Commenting on WCF 6.3 and especially the phrase, "Adam as a public person" (WLC # 22) Hodge writes,
"That Adam was, as our Standards say, "a public person," and that the covenant was made with him "not for himself only, but for his posterity," is proved from the facts --
1) That he was called by a generic name, Adam -- the Man.
2) That everything that God commanded, promised, or threatened him related to his decendants as much as to himself personally. Thus, "obedience," "a cursed earth," "the reign of death," "painful child-bearing," and the subsequent promise of redemption through the Seed of the woman, were spoken with reference to us as much as with reference to our first parents.
3) As a matter of fact, the very penalty denounced and executed upon Adam has been executed upon all of his descendants, from birth upward. All are born spiritually dead, "by nature children of wrath" (Emphasis mine). A.A. Hodge, The Westminster Confession of Faith: A Commentary, pp. 111-112.