Just because a sacrament also serves a second purpose of visibly marking out the Church does not mean the former truth of the sacrament sealing their obligation to God is negated. Those under obligation are under covenant. So, is the Church of P4 held to any covenant stipulations. If it is, than it is under the covenant (and, as the argument starts, this is with the elect alone).
First, I apologize for getting exasperated. It was a long day when I replied. I had taught twice that day and was exhausted. In one sense my sin is compounded having taught on sin that very morning and I proved myself to be chief of sinners.
Next, I think our interaction has kind of moved beyond the point of the thread. What's difficult in this scenario is that I'm not working within paedobaptist theology in this case but a theoretical theology of a credobaptist reading of Jer 31 and Heb 8 (P1) and then making an argument for paedobaptism on the basis that the same person who concludes P1 also sees the command in P9.
That said, let's take you mind off of this particular problem for a second and look at what your own confession says as you really need to wrestle with the same question you just asked for your Confession:
P1: Baptism is an ordinance of the New Testament, ordained by Jesus Christ, to be unto the party baptized, a sign of his fellowship with him, in his death and resurrection; of his being engrafted into him;3 of remission of sins;4 and of giving up into God, through Jesus Christ, to live and walk in newness of life.5
3 Rom. 6:3-5; Col. 2:12; Gal. 3:27
4 Mark 1:4; Acts 22:16
5 Rom. 6:4
P2. Those who do actually profess repentance towards God, faith in, and obedience to, our Lord Jesus Christ, are the only proper subjects of this ordinance.6
6 Mark 16:16; Acts 8:36,37, 2:41, 8:12, 18:8
Notice the spiritual aspects in P1 that can only be true of the elect and the visible aspect of P2 with which the Church decides to baptize. (Incidentally, if you want to complete your syllogism in the other thread, this is the "regulative principle" that you would need to shore up your argument to make it valid).
Now, do you want to say this in conclusion by connecting the two:
Conclusion: Those who do actually profess repentance towards God, faith in, and obedience to, our Lord Jesus Christ, have fellowship with Christ, in his death and resurrection; are engrafted into him, have their sins remitted, and are given up into God, through Jesus Christ, to live and walk in newness of life.
Do you see it?
In other words, in your own Confession, the ordinance serves as a "hinge". On the one hand the ordinance signifies everything in P1 for the party baptized and P2 notes that the ordinance belongs to credible professors.
We both understand, however, that the ordinance can serve a spiritual purpose for the elect (by the power of God) while the sign may be applied and the person baptized may possess none of those realities but he is baptized because, from all outward appearances, the Church makes the best spiritual judgment it can make.
As I noted as well, if we look at the way the Covenant of Circumcision operates in the 1689 LBCF (see especially the Appendix), circumcision serves a dual purpose. On the one hand, it is both a sign and a seal of the faith that Abraham had by faith while still uncircumcised AND it is said to be a national marker to separate out a people through which the Seed would come. It fulfills the "Two Nation" promise that the framers of your Confession envision in it.
Furthermore, if you look at the way the Sacrament operates in my arguments above notice something important:
1. It is a sign AND seal for the elect.
2. It is a sign to the rest of the world.
The benefits of the Sacrament are not sealed in the second aspect but it only serves a signatory function. I don't know if that helps but it is not operating at the same level in the visible marker category as it is for the elect with spiritual things. The connection is made sovereignly by the Holy Spirit to those He knows.