In browsing through old issues of the Princeton Theological Review, I came across this article from 1905 by T. F. Fotheringham, “The Doctrine of Baptism in Holy Scripture and the Westminster Standards.” Fotheringham’s thesis is that the dominant understanding of baptism in Presbyterian circles of his day is wrong (nothing’s changed). Baptism for infants and for adults must have the same meaning, he argues. The language of scripture is clear that baptism is about fulfillment, thus infant baptism cannot merely indicate promise (OT category). It’s an interesting read.
In other words, he realizes what Baptists and Catholics have been saying all along: baptism indicates union with Christ, adoption by the Father, and sealing by the Holy Spirit.