is as such beyond the understanding of being and the faith in God " (p. 77). Turning to the specific form of reason which is the hook's chief concern, Scharlemann devotes a central chapter to " The Exstantial I in Christological Reason." After a critique of traditional christologies, he adumbrates a christology which seeks to depict the self of discipleship as one in which " the other to which the self relates itself is the inwardness of the self without being a projection from that inwardness " (p. 96). Appealing to the principle that the notion of the self as related to... (shrink)

The overarching guiding principle of Alan Turing’s work was directed towards modelling the human mind as a machine. It is extraordinary that Turing introduced, in his early papers, ideas that are only now beginning to be investigated. Throughout his life, he considered conjectures to be of great importance because they suggest useful lines of research. In my own conjecture, I am asking the question: what is the brain’s geometry? Can it ever be unravelled, or does its complexity defy (...) any form of visual representation? Recent research reveals that the detailed workings of the brain take place in a ‘global workspace’, where conscious contents appear to be disseminated globally to a great multitude of networks throughout the brain that are unconscious. During conscious tasks, neurons contributing to the global workspace enter into a coherent activation pattern by being tightly connected through long axons. Is it possible, therefore, that my proposed geometric pattern (an Islamic latticework) can be envisaged as a useful means of interconnecting multiple long axons in a unified global workspace dedicated to conscious thought? I share and communicate my idea through a process that combines visual imagery with musical performance (i.e. visual music). It is a method that can assist in clarifying concepts that might otherwise remain elusive or esoteric. (shrink)

A sketchy subquantum theory deeply influenced by Wheeler’s ideas (Am. J. Phys. 51:398–404, 1983) and by the de Broglie-Bohm interpretation (Goldstein in Stanford Encyclopedia of Philosophy, 2006) of quantum mechanics is further analyzed. In this theory a fundamental system is defined as a dual entity formed by bare matter and a methodological probabilistic classical Turing machine. The evolution of the system would be determined by three Darwinian informational regulating principles. Some progress in the derivation of the postulates of quantum (...) mechanics from these regulating principles is reported. The entanglement in a bipartite system is preliminarily considered. (shrink)

Reinhardt 's strong mechanistic thesis, a formalization of “I know I am a Turing machine”, is shown to be consistent with Epistemic Arithmetic.

In "The Status and Future of the Turing Test" (Moor, 2001), which appeared in an earlier issue of this journal, James Moor remarks on my paper "Turing's Two Tests for Intelligence." In my paper I had claimed that, whatever Turing may or may not have thought, the test described in the opening section of Turing's now legendary 1950 paper "Computing Machinery and Intelligence" is not equivalent to, and in fact is superior to, the test described in (...) a passage that occurs much later in Turing's paper (i.e., in Section 5 of Turing, 1950). I'm pleased Moor chose to give such prominence to my point, and very happy to see that he recognized that my claim was a normative one about the superiority of one test over another, rather than a claim about Turing's intentions. However, as I think the way he describes my point could lead to misunderstandings, I'd like to clarify the points I made. One major clari?cation is which two tests I am contrasting; another is that the difference in overall structure of the two tests is of philosophical signi?cance. (shrink)

Turing’s famous 1936 paper “On computable numbers, with an application to the Entscheidungsproblem” defines a computable real number and uses Cantor’s diagonal argument to exhibit an uncomputable real. Roughly speaking, a computable real is one that one can calculate digit by digit, that there is an algorithm for approximating as closely as one may wish. All the reals one normally encounters in analysis are computable, like π, √2 and e. But they are much scarcer than the uncomputable reals because, (...) as Turing points out, the computable reals are countable, whilst the uncomputable reals have the power of the continuum. Furthermore, any countable set of reals has measure zero, so the computable reals have measure zero. In other words, if one picks a real at random in the unit interval with uniform probability distribution, the probability of obtaining an uncomputable real is unity. One may obtain a computable real, but that is in- finitely improbable. But how about individual examples of uncomputable reals? We will show two: H and the halting probability Ω, both contained in the unit interval. Their construction was anticipated in.. (shrink)

This paper reassesses the criticism of the Lucas-Penrose anti-mechanist argument, based on Gödel’s incompleteness theorems, as formulated by Krajewski : this argument only works with the additional extra-formal assumption that “the human mind is consistent”. Krajewski argues that this assumption cannot be formalized, and therefore that the anti-mechanist argument – which requires the formalization of the whole reasoning process – fails to establish that the human mind is not mechanistic. A similar situation occurs with a corollary to the argument, that (...) the human mind allegedly outperforms machines, because although there is no exhaustive formal definition of natural numbers, mathematicians can successfully work with natural numbers. Again, the corollary requires an extra-formal assumption: “PA is complete” or “the set of all natural numbers exists”. I agree that extra-formal assumptions are necessary in order to validate the anti-mechanist argument and its corollary, and that those assumptions are problematic. However, I argue that formalization is possible and the problem is instead the circularity of reasoning that they cause. The human mind does not prove its own consistency, and outperforms the machine, simply by making the assumption “I am consistent”. Starting from the analysis of circularity, I propose a way of thinking about the interplay between informal and formal in mathematics. (shrink)

Theoretiker der Künstlichen Intelligenz und deren Wegbegleiter in der Philosophie des Geistes haben auf unterschiedliche Weise auf Kritik am ursprünglichen Theorieziel der KI reagiert. Eine dieser Reaktionen ist die Zurücknahme dieses Theorieziels zugunsten der Verfolgung kleinerformatiger Projekte. Eine andere Reaktion ist die Propagierung konnektionistischer Systeme, die mit ihrer dezentralen Arbeitsweise die neuronalen Netze des menschlichen Gehirns besser simulieren sollen. Eine weitere ist die sogenannte robot reply. Die Roboterantwort besteht aus zwei Elementen. Sie enthält (a) das Zugeständnis, daß das Systemverhalten eines (...) wie auch immer programmierten konventionellen Digitalrechners mit von Neumann-Architektur nicht schon menschenähnliche Intelligenz aufweist, und (b) die Behauptung, daß es für bestimmte Arten von Maschinen doch zur Intelligenz reicht. In die Liga der intelligenten Wesen könnten Maschinen genau dann aufsteigen, wenn sie Roboter sind. Damit ist gemeint: wenn sie über Wahrnehmungskomponenten (Rezeptoren) und Handlungskomponenten (Effektoren) verfügen, mithilfe deren sie aktiv in kausale Interaktionen mit ihrer Umwelt eintreten können. Im Beitrag wird für die These argumentiert, daß der Roboterantwort eine richtige Intuition zugrunde liegt, von der die Roboterfreunde sich aber zu einer kurzschlüssigen Folgerung verleiten lassen. Es ist richtig, mentale Zustände und Handlungskompetenz eng aneinander zu binden. Einem Wesen, dem man Handlungsfähigkeit zuerkennt, kann man mentale Zustände nicht absprechen. Doch Handelnkönnen und Geisthaben sind nicht hinreichend unabhängig voneinander, als daß man das eine als Rechtfertigung für die Zuerkennung des anderen verwenden könnte. Man sollte Robotern beides absprechen. (shrink)

THE MIND-BODY PROBLEM: A GUIDE TO THE CURRENT DEBATE (EDITED BY RICHARD WARNER AND TA D E U S Z SZUBKA) contains recent essays by the key players in the the field of the Mind-Body problem: Searle, Fodor, Problem Honderich, Nagel, McGinn, Stich, Rorty and others. But there are a few interesting exceptions, for example Edelman, Popper, Putnam and Dennett. Nevertheless, these thinkers do get a mention here and there, and nearly all the exciting topical issues are dealt with, including (...) externalism, functionalism, intentionality, Turing computational models, and the relationship between these philosophical problems and psychology. I am particularly struck by the tendency to engage in an evasive stratagem when it comes to stating the physicalist thesis. Instead of a clear definitive position about what kind of physical science would achieve the hoped-for reduction, what I found was variations on Lewis's claim that the reduction would be effected by a "unified body of scientific theories of the sort we now accept". Materialism used to be a clear doctrine: a clockwork Universe of impenetrable particles. But materialism transcended itself. First through Hobbes' and Leibniz's criticisms of Descartes, then Newton's demolition of the Cartesian idea that matter was essentially extension by introducing gravity (action at a distance) and then through the field theories of Faraday and Maxwell, and more recently through Einstein's work, which undermined the "substance" view of matter, something that remained permanent while other changes occurred. I contrast the perspectives of the Churchlands with those of Donald T. Campbell, Karl Popper and other evolutionary and emergentist views. -/- . (shrink)

Though less well known than his other work, Turings 1938 Princeton Thesis, this title which includes his notion of an oracle machine, has had a lasting influence on computer science and mathematics. It presents a facsimile of the original typescript of the thesis along with essays by Appel and Feferman that explain its still-unfolding significance.

[1] ʻAl ʻinyene ḥinukh ha-banim ṿeha-banot ṿi-yeme ha-baḥarut-- [2] ʻAl ʻinyene derekh ha-Ḥasidut lesayeaʻ le-zulato be-ruḥaniyut ṿe-nilṿeh elaṿ mikhteve ḳodesh be-ʻinyan zeh.

I propose to consider the question, "Can machines think?" This should begin with definitions of the meaning of the terms "machine" and "think." The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous, If the meaning of the words "machine" and "think" are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to (...) the question, "Can machines think?" is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words. The new form of the problem can be described in terms of a game which we call the 'imitation game." It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart front the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A." The interrogator is allowed to put questions to A and B. We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?". (shrink)

There are many complex characters in this paper; if you find them difficult to distinguish, you are advised to increase the viewing size.

Los partidos políticos en Córdoba desde la hora del pueblo hasta la caída de Levingston.