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)

The Turing test has been studied and run as a controlled experiment and found to be underspecified and poorly designed. On the other hand, it has been defended and still attracts interest as a test for true artificial intelligence (AI). Scientists and philosophers regret the test’s current status, acknowledging that the situation is at odds with the intellectual standards of Turing’s works. This article refers to this as the Turing Test Dilemma, following the observation that the test has been under (...) discussion for over seventy years and still is widely seen as either too bad or too good to be a valuable experiment for AI. An argument that solves the dilemma is presented, which relies on reconstructing the Turing test as a thought experiment in the modern scientific tradition. It is argued that Turing’s exposition of the imitation game satisfies Mach’s characterization of the basic method of thought experiments and that Turing’s uses of his test satisfy Popper’s conception of the critical and heuristic uses of thought experiments and Kuhn’s association of thought experiments to conceptual change. It is emphasized how Turing methodically varied the imitation game design to address specific challenges posed to him by other thinkers and how his test illustrates a property of the phenomenon of intelligence and suggests a hypothesis on machine learning. This reconstruction of the Turing test provides a rapprochement to the conflicting views on its value in the literature. (shrink)

This personal, yet scientific, letter to Alan Turing, reflects on Turing's personality in order to better understand his scientific quest. It then focuses on the impact of his work today. By joining human attitude and particular scientific method, Turing is able to “immerse himself” into the phenomena on which he works. This peculiar blend justifies the epistolary style. Turing makes himself a “human computer”, he lives the dramatic quest for an undetectable imitation of a man, a woman, a machine. He (...) makes us see the continuous deformations of a material action/reaction/diffusion dynamics of hardware with no software. Each of these investigations opens the way to new scientific paths with major consequences for contemporary live and for knowledge. The uses and the effects of these investigations will be discussed: the passage from classical AI to today's neural nets, the relevance of non-linearity in biological dynamics, but also their abuses, such as the myth of a computational world, from a Turing-machine like universe to an encoded homunculus in the DNA. It is shown that these latter ideas, which are sometimes even made in Turing's name, contradict his views. (shrink)

In the popular imagination, the relevance of Turing's theoretical ideas to people producing actual machines was significant and appreciated by everybody involved in computing from the moment he published his 1936 paper ‘On Computable Numbers’. Careful historians are aware that this popular conception is deeply misleading. We know from previous work by Campbell-Kelly, Aspray, Akera, Olley, Priestley, Daylight, Mounier-Kuhn, Haigh, and others that several computing pioneers, including Aiken, Eckert, Mauchly, and Zuse, did not depend on Turing's 1936 universal-machine concept. Furthermore, (...) it is not clear whether any substance in von Neumann's celebrated 1945 ‘First Draft Report on the EDVAC’ is influenced in any identifiable way by Turing's work. This raises the questions: When does Turing enter the field? Why did the Association for Computing Machinery honor Turing by associating his name to ACM's most prestigious award, the Turing Award? Previous authors have.. (shrink)

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. (shrink)

In this paper, I explore an intriguing view of definable numbers proposed by a Cambridge mathematician Ernest Hobson, and his solution to the paradoxes of definability. Reflecting on König’s paradox and Richard’s paradox, Hobson argues that an unacceptable consequence of the paradoxes of definability is that there are numbers that are inherently incapable of finite definition. Contrast to other interpreters, Hobson analyses the problem of the paradoxes of definability lies in a dichotomy between finitely definable numbers and not finitely definable (...) numbers. To bypass this predicament, Hobson proposes a language dependent analysis of definable numbers, where the diagonal argument is employed as a means to generate more and more definable numbers. This paper examines Hobson’s work in its historical context, and articulates his argument in detail. It concludes with a remark on Hobson’s analysis of definability and Alan Turing’s analysis of computability. (shrink)

According to the conventional wisdom, Turing (1950) said that computing machines can be intelligent. I don't believe it. I think that what Turing really said was that computing machines –- computers limited to computing –- can only fake intelligence. If we want computers to become genuinelyintelligent, we will have to give them enough “initiative” (Turing, 1948, p. 21) to do more than compute. In this paper, I want to try to develop this idea. I want to explain how giving computers (...) more ``initiative'' can allow them to do more than compute. And I want to say why I believe (and believe that Turing believed) that they will have to go beyond computation before they can become genuinely intelligent. (shrink)

After giving a brief overview of the renewal of interest in logic and the foundations of mathematics in Göttingen in the period 1914-1921, I give a detailed presentation of the approach to the foundations of mathematics found in Behmann's doctoral dissertation of 1918, Die Antinomie der transfiniten Zahl und ihre Auflösung durch die Theorie von Russell und Whitehead. The dissertation was written under the guidance of David Hilbert and was primarily intended to give a clear exposition of the solution to (...) the antinomies as found in Principia Mathematica. In the process of explaining the theory of Principia, Behmann also presented an original approach to the foundations of mathematics which saw in sense perception of concrete individuals the Archimedean point for a secure foundation of mathematical knowledge. The last part of the paper points out an important numbers of connections between Behmann's work and Hilbert's foundational thought. (shrink)