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1 constructive mathematics
Математика: конструктивная математикаУниверсальный англо-русский словарь > constructive mathematics
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2 constructive mathematics
English-Russian scientific dictionary > constructive mathematics
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3 mathematics
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4 constructible
конструируемый constructible [constructive] mathematics ≈ конструктивная математика - constructible class - constructible set - constructible sheaf - constructible topology - constructible universe ConstructibleБольшой англо-русский и русско-английский словарь > constructible
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5 positive
positive ['pɒzɪtɪv]∎ are you positive about that? en êtes-vous sûr?;∎ are you absolutely sure? - yes, positive en êtes-vous absolument sûr? - sûr et certain;∎ I'm positive (that) he wasn't there je suis absolument sûr qu'il n'y était pas;∎ it's absolutely positive c'est sûr et certain(b) (constructive) positif, constructif;∎ it's one of my few positive achievements c'est une des rares choses positives ou constructives que j'aie faites;∎ haven't you got any positive suggestions? n'avez-vous rien à proposer qui fasse avancer les choses?;∎ she has a very positive approach to the problem son approche du problème est très positive ou constructive∎ there was a tremendously positive response to this idea cette idée a été extrêmement bien accueillie ou reçue(d) (definite → fact, progress) réel, certain; (clear → change, advantage) réel, effectif; (precise → instructions) formel, clair;∎ we have positive evidence of his involvement nous avons des preuves irréfutables de son implication;∎ his intervention was a positive factor in the release of the hostages son intervention a efficacement contribué à la libération des otages;∎ the team needs some positive support l'équipe a besoin d'un soutien réel ou effectif;∎ positive proof, British proof positive preuve f formelle(e) (as intensifier → absolute) absolu, véritable, pur;∎ the whole thing was a positive nightmare tout cela était un véritable cauchemar;∎ a positive delight un pur délice;∎ a positive pleasure un véritable plaisir;∎ it's a positive lie c'est un mensonge, ni plus ni moins∎ she answered in a very positive tone elle a répondu d'un ton très assuré ou très ferme∎ positive degree (of adjective, adverb) degré m positif2 noun∎ in the positive à la forme positive∎ to reply in the positive répondre par l'affirmative ou affirmativement(c) Photography épreuve f positive(d) Electricity borne f positive►► positive discrimination (UNCOUNT) discrimination f positive (mesures favorisant les membres de groupes minoritaires);∎ positive discrimination in favour of people with disabilities mesures fpl en faveur des handicapés;positive feedback (in electronic circuit) réaction f positive; (in mechanical or cybernetic system) feed-back m inv positif, rétroaction f positive;∎ figurative I didn't get much positive feedback on my suggestion ma proposition n'a pas enthousiasmé grand monde;American positive ID papiers mpl d'identité (avec photo);Finance positive prescription prescription f acquisitive;Photography positive print positif m, épreuve f positive;positive proof preuve f formelle;Psychology positive reinforcement renforcement m positif;positive thinking idées fpl constructives;positive vetting contrôle m ou enquête f de sécurité (sur un candidat à un poste touchant à la sécurité nationale) -
6 positive
positive [ˈpɒzɪtɪv]1. adjectivea. ( = not negative) positifb. ( = definite) [change, increase, improvement] réel• there is positive evidence that... il y a des preuves formelles que...• are you sure? -- positive! tu es sûr ? -- certain !2. noun• the positives far outweigh the negatives les points positifs compensent largement les points négatifs3. adverb4. compounds* * *['pɒzətɪv] 1.1) Linguistics (degré m) affirmatif m2) Photography positif m3) Mathematics nombre m positif4) Electricity (pôle m) positif m2.1) ( affirmative) [answer] positif/-ive2) ( optimistic) [message, person, response, tone] positif/-iveto be positive about — être enthousiaste à propos de [idea, proposal]
3) ( constructive) [contribution, effect, progress] positif/-ive; [advantage, good] réel/réelle4) ( pleasant) [experience, feeling] positif/-ive5) ( sure) [identification, proof] formel/-elle; [fact] indéniableto be positive — être sûr ( about de; that que)
‘positive!’ — ‘certain!’
6) ( forceful) [action, measure] catégorique7) Medicine [reaction, result, test] positif/-ive8) Chemistry, Electricity, Mathematics, Photography, Physics positif/-ive9) (épith) ( extreme) [pleasure] pur (before n); [disgrace, outrage, genius] véritable (before n) -
7 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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