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1 mathematics of logic
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математическая логика математическая логикаБольшой англо-русский и русско-английский словарь > mathematics of logic
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4 mathematics of logic
Вычислительная техника: математическая логика -
5 mathematics of logic
English-Russian electronics dictionary > mathematics of logic
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6 mathematics of logic
The New English-Russian Dictionary of Radio-electronics > mathematics of logic
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7 mathematics of logic
English-Russian dictionary of computer science and programming > mathematics of logic
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8 mathematics of logic
English-Russian scientific dictionary > mathematics of logic
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9 mathematics of logic
The English-Russian dictionary on reliability and quality control > mathematics of logic
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10 mathematics
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11 mathematics
а) наука, изучающая количественные соотношения между величинами и пространственными формами в символическом представленииб) математический аппарат; математические действия, процедуры, методы и свойства- applied mathematics
- Boolean mathematics
- calculus mathematics
- combinatorial mathematics
- computational mathematics
- concrete mathematics
- crystal mathematics
- discrete mathematics
- elementary mathematics
- higher mathematics
- pure mathematics
- recreational mathematics -
12 mathematics
а) наука, изучающая количественные соотношения между величинами и пространственными формами в символическом представленииб) математический аппарат; математические действия, процедуры, методы и свойства•- Boolean mathematics
- calculus mathematics
- combinatorial mathematics
- computational mathematics
- concrete mathematics
- crystal mathematics
- discrete mathematics
- elementary mathematics
- higher mathematics
- mathematics of logic
- pure mathematics
- recreational mathematicsThe New English-Russian Dictionary of Radio-electronics > mathematics
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13 mathematics
English-Russian dictionary of computer science and programming > mathematics
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14 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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15 mathematics
mæƟə'mætiks(( abbreviation maths mæ, (American) math mæƟ) the science or branch of knowledge dealing with measurements, numbers and quantities.) matematikk (matte)- mathematically
- mathematicianmatematikksubst. \/ˌmæθəˈmætɪks\/1) ( tar verb i entall) matematikk2) ( tar verb i flertall) kalkulasjoner, utregningerapplied mathematics anvendt matematikk -
16 logic
Iதர்க்கவியல், அறிவுப்பூர்வமானIIதருக்க இயல்தருக்க இயல்IVலாஜிக்VமுறைமைVIதருக்க நூல்தர்க்கவியல்அறிவுப்பூர்வமானIXஏரணம்Xதர்க்கம் (ஒரு கருத்திலிருந்து இன்னொன்றை உருவாக்கும் செயல்) -
17 ladder logic
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18 arithmetic and logic unit
mathematics• aritmeettislooginen yksikkö -
19 arithmetik-logic unit
mathematics• aritmeettislooginen yksikkö -
20 математический логика
Большой англо-русский и русско-английский словарь > математический логика
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Logic and the philosophy of mathematics in the nineteenth century — John Stillwell INTRODUCTION In its history of over two thousand years, mathematics has seldom been disturbed by philosophical disputes. Ever since Plato, who is said to have put the slogan ‘Let no one who is not a geometer enter here’ over the… … History of philosophy
Logic (disambiguation) — Logic is the study of the principles and criteria of valid inference and demonstration.Logic may also refer to:In logic and mathematics*A branch of logic: **Inductive logic, also called induction or inductive reasoning **Informal logic, the study … Wikipedia
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logic, philosophy of — Philosophical study of the nature and scope of logic. Examples of questions raised in the philosophy of logic are: In virtue of what features of reality are the laws of logic true? ; How do we know the truths of logic? ; and Could the laws of… … Universalium
mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… … Universalium
Logic and the mind — This article discusses the relationship between the formal logic and the mind.For a long time people believed that intelligence is equivalent to conceptual understanding and reasoning. A part of this belief was that the mind works according to… … Wikipedia
mathematics, philosophy of — The philosophy of mathematics attempts to explain both the nature of mathematical facts and entities, and the way in which we have our knowledge of both. Modern philosophy of mathematics began with the foundational studies of Cantor, R. Dedekind … Philosophy dictionary
Mathematics and art — have a long historical relationship. The ancient Egyptians and ancient Greeks knew about the golden ratio, regarded as an aesthetically pleasing ratio, and incorporated it into the design of monuments including the Great Pyramid,[1] the Parthenon … Wikipedia
Logic in Islamic philosophy — Logic (Arabic: Mantiq ) played an important role in early Islamic philosophy. Islamic law placed importance on formulating standards of argument, which gave rise to a novel approach to logic in Kalam, as seen in the method of qiyas . This… … Wikipedia
Logic in computer science — describes topics where logic is applied to computer science and artificial intelligence. These include:*Investigations into logic that are guided by applications in computer science. For example: Combinatory logic and Abstract interpretation;… … Wikipedia
