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101 ἄν
1I. ἄν (after relatives ἐάν [q.v.] is oft. used for ἄν, but the mss. vary greatly, s. B-D-F §107; 377; Mlt. 42ff, 165ff; Mayser 152f; Crönert 130f; Thackeray 67; Dssm., NB 30ff [BS 202ff]). A particle peculiar to Gk. (Hom.+) denoting aspect of contingency, incapable of translation by a single English word; it denotes that the action of the verb is dependent on some circumstance or condition; the effect of ἄν upon the meaning of its clause depends on the mood and tense/aspect of the verb w. which it is used. The NT use of ἄν corresponds in the main to older Gk., although the rich variety of its employment is limited, as is generally the case in later Greek. In certain constructions (s. aβ) an aspect of certainty is indicated, suggesting the gloss would. In most other instances aspects of varying possibility or conditionality find expression in ways that can be rendered ever, but with other glosses required when ἄν is used in conjunction with other particles.ⓐ ἄν w. aor. or impf. indic.α. denoting repeated action in past time, but only under certain given conditions, esp. after relatives (B-D-F §367; Rob. index): aor. (Gen 30:42; Num 9:17; 1 Km 14:47; Ezk 10:11) ὅσοι ἂν ἥψαντο αὐτοῦ, ἐσῴζοντο whoever touched him was cured Mk 6:56. Impf. (Ezk 1:20; 1 Macc 13:20; Tob 7:11) ὅπου ἂν εἰσεπορεύετο εἰς κώμας wherever he went (as he was accustomed to do—ADebrunner, D. hellenist. Nebensatziterativpräteritum mit ἄν: Glotta 11, 1920, 1–28) into villages Mk 6:56. καθότι ἄν τις χρείαν εἶχεν as anyone was in need Ac 2:45; 4:35. Similarly ὡς ἂν ἤγεσθε (v.l. ἀνήγεσθε) 1 Cor 12:2. Cp. also ὅταν 1bγ and δ.β. in the apodosis of a contrary to fact (unreal) condition w. εἰ (B-D-F §360; but ἄν is not always used [s. the vv.ll. J 18:36]: §360, 1; Mlt. 199ff; PMelcher, De sermone Epicteteo 1905, 75); it is foundא. w. impf. (4 Macc 17:7; Bar 3:13; ParJer 5:20; GrBar 6:6; ApcMos 39) οὗτος εἰ ἦν προφήτης, ἐγίνωσκεν ἄν if he were a prophet, he would (now) know (but he does not) Lk 7:39. εἰ ἔχετε πίστιν …, ἐλέγετε ἄν if you had faith …, you would say 17:6. εἰ ἐπιστεύετε Μωϋσεῖ, ἐπιστεύετε ἂν ἐμοί J 5:46. εἰ ἐμὲ ᾔδειτε, καὶ τὸν πατέρα μου ἄν ᾔδειτε 8:19; cp. vs. 42; 9:41; 15:19. εἰ ἔτι ἀνθρώποις ἤρεσκον, Χριστοῦ δοῦλος οὐκ ἂν ἤμην Gal 1:10; cp. 3:21. εἰ ἑαυτοὺς διεκρίνομεν, οὐκ ἂν ἐκρινόμεθα 1 Cor 11:31. εἰ ἦν ἐπὶ γῆς, οὐδʼ ἂν ἦν ἱερεύς if he were on earth, he would not even be a priest Hb 8:4; cp. 4:8; 8:7; 11:15.ב. w. aor., placing the assumption in the past (Gen 30:27; Wsd 11:25; Jdth 11:2; 4 Macc 2:20; TestJob 7:9 al.; ParJer 5:5; GrBar 8:7; PGiss 47, 17) εἰ ἐγένοντο αἱ δυνάμεις, πάλαι ἂν … μετενόησαν if the miracles had been performed, they would long ago have repented Mt 11:21. εἰ ἔγνωσαν, οὐκ ἂν ἐσταύρωσαν 1 Cor 2:8; cp. Ro 9:29 (Is 1:9). εἰ ἐγνώκειτε, οὐκ ἂν κατεδικάσατε if you had recognized, you would not have condemned Mt 12:7. εἰ ἠγαπᾶτέ με, ἐχάρητε ἄν if you loved me, you would have rejoiced J 14:28; cp. 11:21. The plpf. for aor. indic. (PGiss 79 II, 6 εἰ δυνατόν μοι ἦν, οὐκ ἂν ὠκνήκειν; BGU 1141, 27f) εἰ ἦσαν, μεμενήκεισαν ἄν 1J 2:19; cp. J 11:21 v.l.—In κἀγὼ ἐλθὼν σὺν τόκῳ ἂν αὐτὸ ἔπραξα Lk 19:23, ἐλθών functions as an unreal-temporal protasis (B-D-F §360, 2); cp. καὶ ἐλθὼν ἐγὼ ἐκομισάμην ἂν τὸ ἐμόν Mt 25:27. Sim. ἐπεὶ οὐκ ἂν ἐπαύσαντο προσφερόμεναι; where ἐπεί functions as protasis, otherwise (i.e. if the sacrifices had really brought about a lasting atonement) would they not have ceased to offer sacrifices? Hb 10:2.ⓑ ἄν w. subjunc. after relatives, the rel. clause forming virtually the protasis of a conditional sentence (B-D-F §380, 1) of the future more vivid or present general type.α. w. fut. or impf. in apodosis, to show that the condition and its results are thought of as in the future, of single and repeated action (IG XIV, 865 [VI B.C.] ὸ̔ς δʼ ἄν με κλέψῃ, τυφλὸς ἔσται; TestAbr B 4 p. 109, 10 [Stone p. 66]). ὸ̔ς δʼ ἂν ποιήσῃ καὶ διδάξῃ, οὗτος μέγας κληθήσεται but whoever does and teaches=if a person does and teaches it Mt 5:19. ὸ̔ς ἂν ἐσθίῃ …, ἔνοχος ἔσται 1 Cor 11:27. οὓς ἐὰν (v.l. ἂν) δοκιμάσητε, τούτους πέμψω 16:3—Mt 10:11; 1 Cor 16:2.β. w. pres. in apodosis, to show that the condition and its results involve repeated action, regardless of the time element: ἃ ἂν ἐκεῖνος ποιῇ, ταῦτα καὶ ὁ υἱὸς ὁμοίως ποιεῖ whatever he does, the Son does likewise J 5:19. ὅπου ἐὰν (v.l. ἂν) αὐτὸν καταλάβῃ, ῥήσσει αὐτόν wherever it seizes him Mk 9:18. ὑμῖν ἐστὶν ἡ ἐπαγγελία …, ὅσους ἂν προσκαλέσηται κύριος Ac 2:39. ὸ̔ς ἐὰν (v.l. ἂν) βουληθῇ φίλος εἶναι τοῦ κόσμου, ἐχθρὸς τοῦ θεοῦ καθίσταται whoever wishes to be a friend of the world Js 4:4. Cp. ὅπου ἄν 3:4 v.l.—Where ὅς or ὅστις appears w. subj. without ἄν (but cp. IG XII/1, 671 ὸ̔ς ἀνασπαράξῃ τ. τάφον; CPR I, 24, 33; 25, 19; AcThom 93 [Aa II/2, 206], 19; Is 7:2; 31:4), the reading that gives the fut. ind. is prob. the right one: ὅστις τηρήσῃ (v.l.-σει) Js 2:10. ὅσοι (without ἄν PPetr I, 13, 3;5; CPR I, 237, 3; IPergamon 249, 26 ὅσοι … ἐγλίπωσι τὴν πόλιν; Vett. Val. 125, 16): ὅσοι μετανοήσωσιν καὶ καθαρίσωσιν Hs 8, 11, 3 (s. W. and Joly app. for the textual tradition). See Reinhold 108; B-D-F §380, 4.ⓒ In temporal clauses ἄν is found w. the subjunct. when an event is to be described which can and will occur, but whose occurrence cannot yet be assumed w. certainty. Soα. ὅταν (=ὅτε ἄν; s. ὅταν) w. pres. subjunct. to indicate regularly recurring action (Wsd 12:18): ὅταν ἄρτον ἐσθίωσιν whenever they eat bread Mt 15:2. ὅταν λαλῇ τὸ ψεῦδος whenever he tells a lie J 8:44. ὅταν λέγῃ τις whenever anyone says 1 Cor 3:4.—W. aor. subjunct. to express action in the future which is thought of as already completed (Sir Prol. ln. 22; Tob 8:21) ὅταν ποιήσητε πάντα when you have done Lk 17:10. ὅταν ἔλθῃ ὁ κύριος when the owner has come Mt 21:40; ὅταν ἔλθῃ ἐν τῇ δόξῃ Mk 8:38; cp. J 4:25; 16:13; Ac 23:35. ὅταν πάλιν εἰσαγάγῃ τὸν πρωτότοκον Hb 1:6.β. ἡνίκα ἄν every time that (Ex 1:10; 33:22; 34:24 al.; POxy 104, 26 [96 A.D.]; PTebt 317, 18 [174/75] ἡνίκα ἐὰν εἰς τὸν νόμον παραγένηται). ἡνίκα ἂν (also ἐάν mss.) ἀναγινώσκηται Μωϋσῆς every time that Moses is read aloud 2 Cor 3:15; cp. vs. 16.γ. ὁσάκις ἐάν as often as: ὁσάκις ἐὰν (also ἄν mss.) πίνητε 1 Cor 11:25. ὁσάκις ἐὰν (also ἄν mss.) ἐσθίητε vs. 26.δ. ὡς ἄν as soon as (PHib 59, 2 [c. 245 B.C.] ὡς ἂν λάβῃς; 66, 4; PEleph 9, 3 [III B.C.]; PParis 46, 18 [143 B.C.]; BGU 1209, 13 [23 B.C.]; Josh 2:14; Jdth 11:15; 1 Macc 15:9): ὡς ἂν πορεύωμαι as soon as I travel Ro 15:24. ὡς ἂν ἔλθω as soon as I come 1 Cor 11:34. ὡς ἂν ἀφίδω τὰ περὶ ἐμέ as soon as I see how it will go with me Phil 2:23. ὡς ἐάν (PFay 111, 16 [95/96]) Hv 3, 8, 9; 3, 13, 2.—ἀφʼ οὗ ἄν after Lk 13:25.—In the case of temporal particles indicating a goal, viz. ἕως οὗ, ἄχρις (οὗ), μέχρις (οὗ), the mss. show considerable variation; the addition of ἄν is prob. correct only in rare cases (see B-D-F §383, 2). Only ἕως ἄν (PPetr II, 40a, 28 [III B.C.] ἕως ἂν ὑγιαίνοντας ὑμᾶς ἴδωμεν; Gen 24:14, 19; 49:10; Ex 23:30 al.) has certain attestation: μείνατε ἕως ἂν ἐξέλθητε stay until you go away Mt 10:11. ἕως ἂν ἴδωσιν τὴν βασιλείαν τοῦ θεοῦ Lk 9:27.—Mt 2:13; 5:26. ἕως ἂν λάβῃ Js 5:7 v.l.—ἄχρις οὗ (+ ἄν v.l.) ἔλθῃ 1 Cor 11:26. ἄχρις οὗ (+ ἄν v.l.) θῇ 15:25; ἄχρις οὗ ἂν ἥξω Rv 2:25 (v.l. ἄχρι). ἄχρις ἂν ἔλθῃ (cp. BGU 830, 13 [I A.D.] ἄχρις ἄν σοι ἔλθω) Gal 3:19 v.l.—πρὶν ἄν: πρὶν ἢ ἂν (vv.ll. πρὶν ἄν, πρὶν ἢ, only πρὶν or ἕως ἂν) ἴδῃ τὸν Χριστόν Lk 2:26 (B-D-F §383, 3).ⓓ In purpose clauses the Attic (EHermann, Griech. Forschungen I, 1912, 267f; JKnuenz, De enuntiatis Graec. finalibus 1913, 13ff; 26ff) ὅπως ἄν, esp. freq. in earlier ins (Meisterhans3-Schw. 254), has become quite rare (LXX still rather often: Gen 18:19; 50:20; Ex 33:13; Jer 7:23 al.) ὅπως ἂν ἀποκαλυφθῶσιν διαλογισμοί Lk 2:35. ὅπως ἂν ἔλθωσιν καιροί Ac 3:20.—15:17 (Am 9:12 v.l.); Ro 3:4 (Ps 50:6); Mt 6:5 v.l.ⓔ The opt. w. ἄν in a main clause (potential opt.) has almost wholly disappeared; a rare ex. is εὐξαίμην (v.l. εὐξάμην) ἄν Ac 26:29 in Paul’s speech before Agrippa (literary usage; s. B-D-F §385, 1; also Rob. 938; Themist. 6 p. 80 D.—On the rarity of the potential opt. in pap, LXX, Apost. Fathers see CHarsing, De Optat. in Chartis Aeg. Usu, diss. Bonn 1910, 28; Reinhold 111). Cp.—also in the literary lang. of Lk—direct rhetor. questions (Gen 23:15; Job 19:23; Sir 25:3; 4 Macc 7:22; 14:10 v.l.; TestJob 13:5 τίς ἄν δώῃ 35:5) πῶς γὰρ ἂν δυναίμην; Ac 8:31. τί ἂν θέλοι οὗτος λέγειν; 17:18. Dg has also preserved the opt. as a mark of elegant style (2:3, 10; 3:3f; 4:5; 7:2f; 8:3). MPol 2:2 has τίς οὐκ ἂν θαυμάσειεν;—More freq. in an indirect question, after an impf. or histor. pres. (B-D-F §386, 1; Rob. 938f) τὸ τί ἂν θέλοι καλεῖσθαι αὐτό what he wanted the child’s name to be Lk 1:62. τίς ἂν εἴη περὶ οὗ λέγει J 13:24. τὸ τίς ἂν εἴη μείζων αὐτῶν which of them was the greatest Lk 9:46; cp. 18:36 v.l. τί ἂν ποιήσαιεν τῷ Ἰησοῦ what they should do to Jesus 6:11. τί ἂν γένοιτο τοῦτο Ac 5:24. τί ἂν εἴη τὸ ὅραμα 10:17. (IMagnMai 215 [I A.D.] ἐπερωτᾷ … τί ἂν ποιήσας … ἀδεῶς διατελοίη; Esth 3:13c πυθομένου δέ μου … πῶς ἂν ἀχθείη τοῦτο.)ⓕ The use of ἄν w. inf. and ptc., freq. in earlier Gk., is not found in the NT at all (B-D-F §396); ἵνα μὴ δόξω ὡς ἂν (or ὡσὰν, q.v.) ἐκφοβεῖν ὑμᾶς 2 Cor 10:9 is surely to be expl. in such a way that ὡς ἂν=Lat. quasi: I would not want it to appear as if I were frightening you; s. B-D-F §453, 3; Mlt. 167.—On εἰ μήτι ἂν (sc. γένηται) ἐκ συμφώνου except perhaps by agreement 1 Cor 7:5 s. B-D-F §376; Mlt. 169.—M-M.2II. ἄν for ἐάν is rare in Hellen. Gk. (B-D-F §107; Mlt. 43 n. 2; cp. Hyperid. 4, 5; 5, 15; Teles p. 31, 6; Plut., Mor. 547a; Epict., index Schenkl; pap [Mayser 152]; ins, esp. of the Aegean Sea [Rdm.2 198, 3; s. also SIG index IV 204]; 1 Esdr 2:16; 4 Macc 16:11; Jos., Ant. 4, 70; 219; Test12Patr; Mel. Fgm. 8b 24), but appears J 13:20; 16:23; 20:23; as v.l. 5:19; 9:22; 12:32; 19:12; Ac 9:2; and IMg 10:1.—Mlt. 63, 1.—M-M. -
102 Computers
The brain has been compared to a digital computer because the neuron, like a switch or valve, either does or does not complete a circuit. But at that point the similarity ends. The switch in the digital computer is constant in its effect, and its effect is large in proportion to the total output of the machine. The effect produced by the neuron varies with its recovery from [the] refractory phase and with its metabolic state. The number of neurons involved in any action runs into millions so that the influence of any one is negligible.... Any cell in the system can be dispensed with.... The brain is an analogical machine, not digital. Analysis of the integrative activities will probably have to be in statistical terms. (Lashley, quoted in Beach, Hebb, Morgan & Nissen, 1960, p. 539)It is essential to realize that a computer is not a mere "number cruncher," or supercalculating arithmetic machine, although this is how computers are commonly regarded by people having no familiarity with artificial intelligence. Computers do not crunch numbers; they manipulate symbols.... Digital computers originally developed with mathematical problems in mind, are in fact general purpose symbol manipulating machines....The terms "computer" and "computation" are themselves unfortunate, in view of their misleading arithmetical connotations. The definition of artificial intelligence previously cited-"the study of intelligence as computation"-does not imply that intelligence is really counting. Intelligence may be defined as the ability creatively to manipulate symbols, or process information, given the requirements of the task in hand. (Boden, 1981, pp. 15, 16-17)The task is to get computers to explain things to themselves, to ask questions about their experiences so as to cause those explanations to be forthcoming, and to be creative in coming up with explanations that have not been previously available. (Schank, 1986, p. 19)In What Computers Can't Do, written in 1969 (2nd edition, 1972), the main objection to AI was the impossibility of using rules to select only those facts about the real world that were relevant in a given situation. The "Introduction" to the paperback edition of the book, published by Harper & Row in 1979, pointed out further that no one had the slightest idea how to represent the common sense understanding possessed even by a four-year-old. (Dreyfus & Dreyfus, 1986, p. 102)A popular myth says that the invention of the computer diminishes our sense of ourselves, because it shows that rational thought is not special to human beings, but can be carried on by a mere machine. It is a short stop from there to the conclusion that intelligence is mechanical, which many people find to be an affront to all that is most precious and singular about their humanness.In fact, the computer, early in its career, was not an instrument of the philistines, but a humanizing influence. It helped to revive an idea that had fallen into disrepute: the idea that the mind is real, that it has an inner structure and a complex organization, and can be understood in scientific terms. For some three decades, until the 1940s, American psychology had lain in the grip of the ice age of behaviorism, which was antimental through and through. During these years, extreme behaviorists banished the study of thought from their agenda. Mind and consciousness, thinking, imagining, planning, solving problems, were dismissed as worthless for anything except speculation. Only the external aspects of behavior, the surface manifestations, were grist for the scientist's mill, because only they could be observed and measured....It is one of the surprising gifts of the computer in the history of ideas that it played a part in giving back to psychology what it had lost, which was nothing less than the mind itself. In particular, there was a revival of interest in how the mind represents the world internally to itself, by means of knowledge structures such as ideas, symbols, images, and inner narratives, all of which had been consigned to the realm of mysticism. (Campbell, 1989, p. 10)[Our artifacts] only have meaning because we give it to them; their intentionality, like that of smoke signals and writing, is essentially borrowed, hence derivative. To put it bluntly: computers themselves don't mean anything by their tokens (any more than books do)-they only mean what we say they do. Genuine understanding, on the other hand, is intentional "in its own right" and not derivatively from something else. (Haugeland, 1981a, pp. 32-33)he debate over the possibility of computer thought will never be won or lost; it will simply cease to be of interest, like the previous debate over man as a clockwork mechanism. (Bolter, 1984, p. 190)t takes us a long time to emotionally digest a new idea. The computer is too big a step, and too recently made, for us to quickly recover our balance and gauge its potential. It's an enormous accelerator, perhaps the greatest one since the plow, twelve thousand years ago. As an intelligence amplifier, it speeds up everything-including itself-and it continually improves because its heart is information or, more plainly, ideas. We can no more calculate its consequences than Babbage could have foreseen antibiotics, the Pill, or space stations.Further, the effects of those ideas are rapidly compounding, because a computer design is itself just a set of ideas. As we get better at manipulating ideas by building ever better computers, we get better at building even better computers-it's an ever-escalating upward spiral. The early nineteenth century, when the computer's story began, is already so far back that it may as well be the Stone Age. (Rawlins, 1997, p. 19)According to weak AI, the principle value of the computer in the study of the mind is that it gives us a very powerful tool. For example, it enables us to formulate and test hypotheses in a more rigorous and precise fashion than before. But according to strong AI the computer is not merely a tool in the study of the mind; rather the appropriately programmed computer really is a mind in the sense that computers given the right programs can be literally said to understand and have other cognitive states. And according to strong AI, because the programmed computer has cognitive states, the programs are not mere tools that enable us to test psychological explanations; rather, the programs are themselves the explanations. (Searle, 1981b, p. 353)What makes people smarter than machines? They certainly are not quicker or more precise. Yet people are far better at perceiving objects in natural scenes and noting their relations, at understanding language and retrieving contextually appropriate information from memory, at making plans and carrying out contextually appropriate actions, and at a wide range of other natural cognitive tasks. People are also far better at learning to do these things more accurately and fluently through processing experience.What is the basis for these differences? One answer, perhaps the classic one we might expect from artificial intelligence, is "software." If we only had the right computer program, the argument goes, we might be able to capture the fluidity and adaptability of human information processing. Certainly this answer is partially correct. There have been great breakthroughs in our understanding of cognition as a result of the development of expressive high-level computer languages and powerful algorithms. However, we do not think that software is the whole story.In our view, people are smarter than today's computers because the brain employs a basic computational architecture that is more suited to deal with a central aspect of the natural information processing tasks that people are so good at.... hese tasks generally require the simultaneous consideration of many pieces of information or constraints. Each constraint may be imperfectly specified and ambiguous, yet each can play a potentially decisive role in determining the outcome of processing. (McClelland, Rumelhart & Hinton, 1986, pp. 3-4)Historical dictionary of quotations in cognitive science > Computers
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103 Nature
To Newtonians, each question had its singular answer, one that would remain the same no matter who asked it, or why. But now, the uncertainty that undercuts every measurement of some fact in the real world compels the observer to choose which question to ask, which aspect of a phenomenon to study.The necessity of choice became overwhelmingly apparent when Heisenberg elevated uncertainty to a principle in quantum mechanics in 1927, having recognized that on the subatomic level the observer had to emphasize only one of a pair of properties to study at any one time. In one of the prominent interpretations of quantum mechanics, the idea took on a larger meaning: that in choosing what to study, the scientist in effect creates the object of his inquiry.... The impossibility of constructing a complete, accurate quantitative description of a complex system forces observers to pick which aspects of the system they most wish to understand....What one studies from among this wealth of choice depends on what one wants to know; the questions create-or at least determine-the range of possible answers. No such answer can be completely "true": instead of saying "This is what nature is like," they can claim only, "This is what nature seems like from here"-a vastly diminished claim from that of Newton. The critical issue raised by such subjectivity is how to decide what value each partial answer has, what connection it actually makes between the real world and our understanding of it. The object of study, the focus of much of modern science, has therefore shifted inward, to examine not nature itself but rather to study the abstract representations of nature, the choices made of what to leave in and what to drop out of any given study. (Levenson, 1995, pp. 228-229)Historical dictionary of quotations in cognitive science > Nature
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