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1 конструктивний доказ
Українсько-англійський юридичний словник > конструктивний доказ
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2 конструктивное доказательство
constructive proof мат.Русско-английский научно-технический словарь Масловского > конструктивное доказательство
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3 конструктивное доказательство
1) Computers: constructive proof2) Accounting: constructive argumentУниверсальный русско-английский словарь > конструктивное доказательство
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4 Logic
My initial step... was to attempt to reduce the concept of ordering in a sequence to that of logical consequence, so as to proceed from there to the concept of number. To prevent anything intuitive from penetrating here unnoticed, I had to bend every effort to keep the chain of inference free of gaps. In attempting to comply with this requirement in the strictest possible way, I found the inadequacy of language to be an obstacle. (Frege, 1972, p. 104)I believe I can make the relation of my 'conceptual notation' to ordinary language clearest if I compare it to the relation of the microscope to the eye. The latter, because of the range of its applicability and because of the ease with which it can adapt itself to the most varied circumstances, has a great superiority over the microscope. Of course, viewed as an optical instrument it reveals many imperfections, which usually remain unnoticed only because of its intimate connection with mental life. But as soon as scientific purposes place strong requirements upon sharpness of resolution, the eye proves to be inadequate.... Similarly, this 'conceptual notation' is devised for particular scientific purposes; and therefore one may not condemn it because it is useless for other purposes. (Frege, 1972, pp. 104-105)To sum up briefly, it is the business of the logician to conduct an unceasing struggle against psychology and those parts of language and grammar which fail to give untrammeled expression to what is logical. He does not have to answer the question: How does thinking normally take place in human beings? What course does it naturally follow in the human mind? What is natural to one person may well be unnatural to another. (Frege, 1979, pp. 6-7)We are very dependent on external aids in our thinking, and there is no doubt that the language of everyday life-so far, at least, as a certain area of discourse is concerned-had first to be replaced by a more sophisticated instrument, before certain distinctions could be noticed. But so far the academic world has, for the most part, disdained to master this instrument. (Frege, 1979, pp. 6-7)There is no reproach the logician need fear less than the reproach that his way of formulating things is unnatural.... If we were to heed those who object that logic is unnatural, we would run the risk of becoming embroiled in interminable disputes about what is natural, disputes which are quite incapable of being resolved within the province of logic. (Frege, 1979, p. 128)[L]inguists will be forced, internally as it were, to come to grips with the results of modern logic. Indeed, this is apparently already happening to some extent. By "logic" is not meant here recursive function-theory, California model-theory, constructive proof-theory, or even axiomatic settheory. Such areas may or may not be useful for linguistics. Rather under "logic" are included our good old friends, the homely locutions "and," "or," "if-then," "if and only if," "not," "for all x," "for some x," and "is identical with," plus the calculus of individuals, event-logic, syntax, denotational semantics, and... various parts of pragmatics.... It is to these that the linguist can most profitably turn for help. These are his tools. And they are "clean tools," to borrow a phrase of the late J. L. Austin in another context, in fact, the only really clean ones we have, so that we might as well use them as much as we can. But they constitute only what may be called "baby logic." Baby logic is to the linguist what "baby mathematics" (in the phrase of Murray Gell-Mann) is to the theoretical physicist-very elementary but indispensable domains of theory in both cases. (Martin, 1969, pp. 261-262)There appears to be no branch of deductive inference that requires us to assume the existence of a mental logic in order to do justice to the psychological phenomena. To be logical, an individual requires, not formal rules of inference, but a tacit knowledge of the fundamental semantic principle governing any inference; a deduction is valid provided that there is no way of interpreting the premises correctly that is inconsistent with the conclusion. Logic provides a systematic method for searching for such counter-examples. The empirical evidence suggests that ordinary individuals possess no such methods. (Johnson-Laird, quoted in Mehler, Walker & Garrett, 1982, p. 130)The fundamental paradox of logic [that "there is no class (as a totality) of those classes which, each taken as a totality, do not belong to themselves" (Russell to Frege, 16 June 1902, in van Heijenoort, 1967, p. 125)] is with us still, bequeathed by Russell-by way of philosophy, mathematics, and even computer science-to the whole of twentieth-century thought. Twentieth-century philosophy would begin not with a foundation for logic, as Russell had hoped in 1900, but with the discovery in 1901 that no such foundation can be laid. (Everdell, 1997, p. 184)Historical dictionary of quotations in cognitive science > Logic
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5 Unconscious
Prior to Descartes and his sharp definition of the dualism there was no cause to contemplate the possible existence of unconscious mentality as part of a separate realm of mind. Many religious and speculative thinkers had taken for granted factors lying outside but influencing immediate awareness.... Until an attempt had been made (with apparent success) to choose awareness as the defining characteristic of mind, there was no occasion to invent the idea of unconscious mind.... It is only after Descartes that we find, first the idea and then the term "unconscious mind" entering European thought. (Whyte, 1962, p. 25)If there are two realms, physical and mental, awareness cannot be taken as the criterion of mentality [because] the springs of human nature lie in the unconscious... as the realm which links the moments of human awareness with the background of organic processes within which they emerge. (Whyte, 1962, p. 63)he unconscious was no more invented by Freud than evolution was invented by Darwin, and has an equally impressive pedigree, reaching back to antiquity.... At the dawn of Christian Europe the dominant influence were the Neoplatonists; foremost among them Plotinus, who took it for granted that "feelings can be present without awareness of them," that "the absence of a conscious perception is no proof of the absence of mental activity," and who talked confidently of a "mirror" in the mind which, when correctly aimed, reflects the processes going on inside it, when aimed in another direction, fails to do so-but the process goes on all the same. Augustine marvelled at man's immense store of unconscious memories-"a spreading, limitless room within me-who can reach its limitless depth?"The knowledge of unconscious mentation had always been there, as can be shown by quotations from theologians like St. Thomas Aquinas, mystics like Jacob Boehme, physicians like Paracelsus, astronomers like Kepler, writers and poets as far apart as Dante, Cervantes, Shakespeare, and Montaigne. This in itself is in no way remarkable; what is remarkable is that this knowledge was lost during the scientific revolution, more particularly under the impact of its most influential philosopher, Rene Descartes. (Koestler, 1964, p. 148)4) The Constructive Nature of Automatic Cognitive Functioning Argues for the Existence of Unconscious ActivityThe constructive nature of the automatic functioning argues the existence of an activity analogous to consciousness though hidden from observation, and we have therefore termed it unconscious. The negative prefix suggests an opposition, but it is no more than verbal, not any sort of hostility or incompatibility being implied by it, but simply the absence of consciousness. Yet a real opposition between the conscious and the unconscious activity does subsist in the limitations which the former tends to impose on the latter. (Ghiselin, 1985, p. 7)Historical dictionary of quotations in cognitive science > Unconscious
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6 В том смысле, что
The proof of the theorem is constructive in that it actually suggests an algorithm for computing the factorizationThis method has the advantage over capacitance methods in that it does not require differentiation to obtain...The computer is only automatic in the sense that it can deal with explicit instructionsРусско-английский словарь по прикладной математике и механике > В том смысле, что
См. также в других словарях:
Constructive proof — In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object with certain properties by creating or providing a method for creating such an object. This is in contrast to a nonconstructive… … Wikipedia
constructive — A constructive proof is one that enables one to give an example, or give a rule for finding an example, of a mathematical object with some property. A nonconstructive proof might result in us knowing that an example exists, but having no idea how … Philosophy dictionary
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constructive notice — Not actual notice; such circumstances as the law deems the equivalent of actual notice since they are such as, under the law, put a party upon inquiry. 55 Am J1st V & P § 697. The substitute in law for actual notice, being based upon a… … Ballentine's law dictionary
Constructive dilemma — Rules of inference Propositional calculus Modus ponens (A→B, A ⊢ B) Modus tollens (A→B, ¬B ⊢ ¬A) … Wikipedia
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Bijective proof — In combinatorics, bijective proof is a proof technique that finds a bijective function f : A → B between two sets A and B , thus proving that they have the same number of elements, | A | = | B |. One place the technique is useful is where we wish … Wikipedia
Turing's proof — First published in January 1937 with the title On Computable Numbers, With an Application to the Entscheidungsproblem , Turing s proof was the second proof of the assertion (Alonzo Church proof was first) that some questions are undecidable :… … Wikipedia
Gentzen's consistency proof — Gentzen s theoremIn 1936 Gerhard Gentzen proved the consistency of first order arithmetic using combinatorial methods. Gentzen s proof shows much more than merely that first order arithmetic is consistent. Gentzen showed that the consistency of… … Wikipedia
