These grids are absolutely necessary, but they also cause blind spots. That is why the church, and individuals, must be in constantly in the process of reforming. Notice I didn't say can cause blind spots, I said that our grids cause blind spots. That is why discussion, reading, and submitting ourselves to expository preaching are so essential.
Infant baptism is part of the covenantal grid. Here is how this system works in Biblical interpretation.
Israel = Church
In Calvin's theology, Israel represents the seed of the Church, and the modern Church is now the true Israel. In many ways, I am in total agreement with that. I believe that I will sit at the table with Abraham, Isaac, and Jacob as a joint-heir of the promise given to Abraham. By faith, I am Abraham's spiritual descendant. However, I do not think that this completely dismisses ethnic Israel anymore more than saying that there is "no more male or female" has eliminated sex.
Once one grasps the idea that the covenant of faith that God made with Abraham is the same covenant that God made with the church, one can easily understand where Calvin is going to go with his idea of baptism and why it should be administered to infants. Now, the above is a very quick, shallow overview of Calvin's theology, anyone who wishes may flesh it out a bit more in the comments. However, I think that it will suffice for the discussion of baptism.
If you made it through the last post, you will notice that I quoted Calvin as saying this:
Therefore, let him who would fully learn the value of baptism, its object, and indeed its entire nature, not fix his thought upon the element and the physical appearance, but rather raise it to God's promises which are there offered to us, and to the inner mysteries which are represented in it (p. 1325).
Calvin wishes for you to forget about the sign for a moment and think of only the thing symbolized. We have already noted that what he believed baptism symbolizes: cleansing from sin, mortification (death) of the flesh, and rebirth into newness of life (cf. 1325).
From here, Calvin will move to circumcision. Watch out, it's a tricky move. Keep your eye on the birdie. This is a long quote but worth it for the studious. Try not to nod off:
Let us examine how these two signs (baptism and circumcision) differ from each other, and in what respects they are alike...the Lord covenants with Abraham that he should walk before him in uprightness and innocence of heart [Gen. 17:1]. This applies to mortification, or regeneration. And lest anyone be in doubt, Moses more clearly explains elsewhere, when exhorting the Israelite people to circumcise the foreskin of their heart for the Lord [Deut. 10:16], that circumcision is the sign of mortification...Moses declares that they ought to be circumcised in heart, explaining the true meaning of this carnal circumcision [Deut. 30:6]...We have, therefore, a spiritual promise given to the patriarchs in circumcision such as is given us in baptism, since it represented for them forgiveness of sins and mortification of flesh. Moreover, as we have taught that Christ is the foundation of baptism, in whom both of these reside, so it is also evident that he is the foundation of circumcision. For he is promised to Abraham, and in him the blessing of all nations [Gen. 12:2-3]. To seal this grace, the sign of circumcision is added (pgs. 1326-1327).
Did you follow that? Remember what Calvin said baptism symbolized? Cleansing, regeneration (rebirth), and mortification. If you compare that list to the above paragraph you will see that he believes circumcision meant the same thing to Israel. Same covenant, same thing symbolized.
So where are the differences he promised? The title of the next section should be a big tip-off. He entitled it: The difference is in externals only. In other words, if one peels back the signs and looks into the heart, you would see the same thing happening in the heart of a "born-again" Israelite that is happening in the heart of someone being saved in the Church. Calvin deftly took away the symbol of being dunked...err...sprinkled, and then he slid the sign of circumcision in on you while your eyes where closed.
I told you from the start that it was neat, tidy, and well thought out. It makes sense, doesn't it? The only problem is that, as neat as it is, it isn't true. I do not believe that circumcision and baptism symbolize the exact same things. I will continue with that thought next post. Hopefully, this will generate a bit of feedback from both sides.