The case for infant baptism within the broader Reformed tradition centers on the continuity between circumcision in the Old Testament and baptism in the New Testament as signs of the same covenant of grace. While Reformed and Presbyterian traditions argue that infants of believing parents are entitled to the covenant sign, many Particular Baptists hold that baptism is the sign of the new covenant reserved for those who personally profess faith in Christ.
In the Reformed and Presbyterian understanding, as articulated in the Heidelberg Catechism Q.74 and Calvin’s Institutes of the Christian Religion Ch.16, baptism is viewed as the successor to circumcision. Just as children under the old covenant were initiated into the community of God's people through circumcision, so too are the children of believers considered to be included in the covenant of grace. It is argued that the promise of redemption is extended to them no less than to adults, and thus the outward sign is applied to testify to their inclusion in the visible church.
As a Particular Baptist, my understanding is grounded in the conviction that the new covenant differs significantly from the old. While the old covenant included the natural descendants of Israel, the new covenant is constituted by those who personally know the Lord through faith, as promised in Jeremiah 31:31-34. Therefore, the 1689 LBCF Ch.29 §2 maintains that baptism is an ordinance of the New Testament to be administered only to those who do actually profess repentance towards God, faith in, and obedience to our Lord Jesus Christ. Scripture states: "For by one Spirit were we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and were all made to drink of one Spirit." (1 Corinthians 12:13).