The idea that the covenant is fully realized only in the elect is a perfectly Scriptural idea, as appears, for instance, from Jer. 31:31-34; Heb. 8:8-12.
-Louis Berkhof. “Systematic Theology.” iBooks.
Throughout his systematic theology, Berkhof is very candid in his discussion of the covenant of grace. He admits many things that paedobaptists today would not admit – most likely because Berkhof did not have any reformed baptists to argue with. It wasn’t on his radar. Paedobaptists today insist that baptists have misread Jer. 31:31-34 and have ignored its context. Berkhof said our observation from the text is a “perfectly Scriptural idea.” However, he goes on to explain that the covenant of grace must be understood in another sense because of Genesis 17:7.
They [reformed theologians] were fully aware of the fact that, according to God’s special revelation in both the Old and the New Testament, the covenant as a historical phenomenon is perpetuated in successive generations and includes many in whom the covenant life is never realized. And whenever they desired to include this aspect of the covenant in their definition, they would say that it was established with believers and their seed.
Thus Jer. 31:31-34 does describe the substance of the covenant of grace made with the elect alone, but Genesis 17:7 says the Abrahamic Covenant is made with Abraham and his physical offspring. The paedobaptist conclusion is that there are two levels or sides or aspects to the covenant of grace: inward/outward, etc (see Berkhof “The Dual Aspect of the Covenant”). The biblical conclusion is that the Abrahamic Covenant is not the New Covenant.