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1 νοέω
νοέω fut. νοήσω LXX; 1 aor. ἐνόησα; pf. νενόηκα; plpf. ἐνενοήκειν (Just.). Pass.: fut. 3 sg. νοηθήσεται Sir 14:21; aor. inf. νοηθῆναι (Just.) (Hom.+; pap, LXX, En, TestSol 11:1 P.; TestAbr B 6 p. 110, 22 [Stone p. 68]; Test12Patr; ApcMos 18; EpArist, Philo, Joseph., apolog. exc. Ar.).① to grasp or comprehend someth. on the basis of careful thought, perceive, apprehend, understand, gain an insight intoⓐ w. obj. in the acc. (X., An. 3, 4, 44; Jos., Vi. 298; SibOr 5, 65) τὴν σύνεσίν μου my insight Eph 3:4. δικαίως ν. τὰς ἐντολάς understand the commandments rightly 10:12b. τὰς παραβολάς understand the parables Hm 10, 1, 4; οὐ δύναμαι νοῆσαι I cannot understand (them) s 5, 3, 1 (cp. Pr 1:6); (w. συνιέναι, as 10:12a) πάντα τὰ λεγόμενα m 10, 1, 6a (Just., D. 73, 3 τὸ λεγόμενον); cp. 6b; τῆς βασάνου τὴν δύναμιν the power of the torment Hs 6, 4, 3a. τὴν πρᾶξιν ἣν ποιεῖ what he is doing 6, 5, 3. τὰ ἐπουράνια understand heavenly things ITr 5:2; τὴν δόξαν τοῦ θεοῦ Hm 12, 4, 2; Hs 5, 3, 1 (w. γινώσκειν [as Plato, Rep. 6, 508d and e]); τοὺς χρόνους τ. ἀπάτης 6, 5, 1. Relative clause as obj. 1 Ti 1:7; Dg 8:11; IRo 6:3. ταῦτα 10:12a; Hs 5, 5, 4. αὐτά 6, 5, 2; 9, 2, 6b; οὐδὲν ν. comprehend nothing Hv 3, 6, 5; Hs 9, 14, 4. ὅλως οὐδὲν ν. understand nothing at all m 4, 2, 1. Also οὐδὲν ὅλως ν. 10, 1, 5 (μηδὲν τούτων Just., D. 125, 5). ὅσα οὐ δύνασαι νοῆσαι whatever you cannot comprehend Hs 9, 2, 6a. οὐδὲ δύναμαι νοῆσαι nor do I understand anything (about it) 9, 9, 2.—W. acc. of pers. (Mel., P. 82, 605 οὐκ ἐνόησας τὸν κύριον): of the angel of wickedness πῶς νοήσω αὐτὸν οὐκ ἐπίσταμαι I do not understand how I am to recognize him Hm 6, 2, 5.—W. περί τινος instead of the obj. ἔτι οὐ νενόηκα ὅλως περὶ τοῦ χρόνου τῆς ἀπάτης I have not yet fully understood concerning the time of deceptive pleasure Hs 6, 5, 1 v.l.—Pass. τὰ ἀόρατα … νοούμενα καθορᾶται what is invisible … is clearly perceived (w. the eye of the understanding) Ro 1:20 (νοῆσαι τὸν θεόν: Herm. Wr. 11, 20b; 12, 20b and PGM 3, 597; Orphica Fgm. 6 Abel [Eus., PE 13, 12, 5; cp. Denis 165, ln. 5f; Holladay p. 128 ln. 16, s. app.] οὐδέ τις αὐτὸν εἰσοράᾳ ψυχῶν θνητῶν, νῷ δʼ εἰσοράαται (difft. Theosophien §56, vs. 10 [p. 180]. S. γνωστός 2). Of the λόγος: ὑπὸ ἀπίστων μὴ νοούμενος Dg 11:2 (cp. Ath. 18, 2 λόγῳ υἱῷ νοουμένῳ ἀμερίστῳ).ⓑ w. ὅτι foll. (BGU 114 I, 9; 2 Km 12:19; EpArist 224; Philo, Virt. 17, Mos. 1, 287; Just. D. 4, 7; 27, 2; B-D-F §397, 2) Mt 15:17; 16:11; Mk 7:18; Ac 16:10 D; 1 Cl 27:3; 7:1; Hm 10, 1, 2; Hs 1:3; (w. οἶδα) 2:8.ⓒ foll. by acc. and inf. (2 Macc 14:30; Just. D. 46, 5 ἃ πάντως ἅγια νοοῦμεν εἶναι; 49, 22; 60, 3; B-D-F §397, 2; Rob. 1036) Hb 11:3; foll. by acc. and ptc. ἐνόησα ὑμᾶς κατηρτισμένους I have observed that you are equipped ISm 1:1 (Kaibel 278, 3 τὸν φίλον ὄντα νόει; Just. D. 46, 5 θεὸν … ἐντειλάμενον ὑμῖν).ⓓ foll. by indirect question (IDefixWünsch 4, 56f ἵνα μὴ νοῶσιν τί ποιῶσιν; Wsd 4:17; SibOr 3, 796; Just. D. 12, 3) Hm 6, 1, 1; μὴ νοῶν ὅτι (τί v.l.) ἐστίν Hs 5, 4, 2; οὐ ν. w. indir. quest. preceding I do not understand m 10, 1, 3. Elliptically πῶς, οὐ νοῶ how (this can be) I do not understand Hs 5, 6, 1.ⓔ abs. (Sir 11:7; TestAbr B 6 p. 110, 22 [Stone p. 68] καλῶς ἐνόησας; Just. D. 119, 1 χάριν τοῦ νοῆσαι) B 6:10; 17:2; Hs 6, 4, 3b; 9, 28, 6; νοῆσαί σε δεῖ πρῶτον you must understand it first v 3, 8, 11. Comprehend, perceive (EpArist 153) Mt 16:9; Mk 8:17. More fully ν. τῇ καρδίᾳ (Is 44:18) J 12:40.② to think over with care, consider, take note of ὁ ἀναγινώσκων νοείτω let the reader/lector note (these words); s. ἀναγινώσκω) Mt 24:15; Mk 13:14. νόει ὸ̔ λέγω consider what I say 2 Ti 2:7 (Pla., Ep. 8, 352c νοήσατε ἃ λέγω) ἔτι κἀκεῖνο νοεῖτε consider this, too 4:14. W. indir. quest. foll. 1 Cl 19:3; 8:2.③ to form an idea about something, think, imagine (En 100:8 ν. τὸ κακόν) ὑπερεκπερισσοῦ ὧν νοοῦμεν far beyond what we imagine Eph 3:20.④ to pay heed with intent to act appropriately, be minded σεμνὰ ν. be honorably minded 1 Cl 1:3.—DELG s.v. νόος. M-M. TW. Sv. -
2 Mathematics
The world of mathematics, which you contemn, is really a beautiful world; it has nothing to do with life and death and human sordidness, but is eternal, cold and passionless. To me pure mathematics is one of the highest forms of art; it has a sublimity quite special to itself, and an immense dignity derived from the fact that its world is exempt from change and time. I am quite serious in this....athematics is the only thing we know of that is capable of perfection; in thinking about it we become Gods. (Russell [to Helen Thomas, 30 December 1901], 1992, Letter No. 98, p. 224)One of the deepest problems of nature is the success of mathematics as a language for describing and discovering features of physical reality. In short, why does mathematics work?...We humans have stripped back the clouds that cloak our understanding of our cosmic beginning and our current persistence to the stage that exposes the mathematical structure of the world more clearly than it has ever been observed before.... Furthermore, the attention of seriously equipped thinkers, those thinkers we call scientists, is at last beginning to turn to that other great conundrum of being: consciousness.... If we can understand why that supreme construct of the human intellect, that archdisembodiment of intellect, mathematics, works as a description of the world, then maybe we shall have an insight into cognition....The name deep structuralism is intended to convey the idea that the physical world has the same logical structure as mathematics. By implication, the reason why mathematics works as a description of physical reality is that they share the same logical structure.... By weak deep structuralism I shall mean that mathematics and physical reality merely share the same logical structure and mathematics is a mirror that can be held up to nature. By strong deep structuralism I shall mean that mathematics and physical reality do not merely share the same logical structure but are actually the same. In other words, according to the hypothesis of strong deep structuralism, physical reality is mathematics and mathematics is physical reality.... The reason why we may be conscious of the world, including the inner, introspective world of emotion and intellect, may be that our brains are material portrayals of the same deep structure. That may also be the reason why brains can generate the mathematics that we need to comprehend the world. (Atkins, 1992, pp. 99-101, 109-111)Historical dictionary of quotations in cognitive science > Mathematics
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