Recent events turned my attention again to the issue of paedobaptism, a subject I have not really thought about since 2008, when I debated credobaptist Gene Cook on the subject. However, a friend, Bnonn Tennant, recently posted a simple argument which he takes to conclusively prove credobaptism. Steve Hays then gave a good reply. This lead me to collate some old files – notes, really – that I had written in 2008 as I prepared for my debate with Gene Cook. I’m posting it here in PDF format for those interested. However, caveat lector: I wrote these, as I said, circa 2008. The writing is very rough (most of it was written for notes, stream-of-consciousness style!), and though I think my writing has improved over the years, I did not want to take the time to do what would amount to an entire rewrite of 40 some odd pages! I’d also like to think that I agree with most of what I wrote, though by now I may reject some of the arguments I made back then. I did not want to spend the time going through the arguments with a fine-toothed comb. However, despite the poor(er) writing and clearness of arguments, I think there are several unique arguments here, arguments I have not seen made elsewhere by paedobaptists. Finally, a note on structure. The file consists of three parts. The first is basically my opening argument for my debate with Cook. The second part is a unique argument I developed, using the arguments of Brian Rosner on Paul’s teaching on excommunication in 1 Cor. 5. This argument is very rough and far from finished, but the nuts-n-bolts are there. The final section is a dozen (or so) very detailed responses to several (a dozen or so!) popular arguments credobaptists have either used to argue for credobaptism or against paedobaptism.
PDF link below
Analytic Theology, et cetera. 
I see no real strength in the argument that anyone laying claim to being in the community is ipso facto in the covenant.
Jeremiah 31 informs not only that inclusion in the New Covenant is a supernatural work, it also clearly informs us about a clear discontinuity that exists between the two covenants.
Your inference about the 1689 LBCF is patently false. The confession in no ways says what you seem to be saying it says. It’s point in 26:2 is that the invisible church is not purely invisible. It is also visible. The language about those you reference is clear: All persons throughout the world, professing the faith of the gospel, and obedience unto God by Christ according unto it, NOT DESTROYING THEIR OWN PROFESSION BY ANY ERRORS EVERTING THE FOUNDATION, OR UNHOLINESS OF CONVERSATION, are and may be called visible saints; and of such ought all particular congregations to be constituted.
To be in the New Covenant is to be in Christ by faith. If the law of God has not been written on the heart, then you are not under the New Covenant according to Jer. 31.
As for the 1 Cor. 5:1-13, if the man were legitimately a member of the New Covenant, and some scholars are correct that he repented in 2 Corinthians, we have a real issue here with a man who was part of the Covenant, out of the Covenant, and back in again. I find such a scenario highly problematic for all kinds of reasons.
The New Covenant people are a people of God, God is their God, and they are God’s people. They will ALL know God. God is merciful to their iniquities. Their sins shall not be remembered. These are the objects of the New Covenant. If these are not experience by the individual, the individual is not under the New Covenant arrangement. We really have to go no further than the limitations of the Jeremiah passage to understand the nature of the New Covenant from what I can see. I believe the only reason we do is because we have a system to defend, a doctrine to protect, a way of life to preserve.
Thanks for the comment, Ed,
1. I gave the argument for , with the appropriate nuances of that expression, etc. Since you only express disagreement and befuddlement, I can’t respond.
2. I gave several arguments against that reading of Jer. 31, especially in parts I and III.
3. I have no idea what “inference” you think I’m trying to make by citing the LBC. Since you don’t state it, I can’t respond.
4. I responded, in multiple places, to that reading of Jer. 31 (e.g., law on heart, etc.). Since you don’t interact, I can’t respond.
5. You only state *that* you have a problem with being in and out of the covenant again (and I specified precisely what I meant by this—if he was a regenerate Christian, he was never out of the internal aspect of the covenant), but you don’t state *why*. Since no argument was given, then, again, I don’t have anything to respond to.
6. Your final paragraph just repeats the traditional baptist reading of Jer. 31, and fails to engage with any of my arguments. Thus, one more time, there’s nothing for me to respond to.
7. Finally, since your final remark imputes intellectual dishonesty to me, stating that I’m denying the clear teaching of the Bible in order to “preserve a system” or “way of life,” rather than granting that I come to these views with intellectual honesty and because I believe the Bible teaches my view, as well as my sincere belief that the traditional baptist arguments and defeaters are theologically and logically uncompelling, then you’ve demonstrated that you’re not here for any honest and meaningful interaction. Thus I won’t be approving further comments, unfortunately.