In light of the recent discussions triggered by the Oct. 1st Mortification of Spin podcast, I think it would be a good time to share a simple illustration that clarifies what aspects of Covenant theology Reformed Baptists and Reformed Paedobaptists really agree upon as well as demonstrating how and why they differ.
The following quote is from a present-day Reformed Presbyterian Pastor (One of the finest preachers of our age) explaining covenant theology by the use of an illustration from a Puritan Congregationalist.
One of the most brilliant illustrations of covenant theology is that used by the Puritan divine Thomas Goodwin. In his exposition entitled Christ Set Forth, he explains that “Adam was reckoned as a common public person, not standing singly or alone for himself, but as representing all mankind to come of him’. In this he was a type of Christ, who is also a representative figure. This is why the apostle Paul, in 1 Corinthians 15:47, speaks of Adam and Christ as ‘the first man’ and ‘the second Man’ respectively ‘He speaks of them’, says Goodwin, ‘as if there had never been any more men in the world, nor were ever to be for time to come, except these two. And why? but because these two between them had all the rest of the sons of men hanging at their girdle.”
Can you visualize the picture which Goodwin draws for us? He imagines two great giants, one called Adam and the other Christ. Each is wearing an enormous leather ‘girdle’ or belt with millions of little hooks on it. You and I, and all humanity, are hanging either at Adam’s belt or at Christ’s belt. There is no third option, no other place for us. And God deals with us only through Adam or through Christ. If you are hanging at Adam’s belt, you share in the experience of sinful, fallen Adam, and your entire relationship with God is through him. But if you are hanging at Christ’s belt, all God’s dealings with you are through Christ. When you received Jesus as your Saviour, you were involved in a massive and momentous transfer. The Almighty himself unhooked you from Adam’s belt and hooked you on to Christ’s. So you now have a different Head, a different Mediator, a new Representative. You have passed from Adam into Christ, and whereas God formerly dealt with you only through Adam, he now deals with you only through his Son. You are in Christ unchangeably and for ever. 
I absolutely concur with Pastor Donnelly that Goodwin’s illustration of covenant theology is brilliant and accurate. The very heart of covenant theology is painted in such a vivid picture that a child can comprehend it, yet the depth of the richness of the doctrine is not lost. Here we see clearly what Reformed Baptists and Reformed Paedobaptists agree upon. You have just read a Reformed Baptist approvingly quoting a Reformed Presbyterian approvingly quoting a Puritan Congregationalist!
All men were in Adam in the garden. All men fell in Adam when he sinned. All stood in Adam, all fell in Adam, all died in Adam. But God chose not to leave His elect in Adam. He unites His elect to Christ in such a way that He took on the guilt of their sins and paid the full penalty for them, and His righteousness is credited as theirs! This is covenant theology. This we can and must agree upon.
I believe we can use the same illustration to demonstrate how and why Reformed Baptists differ from our paedobaptist brethren as well. What does the Bible characterize as the chord by which the elect are attached to Christ’s belt? What does the Bible represent as that by which sinners are united to Jesus Christ? Faith, as Pastor Donnelly points out, “When you received Jesus as your Saviour, you were involved in a massive and momentous transfer. The Almighty himself unhooked you from Adam’s belt and hooked you on to Christ’s.” Surely Baptist and Paedobaptists can agree on this as well. But this is also where the difference becomes patently clear.
If this illustration is an accurate expression of what the Bible teaches, as I think we can agree it is, then it also sheds a great deal of light on the problem we Baptists have with the practice of infant baptism. Our children, quite frankly, are born in Adam. Our children remain in Adam until that point in time at which Almighty God transfers them from Adam’s belt to Christ’s belt. In other words, our children remain in Adam until they are joined to Christ by faith. (I am not addressing the issue of those who die in infancy etc.) So we as Baptists simply ask: Why would I give my children the sign that signifies union with Christ while they are still in Adam? The Bible specifically tells us who we are to baptize, disciples. It also represents faith and repentance as prerequisites for baptism and associates baptism with union with Christ, which my children do not have before they are joined to Him by faith.
Make disciples …baptizing them. Matt 28:18
Repent, and let every one of you be baptized Acts 2:38
Then those who gladly received his word were baptized; Acts 2:41
For as many of you as were baptized into Christ have put on Christ. Gal. 3:27
I’m fully aware of how paedobaptists respond to this type of presentation, but my purpose at this point is simply to make plain that the differences Reformed Baptists have from our paedobaptist brethren are not rooted in a rejection of covenant theology. They actually spring forth from our understanding of covenant theology.
Let us continue to stand firm on what we believe the Bible teaches about who should be baptized. But let us always keep in mind: that which unites us with our paedobaptist brethren is far greater and more fundamental than that which divides us. As God sees us in Christ, let us see one another as in Christ!
If you have never heard them, you NEED to listen to Edward Donnelly’s sermon series on Heaven and Hell. Here.
He has published the essence of these sermons in the book Heaven and Hell.
For great resources on the Reformed Baptist view of Covenant Theology start here.
His Throne is Forever and Ever!
 Edward Donnelly, Heaven and Hell p. 87, citing ‘ Goodwin’s Works, James Nichol edition, 1862, Vol. 4, p. 31.