-
1 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
-
2 конструктивная логика
Русско-английский технический словарь > конструктивная логика
-
3 канструктыўная логіка
constructive logicБеларуска-ангельскі слоўнік матэматычных тэрмінаў і тэрміналагічных словазлучэнняў > канструктыўная логіка
-
4 конструктивная логика
Русско-английский словарь по вычислительной технике и программированию > конструктивная логика
-
5 logika konstruktywna
• constructive logicSłownik polsko-angielski dla inżynierów > logika konstruktywna
-
6 конструктивная логика
Русско-английский математический словарь > конструктивная логика
-
7 конструктивная логика
Русско-английский большой базовый словарь > конструктивная логика
-
8 конструктивная логика
-
9 конструктивная логика
Русско-английский словарь по информационным технологиям > конструктивная логика
-
10 логика
ло́гика ж.
logicадапти́вная ло́гика — adaptive logicбина́рная ло́гика — binary logicло́гика «большинства́» — majority logicвероя́тностная ло́гика — probabilistic logicло́гика выска́зываний — propositional logicдиалекти́ческая ло́гика — dialectical logicN-зна́чная ло́гика — N-valued logicинтенсиона́льная ло́гика — intensional logicинтуициони́стская ло́гика — intuitiotistic logicкомбинато́рная ло́гика — combinatorial [combinatory] logicконструкти́вная ло́гика — constructive logicмажорита́рная ло́гика — majority logicматемати́ческая ло́гика — mathematical logicмногозна́чная ло́гика — many-valued logicмода́льная ло́гика — modal logicнерегуля́рная ло́гика — irregular logicотрица́тельная ло́гика — negative logicположи́тельная ло́гика — positive logicпоро́говая ло́гика — threshold logicло́гика предика́тов — predicate logicло́гика прерыва́ния — interrupt logicпрограмми́руемая ло́гика — programmable logicсимволи́ческая ло́гика — symbolic logicстати́ческая ло́гика — static logicтеорети́ческая ло́гика — mathematical logicтрои́чная ло́гика — ternary logicформа́льная ло́гика — formal logic -
11 логика
ж. logicлогика «большинства» — majority logic
-
12 конструктивная логика
Mathematics: constructive logicУниверсальный русско-английский словарь > конструктивная логика
-
13 Memory
To what extent can we lump together what goes on when you try to recall: (1) your name; (2) how you kick a football; and (3) the present location of your car keys? If we use introspective evidence as a guide, the first seems an immediate automatic response. The second may require constructive internal replay prior to our being able to produce a verbal description. The third... quite likely involves complex operational responses under the control of some general strategy system. Is any unitary search process, with a single set of characteristics and inputoutput relations, likely to cover all these cases? (Reitman, 1970, p. 485)[Semantic memory] Is a mental thesaurus, organized knowledge a person possesses about words and other verbal symbols, their meanings and referents, about relations among them, and about rules, formulas, and algorithms for the manipulation of these symbols, concepts, and relations. Semantic memory does not register perceptible properties of inputs, but rather cognitive referents of input signals. (Tulving, 1972, p. 386)The mnemonic code, far from being fixed and unchangeable, is structured and restructured along with general development. Such a restructuring of the code takes place in close dependence on the schemes of intelligence. The clearest indication of this is the observation of different types of memory organisation in accordance with the age level of a child so that a longer interval of retention without any new presentation, far from causing a deterioration of memory, may actually improve it. (Piaget & Inhelder, 1973, p. 36)4) The Logic of Some Memory Theorization Is of Dubious Worth in the History of PsychologyIf a cue was effective in memory retrieval, then one could infer it was encoded; if a cue was not effective, then it was not encoded. The logic of this theorization is "heads I win, tails you lose" and is of dubious worth in the history of psychology. We might ask how long scientists will puzzle over questions with no answers. (Solso, 1974, p. 28)We have iconic, echoic, active, working, acoustic, articulatory, primary, secondary, episodic, semantic, short-term, intermediate-term, and longterm memories, and these memories contain tags, traces, images, attributes, markers, concepts, cognitive maps, natural-language mediators, kernel sentences, relational rules, nodes, associations, propositions, higher-order memory units, and features. (Eysenck, 1977, p. 4)The problem with the memory metaphor is that storage and retrieval of traces only deals [ sic] with old, previously articulated information. Memory traces can perhaps provide a basis for dealing with the "sameness" of the present experience with previous experiences, but the memory metaphor has no mechanisms for dealing with novel information. (Bransford, McCarrell, Franks & Nitsch, 1977, p. 434)7) The Results of a Hundred Years of the Psychological Study of Memory Are Somewhat DiscouragingThe results of a hundred years of the psychological study of memory are somewhat discouraging. We have established firm empirical generalisations, but most of them are so obvious that every ten-year-old knows them anyway. We have made discoveries, but they are only marginally about memory; in many cases we don't know what to do with them, and wear them out with endless experimental variations. We have an intellectually impressive group of theories, but history offers little confidence that they will provide any meaningful insight into natural behavior. (Neisser, 1978, pp. 12-13)A schema, then is a data structure for representing the generic concepts stored in memory. There are schemata representing our knowledge about all concepts; those underlying objects, situations, events, sequences of events, actions and sequences of actions. A schema contains, as part of its specification, the network of interrelations that is believed to normally hold among the constituents of the concept in question. A schema theory embodies a prototype theory of meaning. That is, inasmuch as a schema underlying a concept stored in memory corresponds to the mean ing of that concept, meanings are encoded in terms of the typical or normal situations or events that instantiate that concept. (Rumelhart, 1980, p. 34)Memory appears to be constrained by a structure, a "syntax," perhaps at quite a low level, but it is free to be variable, deviant, even erratic at a higher level....Like the information system of language, memory can be explained in part by the abstract rules which underlie it, but only in part. The rules provide a basic competence, but they do not fully determine performance. (Campbell, 1982, pp. 228, 229)When people think about the mind, they often liken it to a physical space, with memories and ideas as objects contained within that space. Thus, we speak of ideas being in the dark corners or dim recesses of our minds, and of holding ideas in mind. Ideas may be in the front or back of our minds, or they may be difficult to grasp. With respect to the processes involved in memory, we talk about storing memories, of searching or looking for lost memories, and sometimes of finding them. An examination of common parlance, therefore, suggests that there is general adherence to what might be called the spatial metaphor. The basic assumptions of this metaphor are that memories are treated as objects stored in specific locations within the mind, and the retrieval process involves a search through the mind in order to find specific memories....However, while the spatial metaphor has shown extraordinary longevity, there have been some interesting changes over time in the precise form of analogy used. In particular, technological advances have influenced theoretical conceptualisations.... The original Greek analogies were based on wax tablets and aviaries; these were superseded by analogies involving switchboards, gramophones, tape recorders, libraries, conveyor belts, and underground maps. Most recently, the workings of human memory have been compared to computer functioning... and it has been suggested that the various memory stores found in computers have their counterparts in the human memory system. (Eysenck, 1984, pp. 79-80)Primary memory [as proposed by William James] relates to information that remains in consciousness after it has been perceived, and thus forms part of the psychological present, whereas secondary memory contains information about events that have left consciousness, and are therefore part of the psychological past. (Eysenck, 1984, p. 86)Once psychologists began to study long-term memory per se, they realized it may be divided into two main categories.... Semantic memories have to do with our general knowledge about the working of the world. We know what cars do, what stoves do, what the laws of gravity are, and so on. Episodic memories are largely events that took place at a time and place in our personal history. Remembering specific events about our own actions, about our family, and about our individual past falls into this category. With amnesia or in aging, what dims... is our personal episodic memories, save for those that are especially dear or painful to us. Our knowledge of how the world works remains pretty much intact. (Gazzaniga, 1988, p. 42)The nature of memory... provides a natural starting point for an analysis of thinking. Memory is the repository of many of the beliefs and representations that enter into thinking, and the retrievability of these representations can limit the quality of our thought. (Smith, 1990, p. 1)Historical dictionary of quotations in cognitive science > Memory
-
14 κατασκευαστικός
A fitted for providing, τινος Arist.VV 1250b29; fitted for bringing about,τοῦ μὴ πλανᾶν Phld.Rh.1.347
S.2 in Logic, constructive, positive, opp. destructive ([etym.] λυτικός, ἀνασκευαστικός), Arist.Rh. 1403a25, Theon Prog.12, etc.: c.gen.,λόγος κ. ζητήματος Corn.Rh.p.377
H., cf. Nicol. Prog.p.29 F. Adv. - κῶς, opp. ἀνασκευαστικῶς, Arist.APr. 52a31.3 ( κατασκευή VIII) systematic,γυμνάσια Gal.6.177
.Greek-English dictionary (Αγγλικά Ελληνικά-λεξικό) > κατασκευαστικός
-
15 κατασκευή
κατασκευ-ή, ἡ,A preparation, ὄντων ἐν κατασκευῇ τοῦ πολέμου being engaged in preparing for it, Th. 8.5; construction,λιμένων ἢ νεωρίων Pl.Grg. 455b
; fitting out,πλοίων Plb.1.21.1
, etc.3 training, Stoic. 3.89.II permanent or fixed assets, opp. what is movable or temporary ([etym.] παρασκευή), fixtures, plant, etc., Th.1.10; ἀνειληφότες τὰς κ. having repaired their estates, Id.2.16; ἡ περὶ τὸν κλῆρον κ. Pl. Lg. 923d; τῆς ἄλλης κ., ἐν ᾗ κατοικοῦμεν καὶ μεθ' ἧς πολιτευόμεθα καὶ δι' ἢν ζῆν δυνάμεθα the aggregate of our possessions, Isoc.4.26;αἱ κ. αἱ ἐπὶ τῶν ἀγρῶν ἢ αἱ ἐντὸς τείχους Id.7.52
; but also, like παρασκευή, any furniture or fittings, τὴν Μαρδονίου κ., i. e. his tent and its furniture, Hdt.9.82;κ. πολυτελέσι χρησαμένων Th.6.31
; φιάλας τε.. καὶ θυμιατήρια καὶ ἄλλην κ. ib.46;ἡ κ. τῆς οἰκίας D.47.54
; τῇ τῶν θεῶν κ. χρῆσθαι whatever the gods provided, X.Ages.9.5.III state, condition, constitution of a thing,θεοῦ κ. βίῳ δόντος τοιαύτην E. Supp. 214
;αἱ.. κ. τῆς ψυχῆς Pl.R. 544e
;ἡ τοῦ βίου κ. Id.Lg. 842c
; ἡ τῶν νόμων κ. ib. 739a; ἐν πάσῃ κ. πολιτικῇ ib. 736b; ἐν χρημάτων κ. in the constitution of a man's fortune, Id.Grg. 477b; ἐν σώματος κ. ibid.; κ. τις παρὰ φύσιν, definition of νόσος, Gal.6.837.IV device, trick,τέχναι καὶ κ. Aeschin.2.1
, v.l. in Din.1.34; ἄνευ κατασκευῆς ᾄδειν artlessly, Ael.NA5.38.V in Logic, constructive reasoning, opp. ἀνασκευή, D.H.Lys.24, Hermog.Prog.5, etc.: in pl., Cic.Att.1.14.4, Longin.11.2, Quint.2.4.18.VI Rhet., artistic treatment,κ. ποιητική Str.1.2.6
, D.H.Comp.1; manipulation, συλλαβῶν, γραμμάτων, ib.15, 16; elaboration, Id.Pomp.2, etc.; correct style, opp. ἰδιωτισμός, Diocl.Stoic.3.214; technical resources,πλάσμα καὶ ἡ ἄλλη κ. δημηγόρου Phld.Rh.1.199
S.VII Geom., construction, Archim.Sph.Cyl. 2.4, cf. Procl.in Euc.p.203 F.; κ. ὀργανική solution by mechanical construction, Papp.174.17.VIII system of gymnastic exercise, as t.t., Gal.6.169.Greek-English dictionary (Αγγλικά Ελληνικά-λεξικό) > κατασκευή
См. также в других словарях:
Logic — For other uses, see Logic (disambiguation). Philosophy … Wikipedia
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 set theory — is an approach to mathematical constructivism following the program of axiomatic set theory. That is, it uses the usual first order language of classical set theory, and although of course the logic is constructive, there is no explicit use of… … Wikipedia
Constructive analysis — In mathematics, constructive analysis is mathematical analysis done according to the principles of constructive mathematics. This contrasts with classical analysis, which (in this context) simply means analysis done according to the (ordinary)… … Wikipedia
logic — logicless, adj. /loj ik/, n. 1. the science that investigates the principles governing correct or reliable inference. 2. a particular method of reasoning or argumentation: We were unable to follow his logic. 3. the system or principles of… … Universalium
Constructive non-standard analysis — In mathematics, constructive nonstandard analysis is a version of Abraham Robinson s non standard analysis, developed by Moerdijk (1995), Palmgren (1998), Ruokolainen (2004). Ruokolainen wrote: The possibility of constructivization of nonstandard … Wikipedia
Constructive dilemma — Rules of inference Propositional calculus Modus ponens (A→B, A ⊢ B) Modus tollens (A→B, ¬B ⊢ ¬A) … Wikipedia
Intuitionistic logic — Intuitionistic logic, or constructive logic, is a symbolic logic system differing from classical logic in its definition of the meaning of a statement being true. In classical logic, all well formed statements are assumed to be either true or… … Wikipedia
Démonstration constructive — Une première vision d une démonstration constructive est celle d une démonstration mathématique qui respecte les contraintes des mathématiques intuitionnistes, c est à dire qui ne fait pas appel à l infini, ni au principe du tiers exclu. Ainsi… … Wikipédia en Français
Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… … Wikipedia
History of logic — Philosophy ( … Wikipedia