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Philosophia: International Journal of Philosophy (2014) 15(1): 50-62
Due to his significant role in the development of computer technology and the discipline of artificial intelligence, Alan Turing has supposedly subscribed to the theory of mind that has been greatly inspired by the power of the said technology which has ev entually become the dominant framework for current researches in artificial intelligence and cognitive science, namely, computationalism or the computational theory of mind. In this essay, I challenge this supposition. In particular, I will try to show tha t there is no evidence in Turing's two seminal works that supports such a supposition. His 1936 paper is all about the notion of computation or computability as it applies to mathematical functions and not to the nature or workings of intelligence. On the other hand, while his 1950 work is about intelligence, it is, however, particularly concerned with the problem of whether intelligence can be attributed to computing machines and not of whether computationality can be attributed to human intelligence or to intelligence in general.
Natural Computing, 2007
Turing's notion of human computability is exactly right not only for obtaining a negative solution of Hilbert's Entscheidungsproblem that is conclusive, but also for achieving a precise characterization of formal systems that is needed for the general formulation of the incompleteness theorems. The broad intellectual context reaches back to Leibniz and requires a focus on mechanical procedures; these procedures are to be carried out by human computers without invoking higher cognitive capacities. The question whether there are strictly broader notions of effectiveness has of course been asked for both cognitive and physical processes. I address this question not in any general way, but rather by focusing on aspects of mathematical reasoning that transcend mechanical procedures. Section 1 discusses Go¨del's perspective on mechanical computability as articulated in his [193?], where he drew a dramatic conclusion from the undecidability of certain Diophantine propositions, namely, that mathematicians cannot be replaced by machines. That theme is taken up in the Gibbs Lecture of 1951; Go¨del argues there in greater detail that the human mind infinitely surpasses the powers of any finite machine. An analysis of the argument is presented in Section 2 under the heading Beyond calculation. Section 3 is entitled Beyond discipline and gives Turing's view of intelligent machinery; it is devoted to the seemingly sharp conflict between Go¨del's and Turing's views on mind. Their deeper disagreement really concerns the nature of machines, and I'll end with some brief remarks on (supra-) mechanical devices in Section 4.
TOPOI, 32 (2):293-299 (2013)
It is the anachronistic review of the classical paper of Turing (as published this year), for discussing current issues and contradictions in AI and Cognitive Science.
2013
In this paper a distinction is made between Turing's approach to computability, on the one hand, and his approach to mathematical reasoning and intelligence, on the other hand. Unlike Church's approach to computability, which is top-down being based on the axiomatic method, Turing's approach to computability is bottom-up, being based on an analysis of the actions of a human computer. It is argued that, for this reason, Turing's approach to computability is convincing. On the other hand, his approach to mathematical reasoning and intelligence is not equally convincing, because it is based on the assumption that intelligent processes are basically mechanical processes, which however from time to time may require some decision by an external operator, based on intuition. This contrasts with the fact that intelligent processes can be better accounted for in rational terms, specifically, in terms of non-deductive inferences, rather than in term of inscrutable intuition.
International Journal of Machine Learning and Computing, 2013
This paper aims to examine the basis of Calculus and computus from first philosophical principles, having a focus on the internal representations and acts of spontaneity, proper of genius that the concept of creativity is affiliate with. Our guiding author is Alan Turing and we will enquire closely the computing classical model. The paper explores the traditions of computing and philosophy, theorizing about the question of bio-machine hybrids in relation with imagination, the form of representation most free from nature. The first section is called calculus et computus. It examines the developments associated with the notions of algorithm, function and rule. In the second section the faculty of imagining is addressed through the abbreviated table, hoping to identify the boundaries both theoretical and practical of the computing classical model, following the seminal paper on computable numbers with Application to the Entscheidungs Problem (1936). We show how much hybridization of ideas fostered by both traditions was to find a place in the imaginary of artificial intelligence. Flanked by intuitions and concepts, imagination, the synthesis of reproduction, is capable of discerning about cosmos through bios and computus, so powerfully as if it sketched ideas in images, as the Turing machine clearly exemplifies.
Minds and Machines, 2003
This paper concerns Alan Turing's ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for Turing, was not a computable sequence (i.e., one that could be generated by a Turing machine). Since computers only contained a finite number of instructions (or programs), one might argue, they could not reproduce human intelligence. Turing called this the "mathematical objection" to his view that machines can think. Logico-mathematical reasons, stemming from his own work, helped to convince Turing that it should be possible to reproduce human intelligence, and eventually compete with it, by developing the appropriate kind of digital computer. He felt it should be possible to program a computer so that it could learn or discover new rules, overcoming the limitations imposed by the incompleteness and undecidability results in the same way that human mathematicians presumably do.
Philosophy Compass, 2009
Computationalism has been the mainstream view of cognition for decades. There are periodic reports of its demise, but they are greatly exaggerated. This essay surveys some recent literature on computationalism and reaches the following conclusions. Computationalism is a family of theories about the mechanisms of cognition. The main relevant evidence for testing computational theories comes from neuroscience, though psychology and AI are relevant too. Computationalism comes in many versions, which continue to guide competing research programs in philosophy of mind as well as psychology and neuroscience. Although our understanding of computationalism has deepened in recent years, much work in this area remains to be done.
Section 3.1 of the present work is an adapted version of section 2 of Gualtiero Piccinini, "Alan Turing and the Mathematical Objection," Minds and Machines 13(1), pp. 23-48.
Studies in History and Philosophy of Science Part A, 2010
One account of the history of computation might begin in the 1930's with some of the work of Alonzo Church, Alan Turing, and Emil Post. One might say that this is where something like the core concept of computation was first formally articulated. Here were the first attempts to formalize an informal notion of an algorithm or effective procedure by which a mathematician might decide one or another logico-mathematical question. As each of these formalisms was shown to compute the same set of functions-the partial recursive functions-each of them might be described as a form of Turing-equivalent computation. This work set the cornerstone for what we might call computation theory. This history might then proceed to give pride of place to this form of computation in subsequent developments in cognitive science and in related disciplines and subdisciplines. Such a history might note that, in the 1940's, the results of this work would have been transferred into the emerging field of computer science with the design and construction of the first electronic digital computers. Here one would mention Turing again, as well as perhaps Norbert Wiener, Julian Bigelow, John von Neumann, and many others. At about the same time, this theory of computation would have been inserted into the theory of neural networks by way of Warren McCulloch and Walter Pitts's seminal work, "A Logical Calculus of the Ideas Immanent in Nervous Activity." Somewhat later, during the 1960's, Hilary
IEEE Annals of the History of Computing
This article presents an overview of Turing's early contributions to machine intelligence, together with a summary of his influence on other early practitioners. Following his famous work on the Entscheidungsproblem in the 1930s, Turing staked out the field of machine intelligence during the 1940s. His wartime Bombe used what we now call heuristic search to do work requiring intelligence when done by humans. In key papers in 1948 and 1950 he discussed search, learning, robotics, chess, the theorem-proving approach to AI, the genetic algorithm concept, and artificial neural networks, as well as introducing the Turing test. He influenced the first generation of programmers in Britain, whose pioneering contributions to machine intelligence included work on board games, learning, language-processing, and reasoningcontributions made years before the term 'Artificial Intelligence' was coined at Dartmouth in 1956. Context: Thinking Machines, Dartmouth, the Turing Machine, and the Entscheidungsproblem Tracing far back along the chain of intellectual precursors to modern AI, one reaches the American philosopher C. S. Peirce. In 1908, Peirce expressed the idea that a machine-'some Babbage's analytical engine or some logical machine'-is capable of all mathematical reasoning [47, p. 434]. He was skeptical, however, calling the idea 'malignant', and firmly placing it among others he deemed 'logical heresies' (ibid.) Peirce was a powerful influence on Hilbert and his group at Göttingen [27, p. 1]. In 1903, Peirce formulated the decision problem for first-order logic in roughly the form in which Turing later tackled it [46]. At Göttingen the decision problem was named the Entscheidungsproblem, it seems by Behmann, a young member of Hilbert's group [34]. As early as 1921, Behmann used the concept of a machine to clarify the nature of the Entscheidungsproblem, saying: 'One might, if one wanted to, speak of mechanical or machine-like thinking' and 'Perhaps one can one day even let it be carried out by a machine' [34, p. 176]. From Göttingen, the Entscheidungsproblem travelled to Cambridge and Turing. His encounter with the Entscheidungsproblem launched him on the trajectory that led to his theoretical work on what he called 'logical computing machines' and then, eventually, to his practical work on the hardware and software designs for the ACE and other early British electronic computers [9, 18, 29, 30]. This same trajectory issued in his early work on what he called 'intelligent machinery'. Researchers that he influenced termed the new field machine intelligence.
Many important lines of argumentation have been presented during the last decades claiming that machines cannot think like people. Yet, it has been possible to construct devices and information systems, which replace people in tasks which have previously been occupied by people as the tasks require intelligence. The long and versatile discourse over, what machine intelligence is, suggests that there is something unclear in the foundations of the discourse itself. Therefore, we critically studied the foundations of used theory languages. By looking critically some of the main arguments of machine thinking, one can find unifying factors. Most of them are based on the fact that computers cannot perform sense-making selections without human support and supervision. This calls attention to mathematics and computation itself as a representational constructing language and as a theory language in analysing human mentality. It is possible to notice that selections must be based on relevance, i.e., on why some elements of sets belong to one class and others do not. Since there is no mathematical justification to such selection, it is possible to say that relevance and related concepts are beyond the power of expression of mathematics and computation. Consequently, Turing erroneously assumed that mathematics and formal language is equivalent with natural languages. He missed the fact that mathematics cannot express relevance, and for this reason, mathematical representations cannot be complete models of the human mind. Preface This paper is of a programmatic nature. We fully acknowledge the enormous achievements of modern science, engineering and design by calling on the most advanced machine models, as we always did in the past and will continue into the future. We will not primarily discuss the physical limitations (Markov 2014), but instead focus on the conceptual constraints, the intuitive assumptions of underlying theories, resp. their foundations (Saariluoma 1997). We try to understand and find an answer to the fundamental question: Is the human mind capable of understanding itself beyond computability? We question the mainstream assumption that everything is (or at least should be) 'computational' (Chatelin 2012, Chalmers 1996, Sun, Wilson, and Lynch 2016). We argue that the foundations of such an assumption are (still) not fully justifiable. Therefore, we imitate Kant's (1781/1922) famous 'Copernican Revolution' from a kind of Wittgensteinian (1921/1974) perspective and ask whether the properties of the theory of language itself used in discourse can explain why the problems have proven to be so hard. In other words, we ask whether formal theory languages (i.e., logic, mathematics and computation) are powerful enough to express problems of human thinking and represent thoughts. Since many of the foundational issues concentrate on one theoretical construct, Turing machines (TM), we must once again consider whether people 'think like machines'.
Science & Technology Studies, 2023
As part of ongoing research bridging ethnomethodology and computer science, in this article we offer an alternate reading of Alan Turing's 1936 paper, "On Computable Numbers". Following through Turing's machinic respecification of computation, we hope to contribute to a deflationary position on AI by showing that the activities attributed to AIs are achieved in the course of methodic hands-on work with computational systems and not in isolation by them. Turing's major innovation was a demonstration that mathematical and logical operations could be broken down into elementary, mechanically executable operations, devoid of intellectual content. Drawing out lessons from a re-enactment of Turing's methods as a means of reflecting on contemporary artificial intelligence (AI), including the way those methods disappear into the technology, we will suggest the interesting question raised in "On Computable Numbers" is less about the possibilities of designing machines that "can think" (cf. Turing, 1950), but the practical work we do, and which is made possible, when we ourselves set out to think like machines.
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.
Cognitive Science, 1998
Turing's analysis of computation is a fundamental part of the background of cognitive science. In this paper it is argued that a re-interpretation of Turing's work is required to underpin theorizing about cognitive architecture. It is claimed that the symbol systems view of the mind, which is the conventional way of understanding how Turing's work impacts on cognitive science, is deeply flawed. There is an alternative interpretation that is more faithful to Turing's original insights, avoids the criticisms made of the symbol systems approach and is compatible with the growing interest in agent-environment interaction. It is argued that this interpretation should form the basis for theories of cognitive architecture.
The emergence of cognitive science as a multi-disciplinary investigation into the nature of mind has historically revolved around the core assumption that the central ‘cognitive’ aspects of mind are computational in character. Although there is some disagreement and philosophical speculation concerning the precise formulation of this ‘core assumption’ it is generally agreed that computationalism in some form lies at the heart of cognitive science as it is currently conceived. Von Eckardt’s recent work on this topic is useful in enabling us to get a sense of the scope of the computational assumption. She makes clear that there are two rather different ways in which we could understand cognitive science’s commitment to computationalism and hence two ways to understand the claim that the ‘mind is a computer’, by appeal to either (1) A mathematical theory of computability or (2) A theory of data-processing or information-processing. Importantly, she also argues that although there are many aspects of claim that the ‘mind is a computer’ that can be nicely captured by Boyd’s account of the way scientific metaphors are employed, not to direct attention to the hitherto unnoticed, but to encourage investigation of the unknown. Nonetheless, cognitive scientists are not making the claim that the ‘mind is a computer’ in a metaphorical sense. If Von Eckhardt is correct, when cognitive scientists assume the ‘mind is a computer’ and give a sense to the notion of the computer in the sense of (2) above, they are making a literal claim about the nature of mind (Von Eckardt, 1993, p. 116). And as she points out that if one reads (2) in a theoretically committed way then there is no a priori reason to exclude the organic brain from the list of entities that might fall under the description of being a ‘computer’. Important, we can truly describe it as a data-processing (or information-processing) device. What is useful about Von Eckardt’s general analysis of computationalism’s core assumption is that it provides a clear angle from which to view the flaws of computationalism. This paper defends the claim that if there is an account of information adequate to capture those aspects of mind that we regard as essential to mentality it is one that requires us to surrender the idea that the mind is a computer.
Isonomia, 2014
The article deals with some ideas by Turing concerning the background and the birth of the well-known Turing Test, showing the evolution of the main question proposed by Turing on thinking machine. The notions he used, especially that one of imitation, are not so much exactly defined and shaped, but for this very reason they have had a deep impact in artificial intelligence and cognitive science research from an epistemological point of view. Then, it is suggested that the fundamental concept involved in Turing's imitation game, conceived as a test for detecting the presence of intelligence in an artificial entity, is the concept of interaction, that Turing adopts in a wider, more intuitive and more fruitful sense than the one that is proper to the current research in interactive computing.
"Classical computationalism considers the Turing Machine to be a psychologically implausible model of human computation. In this paper, I will first elaborate on Andrew Wells' thesis that the claim of psychological implausibility derives from a wrong interpretation of the TM as originally conceived by Turing. Then, I will show how Turing's original interpretation of the TM could be useful to construct cognitive models of simple phenomena of human computation, such as counting using our fingers or performing arithmetical operations using paper and pencil."
Turing starts on an equivocation. We know now that what he will go on to consider is not whether or not machines can think, but whether or not machines can do what thinkers like us can do--and if so, how. Doing is performance capacity, empirically observable. Thinking (or cognition) is an internal state, its correlates empirically observable as neural activity (if we only knew which neural activity corresponds to thinking!) and its associated quality introspectively observable as our own mental state when we are thinking.
In this paper, I review the objections against the claim that brains are computers, or, to be precise, information-processing mechanisms. By showing that practically all the popular objections are based on uncharitable (or simply incorrect) interpretations of the claim, I argue that the claim is likely to be true, relevant to contemporary cognitive (neuro)science, and non-trivial. The computational theory of mind, or computationalism, has been fruitful in cognitive research. The main tenet of the computational theory of mind is that the brain is a kind of information-processing mechanism, and that information-processing is necessary for cognition; it is non-trivial and is generally accepted in cognitive science. The positive view will not be developed here, in particular the account of physical computation, because it has already been elucidated in book-length accounts (Fresco, 2014; Miłkowski, 2013; Piccinini, 2015). Instead, a review of objections is offered here, as no comprehensive survey is available. The survey suggests that the majority of objections fail just because they make computationalism a straw man. Some of them, however, have shown that stronger versions of the computational theory of mind are untenable, as well. Historically, they have helped to shape the theory and methodology of computational modeling. In particular, a number of objections show that cognitive systems are not only computers, or that computation is not the sole condition of cognition; no objection, however, establishes that there might be cognition without computation.
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