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Here is the full entry of meanings of kephalē copied and pasted from Liddel, Scott and Jones’s Greek-English Lexicon (LSJ)* without any editing or erasures. The LSJ is one of the most exhaustive and respected lexicons of ancient Greek. The words in this lexicon have come from numerous sources of Greek literature, papyri and inscriptions.
While the LSJ only cites texts from the New Testament (Novum Testamentum) infrequently, it does consider and include NT vocabulary in its lexicon. (It lists the books of the NT on page xxx of ‘Authors and Works’, 9th ed., 1996.) The LSJ also includes the vocabulary of other Hellenist/Koine texts contemporary with NT. The LSJ cuts off at, and does not include, Patristic or Byzantine Greek.
The LSJ has not been influenced by later theological uses of kephalē, and so it does not give “authority” or “leader” as meanings of kephalē. It does, however, give “source”, “origin” and “starting point” as possible meanings in II.d below.
A. head of man or beast, Hom. (v.infr.), Alc.15, etc.; once in A., Th.525 (lyr.), once in S., Aj.238 (anap.), also in E., Fr.308 (anap.), Rh.226 (lyr.), al.;“ἄλλουοὐδενὸςἐμψύχουκ. γεύσεταιΑἰγυπτίωνοὐδείς” Hdt.2.39; κεφαλῇ . . μείζονες taller in stature, Il.3.168; so μείων . . κεφαλήν ib.193Aristarch.: freq. with Preps.,
b. κατὰκεφαλήν, Ep. κὰκκεφαλήνon the head, “Ἐρύλαον . . βάλεπέτρῳμέσσηνκὰκκεφαλήν” Il.16.412, cf. 20.387, 475: in Prose, from above, X.HG7.2.8: c.gen., above, κ. κ. τινῶνγενέσθαι ib.7.2.11; τὸκ. κ. ὕδωρ, of rain water, Thphr. HP4.10.7 (-ὴν codd.), CP6.18.10 (-ῆς): in Archit., upright,IG22.463.42;
also, per head, each person (cf. infr. 1.2), Arist.Pol.1272a14, LXX Ex.16.16; “κατὰκεφαλὴντῶνκωμητῶν” PPetr.2p.17 (iii B. C.).
d. ἐπὶκεφαλήνhead foremost, ἐπὶκ. κατορύξαι to bury head downwards, Hdt.3.35; ἐπὶκ. ὠθέεσθαι to be thrust headlong, Id.7.136, cf. Hyp.Fr.251;
“ἐπὶκ. ὠθεῖντιναἐκτοῦθρόνου” Pl.R.553b; “ἐπὶτὴνκ. εἰςκόρακαςὦσον” Men.Sam. 138; “εὐθὺςἐπὶκ. εἰςτὸδικαστήριονβαδίζειν” D.42.12; οὐβουλόμενοςπολίταςἄνδραςἐπὶκ. εἰσπράττειντὸνμισθόνrecklessly, Hyp.Lyc.17; ἐπὶταῖςκεφαλαῖςπεριφέρειν carry on high, in token of admiration, Pl. R.600d.
2. as the noblest part, periphr. for the whole person, “πολλὰςἰφθίμουςκ.” Il.11.55, cf. Od.1.343, etc.; ἶσονἐμῇκ. no less than myself, Il.18.82; “ἑᾷκ.” Pi.O.7.67; esp. in salutation, “φίληκ.” Il.8.281, cf. 18.114; “ἠθείηκ.” 23.94; “Ἄπολλον, ὦδίακ.” E.Rh.226 (lyr.): in Prose, “Φαῖδρε, φίληκ.” Pl.Phdr.264a; “τῆςθείαςκ.” Jul.Or. 7.212a: in bad sense, “ὦκακαὶκεφαλαί” Hdt.3.29; “ὦμιαρὰκ.” Ar.Ach. 285: periphr. in Prose, “πεντακοσίαςκεφαλὰςτῶνΞέρξεωπολεμίων” Hdt.9.99: in bad sense, “ἡμιαρὰκαὶἀναιδὴςαὕτηκ.” D.21.117, cf. 18.153; “ἡκ. τῶναὐτοῦ” PRein.57.8 (iv A.D.); μεγάληκ. a great personage, Vett. Val.74.7; cf. supr. 1 b fin.
4. in imprecations, ἐςκεφαλὴντράποιτ᾽ἐμοί on my head be it! Ar.Ach.833; “ἐςτὴνκ. ἅπαντατὴνσὴντρέψεται” Id.Nu.40; “ἃσοὶκαὶτοῖςσοῖςοἱθεοὶτρέψειανεἰςκ.” D.18.290; ἐςκ. σοί (sc. τράποιτο) Ar.Pax1063, Pl.526; “σοὶεἰςκ.” Pl.Euthd.283e; “τὰμὲνπρότερον . . ἐγὼκεφαλῇἀναμάξαςφέρω” Hdt.1.155; “οἷςἂν . . τὴναἰτίανἐπὶτὴνκ. ἀναθεῖεν” D.18.294; “τὸαἷμαὑμῶνἐπὶτὴνκ. ὑμῶν” Act.Ap. 18.6.
II. of things, extremity,
b. in Anatomy, κεφαλαὶτῆςκάτωγνάθου, prob. the condyloid and coronoid processes, Hp.Art.30; ἡκ. τοῦὄρχεως, = ἐπιδιδυμίς, Arist.HA510a14, cf. Gal.4.565; μηροῦ, κνήμηςκ., Poll.2.186, 188; of the base of the heart, Gal.UP6.16; but, apex, Hp.Cord.7; of the sac in poulps, Arist.PA654a23, 685a5; of muscles, origin, Gal.UP7.14.
d. in pl., source of a river, Hdt.4.91 (butsg., mouth, “οἶδαΓέλαποταμοῦκεφαλῇἐπικείμενονἄστυ” Call.Aet.Oxy.2080.48): generally, source, origin, Ζεὺςκ. (v.l. ἀρχή）, Ζεὺςμέσσα, Διὸςδ᾽ἒκπάντατελεῖται῾τέτυκται codd.) Orph.Fr.21a; starting-point, “κ. χρόνου” Placit. 2.32.2 (κρόνου codd.), Lyd.Mens.3.4;
κ. μηνός ib.12.
e. extremity of a plot of land, PPetr.3p.72 (iii B.C.), PFlor.50.83 (iii A.D.).
*Henry George Liddell and Robert Scott, A Greek-English Lexicon, revised and augmented throughout by Sir Henry Stuart Jones, with the assistance of Roderick McKenzie, Oxford: Clarendon Press, 1940. http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dkefalh%2F
I personally own the latest edition of the LSJ, the 9th edition (1996). This updated edition, also, does not give “leader” or “authority”, etc, as possible meanings for kephalē.
Other Greek Lexicons
Here is a screen shot of a paragraph from Richard S. Cervin’s article “Does Kephalē (“head”) Mean “Source” or “Authority Over” in Greek Literature: A Rebuttal”. [His article may be viewed here.] In this paragraph Richard states that lexicons for individual Greek authors (pre-classical, classical and Hellenist authors) do not give “leader” as a meaning for kephalē.
Note the last sentence in this paragraph where Richard quotes Dhimitrakou who states that “leader” as a meaning of kephalē is medieval. That is, kephalē did not mean “leader” when the New Testament was being written, but it did in medieval times. Richard then goes on in his article to explain the reasons why most New Testament lexicons do have ‘leader” as a possible meaning.