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Hastings' Dictionary of the New Testament [1]

(ἀρχή,  Hebrews 5:12;  Hebrews 6:1)

In Greek philosophy ἀρχή is an element or first principle-that by which anything begins to be. When it is distinguished from στοιχεῖον-the terms are often interchanged-it means the formal and active as opposed to the material cause. The two words are used together in  Hebrews 5:12, ‘the rudiments of the first principles of the oracles of God’ (τὰ στοιχεῖα τῆς ἀρχῆς τῶν λογίων τοῦ θεοῦ). The tautology is studied and effective. The writer is chiding his readers for not endeavouring or perhaps caring to advance beyond the ABC (in Luther’s phrase, die ersten Buchstaben) of the gospel. He reminds them that they are no longer νήπιοι. Milk is the natural food of babes, but babes are potential adults, and the food of men (τελείων, ‘perfect,’ i.e. ‘full-grown,’ is emphatic), and of those who aspire to be such, has to be more solid than that of infants ( Hebrews 5:14). The backwardness which the writer reproves is alike intellectual and spiritual, while his grave tone differs from that of Horace’s ‘blandi doctores,’ who give their pupils cakes ‘elementa velint ut discere prima’ (Sat. I. i. 25 f.). That there is an immense difference between the ἀρχή and the τέλος of Christianity; that Jesus is not only the Beginner but the Perfecter of our faith (ἀρχηγὸν καὶ τελειωτὴν,  Hebrews 12:2)-these are the truths he wishes to drive home. Childhood is beautiful, but only a false sentiment would prolong it. The same thought is frequent in St. Paul’s writings ( 1 Corinthians 3:1;  1 Corinthians 13:11,  Ephesians 4:14). The Rabbis spoke of their younger pupils as ‘sucklings.’ Perhaps in  Hebrews 5:13-14 we have a case of one Alexandrian echoing another, for Philo says (de Agric. ii.): ‘Since milk is the food of infants, but cakes of wheat (τὰ ἐκ πυρῶν πέμματα) are the food of full-grown men, so also the soul must have a milk-like nourishment in its age of childhood, namely, the elementary lessons of art and science (τὰ τῆς ἐγκυκλίου μουσικῆς προπαιδεύματα), but the perfect food which is for men is education in prudence, temperance, and every virtue.’

James Strahan.

Vine's Expository Dictionary of NT Words [2]

1: Ἀρχή (Strong'S #746 — Noun Feminine — arche — ar-khay' )

"beginning," is used in  Hebrews 6:1 , in its relative significance, of the beginning of the thing spoken of; here "the first principles of Christ," lit., "the account (or word) of the beginning of Christ," denotes the teaching relating to the elementary facts concerning Christ. See Begin , B.

2: Στοιχεῖον (Strong'S #4747 — Noun Neuter — stoicheion — stoy-khi'-on )

is translated "principles" in  Hebrews 5:12 . See Elements.

International Standard Bible Encyclopedia [3]

prin´si - p ' lz  : Found twice (  Hebrews 5:12;  Hebrews 6:1 ). The Greek word (στοιχεῖον , stoicheı́on ) is also translated in the King James Version as "elements" and "rudiments." As rendered in He, its meaning is clearly related to the elementary knowledge of Christian truth or doctrine. See Elements; Rudiments .