Turing's Error-revised

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.

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.

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.

An overview of essays in this volume, with an emphasis on the philosophical legacy of Turing's work, specifically the ways in which his work bridges not only the gap between the sciences and the humanities, but also foundational and practical aspects of science and everyday life. Three sections of the volume are outlined, framing the overarching structure of Turing's intellectual development: I) Turing on the foundations of mathematics, incompleteness, the the limits of analysis; II) Turing's Universal Machine, implying the ubiquity of computational processes in our world, exemplified by applications in the early history of voice encryption, the history of computer music, the frontiers of computation, and the topic of emergence; III) Turing's work on machines and mind, including his famed "Turing test" as a societal mechanism, the nature of perception as cognition, his views on freedom of the will and the integration of human and machine intelligence, and the developing idea of social algorithms.

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.

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.

Minds and Machines, 2008

Forum Philosophicum

In this paper we discuss the views on the Turing test of four influential thinkers who belong to the tradition of analytic philosophy: Ludwig Wittgenstein, Noam Chomsky, Hilary Putnam and John Searle. Based on various beliefs about philosophical and/or linguistic matters, they arrive at different assessments of both the significance and suitability of the imitation game for the development of cognitive science and AI models. Nevertheless, they share a rejection of the idea that one can treat Turing test as a test for “machine thinking.” This seems to stem from a concern for the proper use of language —one that is a fundamental methodological commitment of analytic philosophy.

I explore the conceptual foundations of Alan Turing's analysis of computability, which still dominates thinking about computability today. I argue that Turing's account represents a last vestige of a famous but unsuccessful program in pure mathematics, viz., Hilbert's formalist program. It is my contention that the plausibility of Turing's account as an analysis of the computational capacities of physical machines rests upon a number of highly problematic assumptions whose plausibility in turn is grounded in the formalist stance towards mathematics. More speciÿcally, the Turing account conates concepts that are crucial for understanding the computational capacities of physical machines. These concepts include the idea of an " operation " or " action " that is " formal, " " mechanical, " " well-deÿned, " and " precisely described, " and the idea of a " symbol " that is " formal, " " uninterpreted, " and " shaped ". When these concepts are disentangled, the intuitive appeal of Turing's account is signiÿcantly undermined. This opens the way for exploring models of hypercomputability that are fundamentally dierent from those currently entertained in the literature.

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.