Feb 06, · Thesis Prospectus Guidelines Department of Philosophy. Philosophy strives to answer the most fundamental questions about the world and our place in it. Learn More. Courses. View the department's undergraduate and graduate course offerings. Learn More. Climate and Diversity Jun 03, · The implications of this view were exposed to a wider circle in his famous paper, “Computing Machinery and Intelligence,” which appeared in Mind in October The appearance of this paper, Turing's first foray into a journal of philosophy, was stimulated by his discussions at Manchester University with Michael Polanyi We would like to show you a description here but the site won’t allow blogger.com more
The Church-Turing Thesis (Stanford Encyclopedia of Philosophy)
Alan Turing's short and extraordinary life has attracted wide interest. It has inspired his mother's memoir E. Turinga detailed biography Hodgesa play and television film Whitemoreand various other works of fiction and art, philosophy paper thesis.
There are many reasons for this interest, but one is that in every sphere of his life and work he made unexpected connections between apparently unrelated areas, philosophy paper thesis. His central contribution to science and philosophy came through philosophy paper thesis treating the subject of symbolic logic as a new branch of applied mathematics, giving it a physical and engineering content.
Unwilling or unable philosophy paper thesis remain within any standard role or department of thought, Alan Turing continued a life full of incongruity. Though a shy, boyish, man, he had a pivotal role in world history through his role in Second World War cryptology. Though the founder of the dominant technology of the twentieth century, philosophy paper thesis, he variously impressed, charmed or disturbed people with his unworldly innocence and his dislike of moral or intellectual compromise.
Alan Mathison Turing was born in London, philosophy paper thesis, 23 Juneto philosophy paper thesis British parents. His scepticism, and disrespect for worldly values, were never tamed and became ever more confidently eccentric. His moody humour swung between gloom and vivacity. His life was also notable as that of a gay man with strong emotions and a growing insistence on his identity. His first true home was at King's College, Cambridge University, noted for its progressive intellectual life centred on J.
Turing studied mathematics with increasing distinction and was elected a Fellow of the college in This appointment was followed by a remarkable and sudden début in an area where he was an unknown figure: that of mathematical logic. Philosophy paper thesis gave a definition of computation and an absolute limitation on what computation could achieve, which makes it the founding work of modern computer science. It led him to Princeton for more advanced work in logic and other branches of mathematics.
He had the opportunity to remain in the United States, but chose to return to Britain inand was immediately recruited for the British communications war. From to Turing was almost totally engaged in the mastery of the German enciphering machine, Enigma, and other cryptological investigations at now-famous Bletchley Park, the British government's wartime communications headquarters.
Turing made philosophy paper thesis unique logical contribution to the decryption of the Enigma and became the chief scientific figure, with a particular responsibility for reading the U-boat communications.
As such he became a top-level figure in Anglo-American liaison, and also gained exposure to the most advanced electronic technology of the day.
Combining his ideas from mathematical logic, his experience in cryptology, and some practical electronic knowledge, his ambition, at the end of philosophy paper thesis war in Europe, was to create an electronic computer in the full modern sense. His plans, commissioned by the National Physical Laboratory, London, were overshadowed by the more powerfully supported American projects. Turing also laboured under the disadvantage that his wartime achievements remained totally secret.
His ideas led the field inbut this was little recognised. Frustrated in his work, he emerged as a powerful marathon runner, and almost qualified for the British team in the Olympic games. Turing's motivations were scientific rather than industrial or commercial, and he soon returned to the theoretical limitations of computation, this time focussing on the comparison of philosophy paper thesis power of computation and the power of the human brain.
His contention was that the computer, when properly programmed, could rival the brain. In he moved to Manchester University, where he partly fulfilled the expectations placed upon him to plan software for the pioneer computer development there, but still remained a free-ranging thinker.
In he was elected a Fellow of the Royal Society for his achievement, yet at the same time he was striking into entirely new territory with a mathematical theory of biological morphogenesis Turing This work was interrupted by Alan Turing's arrest in February for his sexual affair with a young Manchester man, and he was obliged, to escape imprisonment, philosophy paper thesis, to undergo the injection of oestrogen intended to negate his sexual drive.
He was disqualified from continuing secret cryptological work. His general libertarian attitude was enhanced rather than suppressed by the criminal trial, and his intellectual individuality also remained as lively as ever. While remaining formally a Reader in the Theory of Computing, he not philosophy paper thesis embarked on more ambitious applications of his biological theory, but advanced new ideas for fundamental physics.
For this reason his death, on 7 Juneat his home in Wilmslow, Cheshire, came as a general surprise. Some commentators, e. Dawsonhave argued that assassination should not be ruled out. But he had spoken of suicide, and his death, which was by cyanide poisoning, was most likely by his own hand, contrived so as to allow those who wished to do so to believe it a result of his penchant for chemistry experiments. The symbolism of its dramatic element—a partly eaten apple—has continued to haunt the intellectual Eden from which Alan Turing philosophy paper thesis expelled.
Alan Turing drew much between and from the work of the mathematical physicist and populariser A. Eddington, from J. von Neumann's account of the foundations of quantum mechanics, and then from Bertrand Russell's mathematical logic.
Meanwhile, his lasting fascination with the problems of mind and matter was heightened by emotional elements in his own life Hodgesp.
In he graduated with an outstanding degree in mathematics from Cambridge University, followed by a successful dissertation in probability theory which won him a Fellowship of King's College, Cambridge, in This was the background to his learning, also inof the problem which was to make his name, philosophy paper thesis. It was from the lectures of the topologist M.
Was there a method by which it could be decided, philosophy paper thesis, for any given mathematical proposition, whether or not it was provable? Turing's solution lay in defining what was soon to be named the Turing machine. Nevertheless Turing's purpose was to embody the most general mechanical process as carried out by a human being.
His analysis began philosophy paper thesis with any existing computing machines, philosophy paper thesis, but with the picture of a child's exercise book marked off in squares. From the beginning, the Turing machine concept aimed to capture philosophy paper thesis the human philosophy paper thesis can do when carrying out a procedure.
If a Turing machine corresponds to a computer program, what is the analogy of the computer? It is what Turing described as a universal machine Turingp. If this seems strange, note the modern parallel that any computer can be simulated by software on another computer. The way that tables can read and simulate the effect of other tables is crucial to Turing's theory, going far beyond Babbage's ideas of a hundred years earlier. It also shows why Turing's ideas go to the heart of the modern computer, in which it is essential that programs are themselves a form of data which can be manipulated by other programs.
Turing's machine formulation allowed the precise definition of the computable: namely, philosophy paper thesis what can be done by a Turing machine acting alone.
More exactly, computable operations are those which can be effected by what Turing called automatic machines. In applying his machine concept to the Entscheidungsproblem, Turing took the step of defining computable numbers. These are those real numbers, considered as infinite decimals, say, which it is possible for a Turing machine, starting with an empty tape, to print out.
For example, the Turing machine which simply prints the digit 1 and moves to the right, then repeats that action for ever, can thereby compute the number. The argument can be presented as follows.
Suppose that such a Turing machine exists. Then it is possible to construct a new Turing machine which works out in turn the Nth digit from the Nth machine possessing a satisfactory description number. This new machine then prints an Nth digit differing from that digit. Yet this number must by construction differ from the outputs of every Turing machine with a satisfactory description number, philosophy paper thesis.
This is a contradiction, so the hypothesis must be false Turingp. From this, Turing was able to answer Hilbert's Entscheidungsproblem in the negative: there can be no such general method. Turing's proof can be recast in many ways, but the core idea depends on the self-reference involved in a machine operating on symbols, which is itself described by symbols and so can operate on its own description.
Indeed, the self-referential aspect of the theory can be highlighted by a different form of the proof, which Turing preferred Turingphilosophy paper thesis, p.
Suppose that such a machine for deciding satisfactoriness does exist; then apply it to its own description number. A contradiction can readily be obtained. It is a non-trivial discovery that philosophy paper thesis some infinite decimals e. π may be encapsulated in a finite table, philosophy paper thesis, other infinite decimals in fact, almost all cannot, philosophy paper thesis.
This is what Turing established, and into the bargain the remarkable fact that anything that is computable can in fact be computed by one machine, a universal Turing machine.
For if it did not, the Entscheidungproblem remained open: there might be some more powerful type of method than was encompassed by Turing computability. One justification lay in showing that the definition included many processes a mathematician would consider to be natural in computation Turingp. Another argument involved a human calculator following written instruction notes.
Turingp. To summarise: Turing found, and justified on very general and far-reaching grounds, a precise mathematical formulation of the conception philosophy paper thesis a general process or method. This opened up new fields of discovery both in practical computation, and in the discussion of human mental processes.
This meant that from the outset Turing's achievement merged with and superseded the formulation of Church's Thesis, namely the assertion that the lambda-calculus formalism correctly embodied the concept of effective process or method. Very rapidly it was shown that the mathematical scope of Turing computability coincided with Church's definition philosophy paper thesis also with the scope of the general recursive functions defined by Gödel.
Turing wrote his own statement Turingp. Church accepted that Turing's definition gave a compelling, intuitive reason for why Church's thesis was true. The recent exposition by Davis emphasises that Gödel also was convinced by Turing's argument that an absolute concept had been identified Gödel The situation has not changed since For further comment, see the article on the Philosophy paper thesis Thesis. The recent selection of Turing's papers edited by Copelandand the review of Hodgescontinue this discussion.
Turing himself did little to evangelise his formulation in philosophy paper thesis world of mathematical logic and early computer science. The textbooks of Davis and Minsky did more. Nowadays Turing computability is often reformulated e. However, computer simulations e. Turing's work also opened new areas for decidability questions within pure mathematics. From the s, Turing machines also took on new life in the development of complexity theory, and as such underpin one of the most important research areas in computer science.
This development exemplifies the lasting value of Turing's special quality of giving concrete illustration to abstract concepts. But it was more than being an analysis within the world of mathematical logic: in Turing's thought the question that constantly recurs both theoretically and practically is the relationship of the logical Turing machine to the physical world.
The tape never holds more than a finite number of marked squares at any point in a computation. Thus it can be thought of as being finite, but always capable of further extension as required.
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, time: 4:12Alan Turing (Stanford Encyclopedia of Philosophy)
A term paper is much simpler in nature and tries to support an existing thesis paper in most cases. That’s why a research paper has a significantly longer length. Despite a research paper being more crucial, it doesn't affect a student’s final grade while a term paper strongly controls the grades Feb 06, · Thesis Prospectus Guidelines Department of Philosophy. Philosophy strives to answer the most fundamental questions about the world and our place in it. Learn More. Courses. View the department's undergraduate and graduate course offerings. Learn More. Climate and Diversity We would like to show you a description here but the site won’t allow blogger.com more
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