Over the weekend, I was once again drawn to discussions (debates) regarding infant baptism (paedobaptism) vs believer’s baptism (credobaptism): James White (Reformed Baptist) vs Bill Shishko (Orthodox Presbyterian Church) and then Tom Schreiner (Southern Baptist) vs David VanDrunen (Orthodox Presbyterian Church).
Perhaps the following is biased, given that I’m a Baptist, but I found that both the Presbyterian debaters were weak on Jeremiah 31:31-34 (cf. Hebrews 8:7-13).
Rather than taking “new” to mean “new,” the Presbyterians take it to mean expansion and something talk of over-realized eschatology on the part of Baptists, who find support for believer’s baptism only, from Jeremiah 31:31-34.
The ancient prophet Jeremiah says it’s “new” and not like the old. He then goes on to outline what’s different about the “new covenant” (vv. 33-34): while members of the old covenant were made up of ethnic Israel (according to Paul, not all who descended from Israel are Israel; there’s a remnant, Romans 9:6ff), “new covenant” members would all be regenerate and indwelt by the Holy Spirit (see Ezekiel 36:24-28).
So much more may be said, but you get the gist here.