Sam Renihan:

When studying historical theology and working on understanding the doctrinal position of a historical figure or group, it is important to consult the opponents of that view. Opponents may misunderstand or misrepresent the view you are studying, but such sources serve as helpful sounding boards for filling in gaps, seeing a view by way of contrast, and confirming that your interpretation of their opponents was sound. John Brinsley, a non-conformist paedobaptist minister, will serve as a helpful reflection of the Particular Baptists’ federal thought.

In this passage, Brinsley makes the standard argument for the justification of infant baptism, namely that because we are in the same covenant as that of Abraham, children ought to be included now as they always have been.
John Brinsley, The doctrine and practice of paedobaptisme, 19-20


He then describes the covenantal counter-argument of the Particular Baptists (everywhere labeled Anabaptists, though falsely), that the old and new covenants are distinct covenants (implying that the Abrahamic covenant is included within the old covenant) and thus children are not included in the new as they were in the old.

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The covenant of circumcision is not the covenant of grace

Having pinpointed the heart of the controversy between Baptists and Paedobaptists with regard to covenant theology (namely the relationship between the Abrahamic covenant and the covenant of grace), Isaac Backus points out some of the difficulties and inconsistencies that he sees in a Paedobaptist position, especially the way that the language of “Administrations” does not match Scripture. Where scripture asserts two covenants, many Paedobaptists assert two administrations of one covenant.

From Isaac Backus

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from Particular Voices