Reformation 21 is blogging through Calvin's Institutes this year. You can find their reading plan here.
In 4.16.4, Calvin writes:
But this is not the only way to preserve the parallel between circumcision and baptism. Clearly the greater spirituality of the New Covenant must count for something. The physical sacrifices of the OT have given way to the greater spiritual sacrifices offered by the NT Christian (1 Pet 2:5). The OT temple finds its counterpart in the greater temple of Christ’s body (John 2:19-21). The OT priesthood has been fulfilled in Christ our High Priest (Heb 7-10), and transformed into the priesthood of all believers (1 Pet 2:9; Heb 13:10, 15; Rom 12:1). Similarly, OT circumcision finds its fulfillment, not in baptism, but in spiritual circumcision, or regeneration (Col 2:11-12 Notice that this text - another favorite proof text for paedobaptists - is talking about believers, and says that those who are “circumcised” in God’s sight are those who have put off the flesh, and have been raised with Christ through their faith. It is this inward experience of spiritual circumcision that is tied to baptism in the NT). Indeed, it is never baptism, but only the Holy Spirit, which is said to be the NT “seal” on believers (Eph 1:13). Given that these historical continuities are in terms of spiritual fulfillment rather than literal identity, we can agree with Calvin that “circumcision… was their first entrance into the Church.” But then the appropriate NT counterpart to this is not water baptism as a means for infants to enter the church. Rather, even as in the OT circumcision followed physical birth into physical Israel, so in the NT baptism follows spiritual birth into spiritual Israel. Here the parallel between circumcision and baptism – much insisted upon by the Reformed – is not only preserved but is seen to actually support a believers’ baptism policy. It preserves the analogy with OT practice, and a theological analogy – not an identity – is all we have to go on with respect to circumcision and baptism. In any event, the paedobaptist will be hard pressed to argue that his construal of the circumcision/baptism parallel is more plausible than the Baptist’s.For just as circumcision, which was a kind of badge to the Jews, assuring them that they were adopted as the people and family of God, was their first entrance into the Church, while they, in their turn, professed their allegiance to God, so now we are initiated by baptism, so as to be enrolled among his people, and at the same time swear unto his name. Hence it is incontrovertible, that baptism has been substituted for circumcision, and performs the same office.
In 4.16.6, Calvin writes:
Here Calvin’s two main assumptions are brought together. Baptism is now “instead of” circumcision, and “the covenant is common, and the reason for confirming it is common.” The only difference pertains to “the mode of confirming it.” So Calvin here acknowledges a distinction between what is “common” and what is “different”. The question is whether this distinction saves paedobaptism from the Baptist critique. It appears that it does not, for it can be easily accommodated by the Baptist.Let it not be objected, that the only symbol by which the Lord ordered his covenant to be confirmed was that of circumcision, which was long ago abrogated. It is easy to answer, that, in accordance with the form of the old dispensation, he appointed circumcision to confirm his covenant, but that it being abrogated, the same reason for confirmation still continues, a reason which we have in common with the Jews. Hence it is always necessary carefully to consider what is common to both, and wherein they differed from us. The covenant is common, and the reason for confirming it is common. The mode of confirming it is so far different, that they had circumcision, instead of which we now have baptism.
Here is a list of items which Calvin would regard as merely pertaining to “the mode of confirming” the covenant, and therefore subject to modification in the historical transition from circumcision to baptism:
(1) Circumcision was the removal of the foreskin; baptism is different because it involves immersion in water (Not everyone is aware of the fact that on Calvin’s view, “it is evident that the term baptise means to immerse, and that this was the form used by the primitive Church” 4.15.19).
(2) Circumcision was applied to males only; baptism is different because it is applied to both males and females.
(3) Circumcision was performed on the eighth day; baptism is different because no particular day is prescribed.
Calvin would regard these as specifics about circumcision which were “in accordance with the form of the old dispensation,” and therefore subject to “being abrogated.” By way of contrast, Calvin insists that “the covenant is common, and the reason for confirming it is common.” The question then is how to classify the fact, additional to the three facts above, that circumcision was applied to infants. Is this, like the three facts above, also a transitory feature of God’s covenantal dealings with men, pertaining only to “the mode of confirming” the covenant at a particular point in history, and therefore subject to abrogation? Or is it (as Calvin would have it) essential to the covenant and the reason for confirming it? What if a Baptist were to say:
(4) Circumcision was applied to infants; baptism is different because it is applied after a credible profession of faith.
This thesis is wholly compatible with Calvin’s distinction between what is “common” and what is “different”. Indeed, Calvin’s distinction gives us no guidance – in itself – as to whether we should affirm or deny (4). But it is noteworthy that (4) above is confirmed by all relevant NT data about baptism. Jesus’ institution of the sign of Christian baptism commanded that it be applied to disciples, as “disciples” is defined by the NT (Matt 28:16-20; Mark 16:16). Throughout the rest of the NT, and especially displayed in the book of Acts, baptism functions in accordance with Jesus’ institution of it. It is a sign for disciples, who have placed their faith in Jesus; after Peter’s Pentecost sermon, it was only “those who accepted his message” who were baptized (cf. Acts 2:38, 41). And so we follow the apostolic policy and example of only baptizing those who received the apostolic gospel. All clear cases of baptism in the NT reflect this “believers’ baptism” policy, for the vast majority of cases of baptism in the NT come after a credible profession of faith. Indeed, the household baptisms in Acts and elsewhere were of believing families (Cornelius, the Philippian jailor, Crispus, Stephanus), and we use this significant datum to interpret the one household baptism (Lydia) where Luke does not tell us the details as he does with all the rest. The consistent policy is to baptize those who received the apostolic gospel. There may be one or two cases where this pattern may not be clearly exemplified, but this offers no support to the view that, in those cases, baptism was applied in the absence of a credible profession of faith, much less to infants. Thus, the reasonable thing to do, in light of the clear NT pattern, is to classify (4) with (1)-(3) above.