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)

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.

Let be a model of a theory T. Depending on wether is decidable or recursive, and on whether T is strongly minimal or -minimal, we find conditions on which guarantee that every infinite independent subset of is not recursively enumerable. For each of the same four cases we also find conditions on which guarantee that every infinite independent subset of has Turing degree 0'. More generally, let be a recursive -structure, R a relation symbol not in , ψ a (...) recursive infiniatary Π2 sentence in the language {R}, and let 0<α<ωCK1. We discuss conditions under which we can construct a recursive -structure such that ,Rψ for every Δ0α relation R on. (shrink)

Alan Turing’s pioneering work on computability, and his ideas on morphological computing support Andrew Hodges’ view of Turing as a natural philosopher. Turing’s natural philosophy differs importantly from Galileo’s view that the book of nature is written in the language of mathematics (The Assayer, 1623). Computing is more than a language used to describe nature as computation produces real time physical behaviors. This article presents the framework of Natural info-computationalism as a contemporary natural philosophy that builds (...) on the legacy of Turing’s computationalism. The use of info-computational conceptualizations, models and tools makes possible for the first time in history modeling of complex self-organizing adaptive systems, including basic characteristics and functions of living systems, intelligence, and cognition. (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 his short life, Alan Turing (1912-1954) made foundational contributions to philosophy, mathematics, biology, artificial intelligence, and computer science. He, as much as anyone, invented and showed how to program the digital electronic computer. From September, 1939, his work on computation was war-driven and brutally practical. He developed high speed computing devices needed to decipher German Enigma Machine messages to and from U-boats, countering the most serious threat by far to Britain..

It has been just over 100 years since the birth of Alan Turing and more than 65 years since he published in Mind his seminal paper, Computing Machinery and Intelligence. In the Mind paper, Turing asked a number of questions, including whether computers could ever be said to have the power of “thinking”. Turing also set up a number of criteria—including his imitation game—under which a human could judge whether a computer could be said to be (...) “intelligent”. Turing’s paper, as well as his important mathematical and computational insights of the 1930s and 1940s led to his popular acclaim as the “Father of Artificial Intelligence”. In the years since his paper was published, however, no computational system has fully satisfied Turing’s challenge. In this paper we focus on a different question, ignored in, but inspired by Turing’s work: How might the Artificial Intelligence practitioner implement “intelligence” on a computational device? Over the past 60 years, although the AI community has not produced a general-purpose computational intelligence, it has constructed a large number of important artifacts, as well as taken several philosophical stances able to shed light on the nature and implementation of intelligence. This paper contends that the construction of any human artifact includes an implicit epistemic stance. In AI this stance is found in commitments to particular knowledge representations and search strategies that lead to a product’s successes as well as its limitations. Finally, we suggest that computational and human intelligence are two different natural kinds, in the philosophical sense, and elaborate on this point in the conclusion. (shrink)

Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing, the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world--including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene--were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as (...) computer science. Though less well known than his other work, Turing's 1938 Princeton PhD thesis, "Systems of Logic Based on Ordinals," which includes his notion of an oracle machine, has had a lasting influence on computer science and mathematics. This book presents a facsimile of the original typescript of the thesis along with essays by Andrew Appel and Solomon Feferman that explain its still-unfolding significance. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal--a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science. (shrink)

In the mid of nineteenth century, the hypothesis, “machine can think,” became very popular after Alan Turing’s article on “Computing Machinery and Intelligence.” This hypothesis, “machine can think,” established the foundations of machine intelligence and claimed that machines have a mind. It has the power to compete with human beings. In the first section, I shall explore the importance of Turing thesis, which has been conceptualized in the domain of machine intelligence. Turing presented a completely different (...) view of the machine itself. It addressed philosophers, rather than the mathematicians, and proclaimed that digital computers might be considered as intelligent machines. This approach was wholly new, both philosophically and technically, and started many philosophical debates which continue to this day. He proposed an imitation game, as a test, what is now referred to as a Turing test to evaluate if a machine thinks. That is to say that the main aim of machine intelligence not only constructs challenging programs to solve our day-to-day problems but also reproduce mentality in machines and claimed that all the mental qualities are ascribable to machines. What will be attempted in this paper is a critical evaluation of the arguments against the Turing test put forward by many philosophers. (shrink)

The papers you will find in this special issue of JoLLI develop letter and spirit of Turing’s original contributions. They do not lazily fall back into the same old sofa, but follow – or question – the inspiring ideas of a great man in the search for new, more precise, conclusions. It is refreshing to know that the fertile landscape created by Alan Turing remains a source of novel ideas.

It is not widely realised that Turing was probably the first person to consider building computing machines out of simple, neuron-like elements connected together into networks in a largely random manner. Turing called his networks 'unorganised machines'. By the application of what he described as 'appropriate interference, mimicking education' an unorganised machine can be trained to perform any task that a Turing machine can carry out, provided the number of 'neurons' is sufficient. Turing proposed simulating both (...) the behaviour of the network and the training process by means of a computer program. We outline Turing's connectionist project of 1948. (shrink)

It is not widely realised that Turing was probably the first person to consider building computing machines out of simple, neuron-like elements connected together into networks in a largely random manner. Turing called his networks unorganised machines. By the application of what he described as appropriate interference, mimicking education an unorganised machine can be trained to perform any task that a Turing machine can carry out, provided the number of neurons is sufficient. Turing proposed simulating both (...) the behaviour of the network and the training process by means of a computer program. We outline Turing's connectionist project of 1948. (shrink)

I live just off of Bell Road outside of Newburgh, Indiana, a small town of 3,000 people. A mile down the street Bell Road intersects with Telephone Road not as a modern reminder of a technology belonging to bygone days, but as testimony that this technology, now more than a century and a quarter old, is still with us. In an age that prides itself on its digital devices and in which the computer now equals the telephone as a medium (...) of communication, it is easy to forget the debt we owe to an era that industrialized the flow of information, that the light bulb, to pick a singular example, which is useful for upgrading visual information we might otherwise overlook, nonetheless remains the most prevalent of all modern day information technologies. Edison’s light bulb, of course, belongs to a different order of informational devices than the computer, but not so the telephone, not entirely anyway. Alan Turing, best known for his work on the Theory of Computation (1937), the Turing Machine (also 1937) and the Turing Test (1950), is often credited with being the father of computer science and the father of artificial intelligence. Less well-known to the casual reader but equally important is his work in computer engineering. The following lecture on the Automatic Computing Engine, or ACE, shows Turing in this different light, as a mechanist concerned with getting the greatest computational power from minimal hardware resources. Yet Turing’s work on mechanisms is often eclipsed by his thoughts on computability and his other theoretical interests. This is unfortunate for several reasons, one being that it obscures our picture of the historical trajectory of information technology, a second that it emphasizes a false dichotomy between “hardware” and “software” to which Turing himself did not ascribe but which has, nonetheless, confused researchers who study the nature of mind and intelligence for generations.. (shrink)

We investigate Turing's contributions to computability theory for real numbers and real functions presented in [22, 24, 26]. In particular, it is shown how two fundamental approaches to computable analysis, the so-called ‘Type-2 Theory of Effectivity' (TTE) and the ‘realRAM machine' model, have their foundations in Turing's work, in spite of the two incompatible notions of computability they involve. It is also shown, by contrast, how the modern conceptual tools provided by these two paradigms allow a systematic interpretation (...) of Turing's pioneering work in the subject. (shrink)

The mathematical genius Alan Turing, well known for his crucial wartime role in breaking the ENIGMA code, was the first to conceive of the fundamental principle of the modern computer. This text contains first hand accounts by Turing and by the pioneers of computing who worked with him on his revolutionary design for an electronic computing machine - his Automatic Computing Engine.

The origin of my article lies in the appearance of Copeland and Proudfoot's feature article in Scientific American, April 1999. This preposterous paper, as described on another page, suggested that Turing was the prophet of 'hypercomputation'. In their references, the authors listed Copeland's entry on 'The Church-Turing thesis' in the Stanford Encyclopedia. In the summer of 1999, I circulated an open letter criticising the Scientific American article. I included criticism of this Encyclopedia entry. This was forwarded to Prof. (...) Ed Zalta, editor of the Encyclopedia, and after some discussion he invited me to submit an entry on ' Alan Turing.'. (shrink)

In 1936, Alan Turing proposed the notion of an automated machine as a model of the computation performed by a human being while only being aided by mechanical resources. Still, it seems that much more can be said about Turing’s own conception of machines in the scope of his later work, both terminologically and conceptually. In this paper we present the terms he used that refer to machines and that according to our understanding are important to give (...) an account of Turing’s concerns and the problems he tackled with after his first recourse to the notion of machine during the late nineteen-thirties. Exploring his usage of such terms we show how it is possible to see an enlargement or extension towards a general notion of machine from the very first automated machine. At the same time, we identify in his work a modelling attitude or stance in which machines can be used as a way to understand and explain a natural or abstract phenomenon. (shrink)

Almost everything Turing wrote is now accessible on-line in some form, much of it in the Turing Digital Archive, which makes available scanned versions of the physical papers held in the archive at King's College, Cambridge University. See..

Well known for this crucial wartime role in breaking the ENIGMA code, this book chronicles Turing's struggle to build the modern computer. Includes first hand accounts by Turing and the pioneers of computing who worked with him.

This volume presents an historical and philosophical revisiting of the foundational character of Turing's conceptual contributions and assesses the impact of the work of Alan Turing on the history and philosophy of science. Written by experts from a variety of disciplines, the book draws out the continuing significance of Turing's work. The centennial of Turing's birth in 2012 led to the highly celebrated "Alan Turing Year", which stimulated a world-wide cooperative, interdisciplinary revisiting of (...) his life and work. Turing is widely regarded as one of the most important scientists of the twentieth century: He is the father of artificial intelligence, resolver of Hilbert's famous Entscheidungsproblem, and a code breaker who helped solve the Enigma code. His work revolutionized the very architecture of science by way of the results he obtained in logic, probability and recursion theory, morphogenesis, the foundations of cognitive psychology, mathematics, and cryptography. Many of Turing's breakthroughs were stimulated by his deep reflections on fundamental philosophical issues. Hence it is fitting that there be a volume dedicated to the philosophical impact of his work. One important strand of Turing's work is his analysis of the concept of computability, which has unquestionably come to play a central conceptual role in nearly every branch of knowledge and engineering. (shrink)

El Test de Turing es un método tan controvertido como desafiante en Inteligencia Artificial. Se basa en la imitación de la conducta lingüística de humanos, y tiene como objetivo recabar evidencia empírica en favor de la tesis de que las máquinas programadas podrían pensar. Alan Turing, su creador, ha sido catalogado como conductista por la mayor parte de los comentaristas. En este capítulo muestro que no lo es. Por el contrario, Turing es un funcionalista, porque todo (...) el énfasis del juego de la imitación está en el engaño de la máquina hacia los humanos. Por ello el género es importante en dicho juego, al menos en su versión preliminar. (shrink)

Turing made strong statements about the future of machines in society. This article asks how they can be interpreted to advance our understanding of Turing’s philosophy. His irony has been largely caricatured or minimized by historians, philosophers, scientists, and others. Turing is often portrayed as an irresponsible scientist, or associated with childlike manners and polite humor. While these representations of Turing have been widely disseminated, another image suggested by one of his contemporaries, that of a nonconformist, (...) utopian, and radically progressive thinker reminiscent of the English Romantic poet Percy B. Shelley, has remained largely underexplored. Following this image, I will reconstruct the argument underlying what Turing called (but denied being guilty of) his “Promethean irreverence” (1947–1951) as a utopian satire directed against chauvinists of all kinds, especially intellectuals who might sacrifice independent thought to maintain their power. These, Turing hoped, would eventually be rivaled and surpassed by intelligent machines and transformed into ordinary people, as work once considered “intellectual” would be transformed into non-intellectual, “mechanical” work. I study Turing’s irony in its historical context and follow the internal logic of his arguments to their limit. I suggest that Turing genuinely believed that the possibilities of the machines he envisioned were not utopian dreams, and yet he conceived them from a utopian frame of mind, aspiring to a different society. His ever-learning child machines, whose intelligence would grow out of their own individual experiences, would help distribute power. (shrink)

Alan Turing is known for both his mathematical creativity and genius and role in cryptography war efforts, and for his homosexuality, for which he was persecuted. Yet there is little work that brings these two parts of his life together. This paper deconstructs and moves beyond the extant stereotypes around perceived associations between gay men and creativity, to consider how Turing’s lived experience as a queer mathematician provides a rich seam of insight into the ways in which (...) his life, relationships, and working environment shaped his work. (shrink)