Gavin Ortlund on Paedobaptism in Reformed Theology

I came across this article by Gavin Ortlund (looking for something completely different) and it reminded me of my own (unfinished) critical interaction with Reformed paedobaptism 10 years ago (here and here).

Gavin Ortlund, scourge of paedobaptists . . . 

Anyway, he takes an unusual route. rather than arguing for credobaptism per se, in this article he shows the logical inconsistency with the "baptism = circumcision" line of argument. His abstract:

Reformed paedobaptism generally argues from continuity with the Abrahamic covenant, situating infant baptism as a continuation of infant circumcision. Credobaptist objections have typically challenged this premise, stressing points of discontinuity across the biblical covenants. This article suggests a different (though not incompatible) response, arguing that even if the paedobaptist vision of continuity between circumcision and baptism is accepted, current paedobaptist practice is not in line with it anyway, since circumcision was never at any time administered to “those who believe and their children.” The argument is buttressed by a historical survey of Reformed baptismal practices from John Calvin through the mid-17th century (often forgotten/unknown today) which, by the same appeal to continuity with circumcision, affirmed intergenerational baptism.