The following excerpt is from Calvin’s Institutes where he makes a clear logical case for infant baptism. This is not his end all argument but one of the many he uses in contra the Anabaptists of his time. Enjoy!
“In order to gain a stronger footing here, they add, that baptism is a sacrament of penitence and faith, and as neither of these is applicable to tender infancy, we must beware of rendering its meaning empty and vain, by admitting infants to the communion of baptism. But these darts are directed more against God than against us; since the fact that circumcision was a sign of repentance is completely established by many passages of Scripture, (Jer. 4:4.) Thus Paul terms it a seal of the righteousness of faith, (Rom. 4:11.) Let God, then, be demanded why he ordered circumcision to be performed on the bodies of infants? For baptism and circumcision being here in the same case, they cannot give any thing to the latter without conceding it to the former. If they recur to their usual evasion, that, by the age of infancy, spiritual infants were then figured, we have already closed this means of escape against them. We say, then, that since God imparted circumcision, the sign of repentance and faith, to infants, it should not seem absurd that they are now made partakers of baptism, unless men choose to clamour against an institution of God. But as in all his acts, so here also, enough of wisdom and righteousness shines forth to repress the slanders of the ungodly. For although infants, at the moment when they were circumcised, did not comprehend what the sign meant, still they were truly circumcised for the mortification of their corrupt and polluted nature,—a mortification at which they afterwards aspired when adults. In fine, the objection is easily disposed of by the fact, that children are baptized for future repentance and faith. Though these are not yet formed in them, yet the seed of both lies hid in them by the secret operation of the Spirit. This answer at once overthrows all the objections which are twisted against us out of the meaning of baptism; for instance, the title by which Paul distinguishes it when he terms it the “washing of regeneration and renewing,” (Tit. 3:5.) Hence they argue, that it is not to be given to any but to those who are capable of such feelings. But we, on the other hand, may object, that neither ought circumcision, which is designated regeneration, to be conferred on any but the regenerate. In this way, we shall condemn a divine institution. Thus, as we have already hinted, all the arguments which tend to shake circumcision are of no force in assailing baptism. Nor can they escape by saying, that everything which rests on the authority of God is absolutely fixed, though there should be no reason for it, but that this reverence is not due to pædobaptism, nor other similar things which are not recommended to us by the express word of God. They always remain caught in this dilemma. The command of God to circumcise infants was either legitimate and exempt from cavil, or deserved reprehension. If there was nothing incompetent or absurd in it, no absurdity can be shown in the observance of pædobaptism.”
John Calvin, vol. 3, Institutes of the Christian Religion (Edinburgh: The Calvin Translation Society, 1845), 369-70.
Here was Calvin’s argument in case anyone missed it.
Calvin had just argued that X can be applied to children. Anticipating objections, he mentions one that argues that X cannot be applied to children because X is a sign (think symbol, not evidence) of repentance and since infants cannot experience repentance, they therefore cannot receive a symbol of repentance.
How does Calvin answer this objection?
Calvin, assuming that the objector accepts the Bible as the word of God and accepting their premise that X is a sign of repentance, reduces the argument to an absurdity by pointing out that Y was also a sign of repentance (X=Y) and yet God commanded Y to be applied to infants.
Given that X=Y (only in the case that both served as a sign of repentance) how then can one thing be conceded to Y but not be conceded to X?
It can’t!
So then, what should a rebuttal to this argument look like? How can one get around it?
Logically, one can not get around it. It is impossible. Does logical validity constitute truth however? No.
So that leaves an objector to explain why one or more of the premises are false. In other words, as far as this argument goes, one needs to explain why X is not a sign of repentance and/or why Y is not.