Lexical Definition

‎κρεῖσσον‎ kreîsson (krice'-son) greater ^G:A
neuter of an alternate form of ‎κρείττων‎

better.

• (as noun) better, i.e. greater advantage

Abbott-Smith

κρείσσων (Epic and old Att.) and κρείττων (later Att.), prop. comparat. of κρατύς, strong, but in sense often (as in cl., v. LS, s.v.) as comparat. of ἀγαθός, [in LXX chiefly for טוֹב;]
better;
(a) as to advantage or usefulness: I Co 11:17, He 11:40 12:24; πολλῷ μᾶλλον κ., Phl 1:23; κρεῖσσον ποιεῖν, I Co 7:38; ἐστιν, seq. inf., I Co 7:9, II Pe 2:21;
(b) as to excellence: He 1:4 6:9 7:7, 19, 22 8:6 9:23 10:34 11:16, 35; κ. ἐστι, seq. inf., I Pe 3:17.†

Abbott-Smith References

Liddell-Scott-Jones

κρείσσων, ον,

genitive ονος, as always in Epic dialect and old Attic dialect; later Attic dialect κρείττων; Ionic dialect κρέσσων [Refs 5th c.BC+] κάρρων (which see); Cretan dialect κάρτων [Refs] — _comparative_ of κρατύς (see. κράτιστος), stronger, mightier, [Refs 8th c.BC+]; especially in battle, [κρείσσων χεῖρας 5th c.BC: Antipho Orator 4.4.7; τὸ τοῦ κ. συμφέρον Plato Philosophus [{5-6th c.BC}] “Respublica” 338c, compare 3rd c.AD: Democritus Epigrammaticus 267 ">Refs 6th c.BC+]: hence, having the upper hand, superior, [Refs 8th c.BC+]: as Law-term, of witnesses, [Refs] [prev. cited]

__2 frequently as comparative of ἀγαθός, better, κρέσσονες one's betters, especially in point of rank, [Refs 5th c.BC+], of the greater gods, as opposed to to Oceanus, [Refs 4th c.BC+] (anapaest meter); οἱ κ. the Higher Powers, [Refs 5th c.BC+] the Almighty, Providence, [Refs 4th c.AD+] one's advantages, [Refs 5th c.BC+].
__3 with infinitive, οὔ τις ἐμεῖο κρείσσων.. δόμεναι no one has a better right to.., [Refs 8th c.BC+]; κρεῖσσόν ἐστι with infinitive, 'tis better to.., [κρείσσων εἰμί">Refs 5th c.BC+] with participle, κ. γὰρ ἦσθα μηκέτ᾽ ὢν ἢ ζῶν τυφλός thou wert better not alive, than living blind, [Refs 5th c.BC+]
__II with genitive or ἤ, too great for, surpassing, beyond, [Refs 5th c.BC+]; of evil deeds, κρείσσον᾽ ἀγχόνης too bad for hanging, [Refs 5th c.BC+] too bad to look on, [Refs 5th c.BC+]; λέγετι σιγῆς κρεῖσσον [Refs 5th c.BC+]; κ. ἢ λόγοισιν (i.e. εἰπεῖν) [Refs]; πρᾶγμα ἐλπίδος κ. γεγενημένον worse than one expected, [Refs 6th c.BC+].
__III having control over, master of, especially of desires and passions, [Refs 6th c.BC+]; γαστρὸς καὶ κερδέων [Refs] over themselves, [Refs 5th c.BC+] superior to the influence of money, [Refs 6th c.BC+]; also, putting oneself above, [Refs 5th c.BC+]; κρείσσους ὄντες.. τῷ λογισμῷ ἐς τὸ ἀνέλπιστον τοῦ βεβαίου having reasoned themselves into an absolute belief of the hopelessness of certainty, [Refs 4th c.BC+]
__IV better, more excellent, [Refs 1st c.AD+]; ὁ κρείττων λόγος (opposed to ὁ ἥσσων) [Refs 5th c.BC+] in a higher sense, opposed to κατὰ τὸ χεῖρον, [Refs 5th c.AD+]
__V adverb [κρείσσων (like μείζων)">Refs 5th c.BC+] probably took ει from ὀλείζων.)