I posted the complete entries from both the 2nd and 3rd editions.
The new LSV(Literal Standard version)
μονογενής, ές (μόνος, γένος; Hes.; LXX; PsSol 18, 4; TestSol 20:2; TestBenj 9:2; ParJer 7:26; ApcEsdr 6:16; ApcSed 9:2; Joseph., Just.; loanw. in rabb.) acc. μονογενῆ (-ῆν J 3:16 v.l.; Hb 11:17 D; also ApcEsdr 6:16)
1. pert. to being the only one of its kind within a specific relationship, one and only, only (so mostly, incl. Judg 11:34; Tob 3:15; 8:17) of children: of Isaac, Abraham’s only son (Jos., Ant. 1, 222) Hb 11:17. Of an only son (PsSol 18:4; TestSol 20:2; ParJer 7:26; Plut., Lycurgus 59 [31, 8]; Jos., Ant. 20, 20) Lk 7:12; 9:38. Of a daughter (Diod. S. 4, 73, 2) of Jairus 8:42. (On the motif of a child’s death before that of a parent s. EpigrAnat 13, ’89, 128f, no. 2; 18, ’91, 94 no. 4 [244/45 AD]; GVI nos. 1663–69.)
2. pert. to being the only one of its kind or class, unique (in kind) of someth. that is the only example of its category (Cornutus 27 p, 49, 13 εἷς κ. μονογενὴς ὁ κόσμος ἐστί. μονογενῆ κ. μόνα ἐστίν=‘unique and alone’; Pla., Timaeus 92c; Theosophien 181, §56, 27). Of a mysterious bird, the Phoenix 1 Cl 25:2.—In the Johannine lit. (s. also ApcEsdr and ApcSed: ὁ μονογενής υἱός; Hippol., Ref. 8, 10, 3; Did., Gen. 89, 18; ὑμνοῦμέν γε θεὸν καὶ τὸν μ. αὐτοῦ Orig., C. Cels. 8, 67, 14; cp. ἡ δύναμις ἐκείνη ἡ μ. Hippol., Ref. 10, 16, 6) μονογενὴς υἱός is used only of Jesus.
The renderings only, unique may be quite adequate for all its occurrences here (so M-M., NRSV et al.; DMoody, JBL 72, ’53, 213–19; FGrant, ATR 36, ’54, 284–87; GPendrick, NTS 41, ’95, 587–600). τὸν υἱὸν τὸν μ. ἔδωκεν J 3:16 (Philo Bybl. [100 AD]: 790 fgm. 2 ch. 10, 33 Jac. [in Eus., PE 1, 10, 33]: Cronus offers up his μονογενὴς υἱός). ὁ μ. υἱὸς τοῦ θεοῦ vs. 18; τὸν υἱὸν τὸν μ. ἀπέσταλκεν ὁ θεός 1J 4:9; cp. Dg 10:2. On the expr. δόξαν ὡς μονογενοῦς παρὰ πατρός J 1:14 s. Hdb. ad loc. and PWinter, Zeitschrift für Rel. u. Geistesgeschichte 5, ’53, 335–65 (Engl.).
See also Hdb. on vs. 18 where, beside the rdg. μονογενὴς θεός (considered by many the orig.)
an only-begotten one, God (acc. to his real being; i.e. uniquely divine as God’s son and transcending all others alleged to be gods) or
a uniquely begotten deity (for the perspective s. J 10:33–36), another rdg. ὁ μονογενὴς υἱός is found. MPol 20:2 in the doxology διὰ παιδὸς αὐτοῦ τοῦ μονογενοῦς Ἰησοῦ Χριστοῦ. Some (e.g. WBauer, Hdb.; JBulman, Calvin Theological Journal 16, ’81, 56–79; JDahms, NTS 29, ’83, 222–32) prefer to regard μ. as somewhat heightened in mng. in J and 1J to
only-begotten or
begotten of the Only One, in view of the emphasis on γεννᾶσθαι ἐκ θεοῦ (J 1:13 al.); in this case it would be analogous to πρωτότοκος (Ro 8:29; Col 1:15 al.).—On the mng. of μονογενής in history of religion s. the material in Hdb.3 25f on J 1:14 (also Plut., Mor. 423a Πλάτων . . . αὐτῷ δή φησι δοκεῖν ἕνα τοῦτον [sc. τὸν κόσμον] εἶναι μονογενῆ τῷ θεῷ καὶ ἀγαπητόν; Wsd 7:22 of σοφία: ἔστι ἐν αὐτῇ πνεῦμα νοερὸν ἅγιον μονογενές.—Vett. Val. 11, 32) as well as the lit. given there, also HLeisegang, Der Bruder des Erlösers: Αγγελος I 1925, 24–33; RBultmann J (comm., KEK) ’50, 47 n. 2; 55f.—DELG s.v. μένω. M-M. EDNT. TW. Sv.
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The new LSV(Literal Standard version)