John Calvin defends the practice of paedobaptism1 thus:
We must concentrate not on the visible element of water itself, but “elevate [our] thoughts to the promises of God which are offered to us in it, and to those internal and spiritual things which it represents to us” .2
Interestingly Calvin does not defend paedobaptism by trying to prove the practice itself occurred in the Biblical narrative, but by “deduc[ing] its nature and meaning” “from the promises given in baptism.” He says baptism represents three things: (1) the redemption and purging from sin obtained in salvation, (2) the putting to death of the flesh in our union with the death of Christ accomplished at regeneration, and (3) a testimony of our faith before men.
Calvin immediately attempts to show the continuity between baptism and circumcision . He argues that the renewal of the Abrahamic covenant and institution of circumcision related in Gen. 17:1-14 included “the promise of eternal life.” He says Christ Himself implies this in Mt. 22:32, and Paul states it almost explicitly in Eph. 2:12. Calvin points out that the proof that circumcision is an external rite corresponding to an internal regenerative work of divine grace is the statements in Dt. 10:16 and 30:6 that God circumcises the hearts; in other words, external circumcision is a counterpart to the previous internal circumcision. Circumcision indicates the purging from sin, the setting aside of the sinful flesh, and a public testimony of obedience, the very things baptism is said to indicate. In sum, both circumcision and baptism signify the previous work of regeneration . The difference between the two ceremonies, asserts Calvin, is not in the internal work both signify, but merely in the external aspect of the rite. He states:
… whatever belongs to circumcision, except the difference of the visible ceremony, belongs also to baptism… . For as circumcision was a pledge to the Jews, by which they were assured of their adoption as the people and family of God, and on their parts professed their entire subjection to him, and therefore was their first entrance into the church, so now we are initiated into the church of God by baptism, are numbered among his people, and profess to devote ourselves to his service .
It is easy then for Calvin to defend paedobaptism . For if the Lord “in former ages” made children partakers of the covenant, He no less today must do so, for the covenant does not change: “[I]f the covenant remains firm and unmoved, it belongs to the children of Christians now, as much as it did to the infants of the Jews under the Old Testament. But if they be partakers of the thing signified [‘the paternal favour of God, remission of sins, and eternal life’], why shall they be excluded from the sign. If they obtain the truth, why shall they be debarred from the figure?” In other words, since that which is signified in baptism is offered to infants of covenant parents, why not offer the sign, which of the two is less important?
This brings up an interesting point in that it obliterates the frequent distinction between infant baptism and “believers’” baptism. For Calvin, covenant infants are baptized on largely the grounds that adults are baptized-we assume they are believers. In other words, infant baptism is, as it were, believers’ baptism.
Next  Calvin provides “a more certain knowledge of the truth” of paedobaptism, namely, the continuation of the Abrahamic covenant. He alludes to 1 Cor. 7 in reminding the reader that the children of even a single covenant parent are called holy, just as they were under the older covenant. If we do not admit this, Calvin insists, what we are really saying is that God’s grace is now less obvious and manifested. Calvin states that, if anything, the manifestation of God’s grace is more “liberal” now since Christ has come. In other words, when we deny covenantal baptism, we are saying Christ’s work diminishes the manifestation and operation of God’s grace.
Calvin then alludes  to the texts describing our Lord’s blessing of the infants brought to Him. While recognizing Christ does not baptize them, he asks, “If of them is the kingdom of heaven, why shall they be denied the sign, which opens, as it were, an entrance into the Church, that, being received into it, they may be enrolled among the heirs of the heavenly kingdom?” He then declares with emotion, “How unjust shall we be, if we drive away from Christ those whom he invites to him; if we deprive them of the gifts with which he adorns them; if we exclude those whom he freely admits!” Lest some think the children to whom Christ refers are of walking age, Calvin points out that the words used for children refer to those who “hang upon the breasts.”
Next , Calvin concedes that while there is no explicit mention of infant baptism in the Bible, since “they are never excluded when mention happens to be made of the baptism of any family, who can rationally conclude from this, that they were not baptized?” He reminds us that if we are to exclude infants from baptism on the grounds that their inclusion is never mentioned explicitly in the Bible, we may equally exclude women from the Lord’s table for precisely the same reason. He reminds his readers too that paedobaptism is a hoary practice: “[T]here is no ancient writer who does not refer to its origin, as a matter of certainty, to the age of the apostles.”
In section 9 Calvin declares that those who despise the baptism of infants under the new covenant would have despised circumcision under the old, since they accomplish the same thing. He reminds us of the precious benefits of paedobaptism which, like circumcision,
ratifies and confirms the promise given to the pious parent, declaring that the Lord will be a God, not only to him, but also to his seed, and that he is determined to exercise his goodness and grace, not only towards him, but towards his posterity even to a thousand generations.
He argues that the mere promise of eternal life is insufficient for us: because of our weakness God has given Christian parents a sign, which will “animate their minds to a stronger confidence, when they actually see the covenant of the Lord engraven on the bodies of their children.” Moreover, it assists the children who, when they come to years, will be stimulated thereby to worship; and it will warn them of the penalties of departing from their God.
In section 10 Calvin begins to deal with specific objections to paedobaptism. First, he notes that some say circumcision and baptism signify different things, inasmuch as the former denotes mortification and the latter does not. He already argued , however, that one signification of baptism is mortification, so the argument is baseless. Second , some insist that circumcision and baptism are simply not similar rites. To this objection he quotes Col. 2:11, 12, which equates circumcision and baptism. Third, it is claimed that the OT saints were a herd of carnal swine to whom God gave carnal promises, while NT saints are truly spiritual and therefore receive spiritual promises, and thus the “carnal” rite of baptism is unnecessary. Calvin counters by pointing out that spiritual promises like eternal life are no less evident under the old covenant than the new.
In sections 12-15 Calvin addresses a more serious objection. Some argue that since the seed of Abraham now constitutes not physical lineage, but spiritual lineage, paedobaptism is unnecessary. Calvin plainly admits that “after the resurrection of Christ, the boundaries of the kingdom of God began to be extended far and wide into all nations, without any distinction… .” He quotes or cites Rom. 4:9-12, Eph. 2:14, and Rom. 9:7, 8 in proving that “equal dignity is attributed to Jews and Gentiles.” Calvin states it is wrong for Jews, who “prided themselves in mere ceremonies,” to trust in their mere lineage and external sign. He concedes that Rom. 9 is calculated to destroy the unbelieving Jews’ vain confidence in natural descent but reminds us of Paul’s remarks that “the natural descendents are not to be deprived of their dignity.” He further mentions the account in Rom. 11 of the olive tree and God’s purpose to preserve his tree of Israel while cutting out those physical Israelites who were ungrateful and disobedient and replacing them with “true Jews,” that is, converted Gentiles.
“Therefore , though we have no doubt that the distinction of the heirs of the kingdom from those who have no share in it, is the free act of the sovereign election of God, yet, at the same time, we perceive that he has been pleased to display his mercy in a peculiar manner on the seed of Abraham, and to testify and seal it by circumcision. The same reason is applicable to the Christian Church.” He cites 1 Cor. 7:14 and comments, “We see how, even after the resurrection of Christ, Paul understands that the promise of the covenant is to be fulfilled, not only in an allegorical sense, but, according to the literal import of the words, to the natural seed [infants] of Abraham.” Likewise he cites Peter’s words at Pentecost that,“The promise [of salvation] is to you and to your children“and Peter’s later reference that those present “are the children of the covenant.” He then asks of the promise of Ex. 20:6, that the seed of the righteous would be blessed, “even to a thousand generations”: “Shall we here have recourse to allegories? That would be a frivolous evasion. Shall we say that this promise is cancelled? That would be subversive of the law, which, on the contrary, Christ came to establish, as a rule, for a holy life. It ought to be admitted, therefore, beyond all controversy, that God is so kind and liberal to his servants, as, for their sakes, to appoint even the children who shall descend from them to be enrolled among his people.”
Following , Calvin sets forth the inconsistency of those who argue for the difference between circumcision and baptism and against paedobaptism on the grounds that circumcision means mortification while baptism means new life, while they simultaneously insist that baptism means burial. In other words, they contradict themselves. Too, against the objection that girls were not circumcised but girls are baptized, he remarks that “there can be no doubt that it [circumcision] was given equally for the sanctification of males and females.”
Calvin goes on [17-20] to address the objection that since infants cannot understand the gospel and therefore cannot be regenerated, they cannot be baptized by stating, “[A]ll these things are uniformly contradicted by the truth of God.” If we say they cannot come to Christ and be saved as infants as the Scripture promises, we drive them away to damnation; for if they are not in Christ, they are surely in Adam, by whose sin they are condemned. It is important to note that there is no middle ground for Calvin-or Paul in Rom. 5 and 1 Cor. 15:22: a person, infant or not, is either in Christ or not in Christ. Calvin cites Jn. 11:25 and 14:6 to prove that since life resides in Christ, we must be in Christ if we are to have life: “It is necessary for us to be engrafted into him, that we may be rescued from the bondage of death.” Calvin perceives that some will ask how an infant can be regenerated even though he has such slight, undeveloped knowledge of good and evil. He responds, “[T]he work of God is not yet without existence, because it is not observed or understood by us.” He points out that some infants are obviously saved and regenerated, John the Baptist being an example, since if they cannot be, then no infants at all could be saved, and all dying in infancy would be consigned to hell. And John is not a special example-Calvin says he is showing we cannot limit God to working regeneration among only those with understanding. He reminds us that the Lord himself was sanctified in infancy, “that he might sanctify in himself all his elect, of every age, without any difference.” It is wrong, says Calvin, to cite 1 Pet. 1:23 to prove one cannot be regenerate unless he hears preaching, for that verse is applying to those old enough to hear and understand, not to infants. He underscores God’s sovereignty by stating, “[I]t would not be safe to affirm, that the Lord cannot reveal himself in any way so as to make himself known to [infants].” In other words, we dare not limit God’s saving work.
Similarly those who cite Rom. 10:17 and Dt. 1:39 to prove infants have no hearing or knowledge and thus cannot be saved, err, according to Calvin. He freely admits that “the ordinary economy and dispensation of the Lord” is by means of hearing and understanding, but we cannot assert that God cannot give faith and regenerate when He desires. Calvin insists he is not claiming regenerate infants possess the same degree of faith or knowledge, but they possess true faith and knowledge nonetheless.
Some argue, says Calvin, that since baptism is a sign of repentance and faith, and since infants cannot repent and believe, infants cannot validly be baptized. But, asserts Calvin, they argue against God who argue thus. Calvin notes Jer. 4:4, and especially Rom. 4:11, which assert that circumcision is “a seal of the righteousness of faith,” in showing that circumcision did involve faith inasmuch as its sign was placed on the infant, and that therefore baptism too may involve faith. He declares that “by saying that [infants] are baptized into future repentance and faith” we argue that “though these graces have not been formed in them, the seeds of both [repentance and faith] are nevertheless implanted in their hearts by the secret operation of the Spirit.” He makes a critical assertion for his view when he states, “[W]hatever arguments tend equally to invalidate circumcision have no force in the controversy against baptism.” In this context he notes that the fact that baptism is associated with regeneration and therefore, according to some, must be administered only to the regenerate, is no argument against paedobaptism, for circumcision denoted regeneration too, and it was administered to infants. Here again, Calvin seems oblivious to any distinction later made between infant and “believers’” baptism: he is saying that just as adults are baptized because they believe, so covenant infants are baptized because they believe.
In section 21 he endeavors to show that the urging of 1 Pet. 3:21 against paedobaptism is not valid, for the “answer of a good conscience” inherent in the meaning of baptism refers to the future, not the past, of the one baptized. He declares they err who assert that “the thing signified should always precede the sign.” In section 22 he answers the objection that only those whose sins are remitted should be baptized by saying that such an objection actually works in the favor of the paedobaptists, for the sins of the covenant infants are remitted; therefore they are qualified for baptism.
Next , he answers those who employ texts like Acts 2:37, 38 and 8:37 to assert that individual confession must precede baptism. Calvin counters by saying that faith is not required in the first passage, and repentance is not required in the second. Shall we then say that faith and repentance are not requisite to salvation since they are not explicitly mentioned in these passages? He then says, in essence, “The antipaedobaptists will say, ‘But you have to go to other passages to find faith and repentance and look at all the passages together.’ Well [asserts Calvin], all I am saying is that you must do the same thing in the case of infant baptism: look at all the passages which bear on baptism in the Bible and you will see my point.” He reminds that just as adults under the old covenant had to be taught the covenant before being circumcised, so adults under the new covenant must be taught the faith; under both old and new, infants are in a slightly different category, not needing previous instruction. He notes  that while Abraham received instruction before circumcision, Isaac received it afterward since he was a child when brought into the covenant. In addition, God Himself calls the children of covenant parents-but not the children of wicked parents-His children (Ez. 16:20, 23:37). Hence, since they belong to his covenant, they should receive the sign of the covenant.
Following , Calvin responds to those who use Jn. 3:5 to show that baptism equals regeneration. He says that the water mentioned is not baptism, but regeneration itself; therefore, it is of no direct relevance to the paedobaptism issue. Next , he argues explicitly against those who deny paedobaptism but hold to baptismal regeneration. He says they consign all unbaptized children to damnation. Here Calvin plainly repudiates baptismal regeneration, showing that faith in Christ, and not baptism, is the exclusive instrument of salvation.
The final sections [27-32] of Calvin’s chapter are devoted largely to refuting the views of the heretic Servetus and a discussion of the relation between the Lord’s Supper and baptism. They do not warrant a long discussion here. However, I would mention that Calvin refutes those who oppose paedobaptism on the grounds that Mt. 28:19, 20 and Mk. 16:16 indicate teaching must precede baptism. Calvin says that these texts are not designed to give a precise order any more than Jn. 3:5 (“the water and the Spirit”) is teaching that regeneration precedes faith. He said such passages involving instruction refer to that of adults and cites 2 Thes. 3:10 to prove his comment. This text commands that those who do not work should not eat, yet no one would say it applies to infants; just so, other texts associating baptism with teaching refer to adults, not to infants.
1 John Calvin, Institutes of the Christian Religion, trans. Allen (Grand Rapids: Eerdmans, 1949), IV: xvi.
2 Bracketed numerals within the text refer to the section of Calvin’s chapter defending paedobaptism.