The doctrine of baptismal regeneration is not only repudiated by all the Reformed Confessions, but, what perhaps, will to many minds be more convincing, it is impossible to reconcile the doctrine with their theology. Every one knows that the Reformed Churches adopted the theological system of Augustin. They all taught that none are born of the Spirit but those who are finally saved. If a man is called (regenerated,) he is justified; and if justified, he is glorified. There is no such thing, according to their doctrine, as falling from grace. If the Reformed therefore believed that all who are baptized are vitally united to Christ, and regenerated by the Holy Ghost, then they held that all the baptized are saved. They assuredly did not hold the latter, and therefore it is no less certain that they did not hold the former. It is impossible for a man to be a Calvinist, and believe the doctrine of baptismal regeneration.

Charles Hodge from his essay, “The Church Membership of Infants,” The Biblical Repertory and Princeton Review 30.2 (April 1858): 382-83.