Infant Baptism, the Covenant, and the Reformed View

"Upon You have I leaned from before my birth; You are He who took me from my mother's womb. My praise is continually of You"(Psalm 71:6). 

When discussing the baptism of infants with Baptists, they often tell me that a little baby can't know anything about God. We should, they claim, wait until a person grows to an age of accountability or moral awareness. It is phrased in different ways. 

Yet, look at the words above from Scripture. Is that not to be our authority? We are not to look to pop psychology or secular educational assumptions. 

Unlike other psalms, Psalm 71 includes no superscription with its authorship. I think it sounds like David. Whether or not it is, is obviously the words of a covenant child, i. e., one born to a believing home. He professes even a preborn experience of the promise of God: "All your children shall be taught of the Lord, and great shall be the peace of your children" (Isaiah 54:13). Note that He doesn't say all children; rather, He says your children. Why the distinction? Because God claims the children of believers as His own (Ezekiel 16:20). Not that He promises that they are or will ever be regenerate, but that He distinguishes them covenantally from the children of pagans. We see it in His discrimination between the sons of Abraham, Isaac and Ishmael. While Ishmael is the heir of the promise, He also blesses Ishmael because of his covenantal status (Genesis 17:18-21). Both sons are members of the visible church, while only Isaac is a member of the invisible church, a proviso that Baptists consistently fail to consider. 

That is why the Reformed baptize the children of our members. God has claimed them as His own, a great privilege! Therefore, they have a right to His covenant sign, baptism. I am not attempting here to explain the Catholic or Lutheran views of baptism; that is for them to do. But the Reformed do not assume the regeneration of our infants, contrary to the oft-repeated strawman argument of Baptists. We just give them the status that God has declared of them.