This post is from an answer form these blog> http://nct-blog.ptsco.org/2012/09/03/christotelic-hermeneutics-part-1/. I find the answer so succinct and so I will post it here:
I will attempt to answer your question regarding the NCT refutation of the supposed link between circumcision an paedobaptism. Now at the start, I must say that there is an analogical connection between circumcision and baptism strictly in the sense that both are analogies of conversion or regeneration/spiritual resurrection or saving faith. For example, Romans 4:11 instructs us that Abraham received the sign of circumcision, a seal of the righteousness of the faith which he had while uncircumcised. The New Testament (NT) uses water baptism as a symbol of spiritual resurrection. Consider Romans 6:4: Therefore we have been buried with Him through baptism into death, in order that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life. 1 Peter 3:21 also states: And corresponding to that, baptism now saves you– not the removal of dirt from the flesh, but an appeal to God for a good conscience– through the resurrection of Jesus Christ. However, in saying that there is an analogical connection between circumcision and baptism, I categorically reject the Presbyterian teaching that this connection in any way justifies the practice of paedobaptism.
Although circumcision and baptism are both analogies of conversion or regeneration/spiritual resurrection or saving faith, Scripture posits a vast chasm of difference between the two. First, circumcision also functioned as an ethnic marker, differentiating Jews from Gentiles. However, with the coming of Christ and the establishment of the New Covenant, race, and therefore circumcision also, is now meaningless as seen in the Apostle Pauls arguments throughout his epistles (Contra Race: Rom 10:12; Gal 3:28; Col 3:11; Contra Circumcision: 1 Cor 7:18-19; Gal 5:2-6, 6:15). In contradistinction to circumcision, baptism is not an ethnic marker. Second, the NT Scriptures (and the NT must have interpretive priority over the OT) indicate that the true counterpart of bodily circumcision is spiritual circumcision, not water baptism. Colossians 2:11: in Him you were also circumcised with a circumcision made without hands, in the removal of the body of the flesh by the circumcision of Christ. Thus, when the Holy Spirit regenerates individuals and leads them to faith, Christ performs a a circumcision made without hands in that He removes the body of the flesh in other words, the believer is given a new heart in fulfillment of Ezekiel 36:25-27, resulting in the reality that not only is the flesh no longer the guiding principle in a believers life but also that the persons heart now craves, thirsts, and seeks after God. Thus, NT baptism parallel circumcision one another analogically, but they are not equivalent to one another. Now, that being said, spiritual circumcision is not a distinctly New Covenant concept, since Moses commands Israel in Deuteronomy 10:16, Circumcise then your heart, and stiffen your neck no more. However, this is impossible for unsaved man to accomplish; spiritual circumcision must be performed by God Himself. God did exactly this for the believing remnant of ethnic Israel, as Deuteronomy 30:6, Moreover the LORD your God will circumcise your heart to love the LORD your God with all your heart and with all your soul, in order that you may live.
Third, although bodily circumcision guaranteed an ethnic Jew a place among the people of Israel as part of the physical seed of Abraham (cf. Gen 17:14), it did not guarantee any Jew a place among the spiritual seed of Abraham (i.e. the believing ethnic remnant). This is confirmed by the Apostle Pauls teaching in Romans 9:6-8: But it is not as though the word of God has failed. For they are not all Israel who are descended from Israel; 7 neither are they all children because they are Abraham’s descendants, but: through Isaac your descendants will be named. 8 That is, it is not the children of the flesh who are children of God, but the children of the promise are regarded as descendants. In other words, just because you were ethnically Jewish (and, therefore, circumcised) you were not guaranteed a place among the redeemed, believing remnant of Israel this honor being bestowed solely by Gods sovereign, distinguishing grace. Thus, we begin to see that Old Testament (OT) Israel was a mixed multitude in that the vast majority was unregenerate with relatively few regenerate Israelites. Hebrews 3:16-4:2 also demonstrates this:
For who provoked Him when they had heard? Indeed, did not all those who came out of Egypt led by Moses? 17 And with whom was He angry for forty years? Was it not with those who sinned, whose bodies fell in the wilderness? 18 And to whom did He swear that they should not enter His rest, but to those who were disobedient? 19 And so we see that they were not able to enter because of unbelief. 4:1 Therefore, let us fear lest, while a promise remains of entering His rest, any one of you should seem to have come short of it. 2 For indeed we have had good news preached to us, just as they also; but the word they heard did not profit them, because it was not united by faith in those who heard.
In other words, the author of the Hebrews warns his readers not to follow the example of the unregenerate Israelites who emerged from Egypt and did not unite what they heard with faith as a result, they died in the wilderness and did not receive what was promised entrance into the Promised Land. This is where the radical distinction between the Old Covenant and the New Covenant begins to come into focus a radical distinction, which traditional Covenant Theology radically undercuts with their theologically-deduced overarching Covenant of Grace.
Fourth, the New Covenant is radically different in nature from the Old Covenant. Both Jeremiah 31:31-34 and Ezekiel 36:25-27 strongly indicate this. The New Covenant is not like the covenant (Jer 31:31-32) which God made at Sinai, that is to say, the Old Covenant that covenant which Israel broke (Jer 31:32). So, how is the New Covenant radically different from the Old Covenant? Whereas under the Old Covenant relatively few of the covenant people knew the Lord, under the New Covenant all covenant members shall know the Lord (Jer 31:34). God promises under the New Covenant that all will know the Lord because God will put His law within them and write it on their hearts (Jer 31:33), give them a new heart (Ezek 36:26), put a new spirit within them (Ezek 36:27), put His Spirit within them (Ezek 36:27), and cause them to walk in My statutes (Ezek 36:27). What is the result? All true members of the New Covenant will be careful to observe the Lords ordinances (Ezek 36:27b). Some have erected the straw man that advocates of New Covenant Theology, by saying this, either do not understand or altogether reject the visible versus invisible Church distinction. This accusation is false. In saying that all members of the New Covenant are regenerate, NCT does not advocate or believe that everyone who sits in a church pew or even claims the name of Christ is truly a member of the New Covenant. Only those who are truly regenerate are truly members of the New Covenant. In other words, an individual may be a member of a visible, local church, but he may not be a member of the invisible Church that is to say the true Church. And, if one is not truly a member of the invisible Church, he or she is not truly a member of the New Covenant. Thus, NCT affirms and maintains the visible versus invisible Church distinction. Furthermore, since all members of the New Covenant are regenerate, the Church, the body formed by the New Covenant, is not a mixed multitude, like Israel, the body formed by the Old Covenant.
This is where the practice of paedobaptism comes into direct conflict with both Biblical teaching, not to mention the Reformed soteriology which has historically characterized Presbyterians. First, recall bodily circumcision in the OT guaranteed an ethnic Jew a place among the people of Israel as part of the physical seed of Abraham (cf. Gen 17:14), but it did not guarantee any Jew a place among the spiritual seed of Abraham (i.e. the believing ethnic remnant; Rom 9:6-8). As a result, OT Israel was a mixed multitude, that is to say, made up of believers and unbelievers. Second, inclusion into the ranks of the elect is bestowed solely by Gods sovereign, distinguishing grace. Third, God promised to establish a new covenant where all its true members would be regenerate and know the Lord (Jer 31:31-34; Ezek 36:25-27). Thus, if all members of the New Covenant are regenerate and know the Lord, the true Church (i.e. the Invisible Church) is not a mixed multitude (i.e. a combination of believers and unbelievers), like OT Israel, where the vast majority of the nation was unregenerate. Fourth, not everyone who sits in a church pew or even claims the name of Christ is truly a member of the New Covenant. Therefore, if God promised that all true members of the New Covenant would be regenerate and know Him, and if God alone sovereignly bestows the gift of salvation upon whomever He will, how can advocates of Covenant Theology legitimately claim their children as covenant children, that is to say, covenant members apart from an informed profession of faith (which in itself is not a 100% guarantee that the individual is a regenerate believer) on the part of the children?
To designate baptized infants as covenant children and include them as members of the New Covenant has four unfortunate consequences. First, it redefines the Church as a mixed multitude (which directly contradicts the New Covenant promises of Jeremiah 31:31-34 and Ezekiel 36:25-27), thus blurring the distinctions between the invisible Church versus visible Church. Second, the Covenant Theologian practice of paedobaptism flattens the radical newness of the New Covenant. The New Covenant is an entirely new covenant not merely a subsequent administration of the theologically-deduced overarching Covenant of Grace. Logically, how can the Old and New Covenants both be distinct administrations of Covenant Theologys Covenant of Grace, when God Himself declares that the New Covenant will not be like the covenant which I made with their fathers in the day I took them by the hand to bring them out of the land of Egypt, My covenant which they broke, although I was a husband to them (Jer 31:31-32). Third, paedobaptism appears to make salvation dependent upon, or at least influenced by, an ecclesial act performed upon an infant at the behest of his or her parents and the local church. This results in making an individuals covenant membership within the New Covenant at least partly dependent on who his or her parents were like it was under the Old Covenant! However, Romans 9 and John 1:12-13 teach with resounding clearness that salvation is not based upon mans will, mans effort, his particular people group, his parents, his genetics, and so forth; salvation is and always has been dependent on the sovereign and distinguishing grace of God I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion (Rom 9:15). The early seventeenth century Particular (i.e. Calvinistic) Baptists (e.g. John Spilsbery and Thomas Patient) leveled the same argument against their Christian brothers who were advocates of paedobaptism. Fourth, paedobaptism is the result of allowing the Old Testament interpretive priority over the New Testament in that it allows OT bodily circumcision to define our understanding of NT water baptism. Although there is an analogical connection between OT bodily circumcision and NT water baptism, the former was a socio-ethnic marker for Israel, whereas the latter is not a socio-ethnic marker for the Church since race is meaningless in the New Covenant. Recall also that Abraham received circumcision as a seal of the faith God gave him; if this is the original intent of circumcision, as the New Testament in Romans 4:11 tells us, should we not likewise on the basis of circumcisions analogical connection with baptism (in that both are symbols of conversion or regeneration/spiritual resurrection or saving faith) only administer water baptism in the presence of the fulfilled prerequisite of an informed and credible profession of faith? After all, Galatians 3:7 instructs us, Therefore, be sure that it is those who are of faith who are sons of Abraham. Furthermore, paedobaptism also comes into conflict with the regulative principle in that there is no explicit command or example of paedobaptism in the entire New Testament (and the New Testament has interpretive priority over the Old Testament).
As an addendum to my comments above, I must point out that whereas circumcision was the sign of the Abrahamic Covenant (Gen 17:11) and the Sabbath was the sign of the Old Covenant (Exod 31:15-17; Ezek 20:12, 20), water baptism is not the sign of the New Covenant another point that undermines Covenant Theologys understanding of the connection between circumcision and baptism. Although water baptism is one of the two ordinances specifically commanded for the Church, the true sign of the New Covenant is the cup of the Lords Table. Lukes account of the Last Supper clearly teaches this: And in the same way He took the cup after they had eaten, saying, This cup which is poured out for you is the new covenant in My blood (Luke 22:20). So, if paedobaptism truly incorporates infants as covenant children of the New Covenant, should not Covenant Theologians also extend to their infants and young children the Lords Table for the sake of theological consistency? However, the New Testament clearly instructs us that individuals must examine themselves prior to partaking of the Lords Table (1 Cor 11:26-31) something that an infant or an extremely young child cannot do. This is very telling, and the implications are obvious. If one is not able to or should not partake of the true sign of the New Covenant (the Lords Table), how can they logically be considered members of the New Covenant or covenant children of the New Covenant? In my opinion, they cannot. In the Old Testament, if one did not honor or fulfill the sign of the Abrahamic or Mosaic Covenants, he was cut off from the people with regard to the former (i.e. the Abrahamic – circumcision) or put to death for the latter (i.e. the Mosaic – Sabbath)! Finally, 1 Peter 3:21 defines baptism as an appeal or a pledge to God for a good conscience (the KJV says an answer of a good conscience toward). How can an infant or a young child who does not understand the faith or does not have the mental faculties yet to properly understand or has not been taught the faith or more importantly has not been elected by the sovereign, distinguishing grace of God (which is not up to parents or the local church) make an answer of a good conscience toward God? Again, I believe infants to be incapable of this.
Brother Bobby, I hope this answers your question. Thanks again. Soli Deo Gloria.”