"Mathematical reasoning may be regarded rather schematically as
the exercise of a combination of two faculties, which we may call intuition and
ingenuity. The activity of the intuition consists in making spontaneous
judgments which are not the result of conscious trains of reasoning. These
judgments are often but by no means invariably correct (leaving aside the
question as to what is meant by 'correct'). Often it is possible to find some other
way of verifying the correctness of an intuitive judgment. One may for instance
judge that all positive integers are uniquely factorable into primes; a
detailed mathematical argument leads to the same result. It will also involve
intuitive judgments, but they will be ones less open to criticism than the
original judgment about factorization." (Alan M Turing, "Systems of Logic Based on Ordinals", Proceedings of the London Mathematical Society Vol 45 (2), 1939)
"The exercise of ingenuity in mathematics consists in aiding
the intuition through suitable arrangements of propositions, and perhaps
geometrical figures or drawings. It is intended that when these are really well
arranged the validity of the intuitive steps which are required cannot
seriously be doubted."
"A computer would deserve to be called intelligent if it could deceive a human into believing that it was human." (Alan M Turing, "Computing Machinery and Intelligence", Mind Vol. 59, 1950)
"If one wants to make a machine mimic the behaviour of the human computer in some complex operation one has to ask him how it is done, and then translate the answer into the form of an instruction table. Constructing instruction tables is usually described as 'programming'." (Alan Turing, "Computing Machinery and Intelligence", Mind Vol. 59, 1950)
"It is unnecessary to design various new machines to do various computing processes. They can all be done with one digital computer, suitably programmed for each case." (Alan Turing, "Computing Machinery and Intelligence", Mind Vol. 59, 1950)
"The idea behind digital computers may be explained by saying that these machines are intended to carry out any operations which could be done by a human computer." (Alan M Turing, "Computing Machinery and Intelligence", Mind Vol. 59, 1950)
"The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are particularly subject. This is the assumption that as soon as a fact is presented to a mind all consequences of that fact spring into the mind simultaneously with it. It is a very useful assumption under many circumstances, but one too easily forgets that it is false. A natural consequence of doing so is that one then assumes that there is no virtue in the mere working out of consequences from data and general principles." (Alan M Turing, "Computing Machinery and Intelligence", Mind Vol. 59, 1950)
"This model will be a simplification and an idealization, and consequently a falsification. It is to be hoped that the features retained for discussion are those of greatest importance in the present state of knowledge." (Alan M Turing, "The Chemical Basis of Morphogenesis" , Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences, Vol. 237 (641), 1952)
"Almost everyone now acknowledges that theory and experiment, model making, theory construction and linguistics all go together, and that the successful development of a science of behavior depends upon a ‘total approach’ in which, given that the computer ‘is the only large-scale universal model’ that we possess, ‘we may expect to follow the prescription of Simon and construct our models - or most of them - in the form of computer programs’." (Alan M Turing)
"Science is a differential equation. Religion is a boundary condition." (Alan M Turing)
"The whole thinking process is rather mysterious to us, but I believe that the attempt to make a thinking machine will help us greatly in finding out how we think ourselves." (Alan M Turing)
"We do not need to have an infinity of different machines doing different jobs. A single one will suffice. The engineering problem of producing various machines for various jobs is replaced by the office work of "programming" the universal machine to do these jobs." (Alan M Turing)
"The idea behind digital computers may be explained by saying that these machines are intended to carry out any operations which could be done by a human computer." (Alan M Turing, "Computing Machinery and Intelligence", Mind Vol. 59, 1950)
"The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are particularly subject. This is the assumption that as soon as a fact is presented to a mind all consequences of that fact spring into the mind simultaneously with it. It is a very useful assumption under many circumstances, but one too easily forgets that it is false. A natural consequence of doing so is that one then assumes that there is no virtue in the mere working out of consequences from data and general principles." (Alan M Turing, "Computing Machinery and Intelligence", Mind Vol. 59, 1950)
"This model will be a simplification and an idealization, and consequently a falsification. It is to be hoped that the features retained for discussion are those of greatest importance in the present state of knowledge." (Alan M Turing, "The Chemical Basis of Morphogenesis" , Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences, Vol. 237 (641), 1952)
"Almost everyone now acknowledges that theory and experiment, model making, theory construction and linguistics all go together, and that the successful development of a science of behavior depends upon a ‘total approach’ in which, given that the computer ‘is the only large-scale universal model’ that we possess, ‘we may expect to follow the prescription of Simon and construct our models - or most of them - in the form of computer programs’." (Alan M Turing)
"Science is a differential equation. Religion is a boundary condition." (Alan M Turing)
"The whole thinking process is rather mysterious to us, but I believe that the attempt to make a thinking machine will help us greatly in finding out how we think ourselves." (Alan M Turing)
"We do not need to have an infinity of different machines doing different jobs. A single one will suffice. The engineering problem of producing various machines for various jobs is replaced by the office work of "programming" the universal machine to do these jobs." (Alan M Turing)
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