1)  Presumptive Regeneration does not teach the Roman version or Auburn Avenue version of baptismal regeneration. Reformed Theology teaches that the benefits of the covenant of grace are only efficaciously conferred by the Holy Spirit to the elect, which may be infants.  Those baptized are presumed to be elect based on God’s promise.

2)  At the same time that the benefits of the Covenant of Grace are only efficaciously conferred by the Holy Spirit to the elect; Genesis 17 is plain that Abraham presumed God’s salvation on Isaac before he was ever born. That presumption was based on promise, not circumcision. Circumcision was taught to Abraham by God with certain benefits annexed to it, but its effectual nature was enacted by the Holy Spirit. Abraham was circumcised as a result of faith in the Word of God, not by the mere act of circumcision.

3)  Circumcision and baptism in and of themselves do not save (which is the Romanist view). They are outward signs that are efficacious only for the elect through the ordinary working of the Holy Spirit who regenerates whom He wants. But the promise is to be believed (that God will be a God to our children) during baptism when we presume election based on the act of baptism under the auspice of God’s promises to those baptized.

4)  Christian parents do not infallibly know who the elect are. In view of this, instead of resting on pessimism, they rest on the hope of the promises to their children.  Presumptive Regeneration presumes children are saved, as Abraham did, but do not know whether they will be when they come to years of age. But no minister in their right mind would baptize a heathen unless explicitly instructed to do so (which he would not do). They only baptize Christians. There is only one exception to this in Scripture and that is the case of Ishmael. Abraham circumcised him even after God told him he would not be the son of promise. This made the sacrament a curse to Ishmael based on special revelation from God.

5)  Presumptive Regeneration does not teach that all infants of believers are infallibly saved.

These points are crucial to understand as one works through this issue. Really, it comes down to being Calvinistic, or Arminian. Do we baptize anyone based on the nature of God’s promise, or based on something we think we know or see in the individual, like an outward profession? If only the latter, then it is based on works. The former is based on Scripture.

[from Presumptive Regeneration, High Calvinism and Resting on the Word of God by C. Matthew McMahon, Ph.D., Th.D. as an intro to Presumptive Regeneration by Westminsterian Cornelius Burgess]