This topic has risen in several discussions over the years and while I have some concerns and unsettled issues with Arminius' comments regarding baptism, his thoughts reflect the general Reformed consensus of his day. Whether one is sprinkled with water or immersed is still open to dispute today as is certainly the issue of baptizing infants and I remain unconvinced of either side in these issues although I tend to lean toward the Baptist denominational practice of baptizing only cognizant adults and children of age who consent to faith.
DISPUTATION 63 ON BAPTISM AND PAEDO-BAPTISM
1. Baptism is the initial sacrament of the New Testament, by which the covenant people of God are sprinkled with water, by a minister of the church, in the name of the Father, of the Son, and of the Holy Ghost — to signify and to testify the spiritual ablution which is effected by the blood and Spirit of Christ. By this sacrament, those who are baptized to God the Father, and are consecrated to his Son by the Holy Spirit as a peculiar treasure, may have communion with both of them, and serve God all the days of their life.
2. The author of the institution is God the Father, in his Son, the mediator of the New Testament, by the eternal Spirit of both. The first administrator of it was John; but Christ was the confirmer, both by receiving it from John, and by afterwards administering it through his disciples.
3. But as baptism is two-fold with respect to the sign and the thing signified — one being of water, the other of blood and of the Spirit — the first external, the second internal; so the matter and form ought also to be two-fold — the external and earthy of the external baptism, the internal and heavenly of that which is internal.
4. The matter of external baptism is elementary water, suitable, according to nature, to purify that which is unclean. Hence, it is also suitable for the service of God to typify and witness the blood and the Spirit of Christ; and this blood and the Spirit of Christ is the thing signified in outward baptism, and the matter of that which is inward. But the application both of the blood and the Spirit of Christ, and the effect of both, are the thing signified by the application of this water, and the effect of the application.
5. The form of external baptism is that ordained administration, according to the institution of God, which consists of these two things:
(1.) That he who is baptized, be sprinkled with this water.
(2.) That this sprinkling be made in the name of the Father, of the Son, and of the Holy Ghost. Analogous to this, is the inward sprinkling and communication both of the blood and the Spirit of Christ, which is done by Christ alone, and which may be called "the internal form of inward baptism."
6. The primary end of baptism is, that it may be a confirmation and sealing of the communication of grace in Christ, according to the new covenant, into which God the Father has entered with us in and on account of Christ. The secondary end is, that it may be the symbol of our initiation into the visible church, and an express mark of the obligation by which we have been bound to God the Father, and to Christ our Lord.
7. The object of this baptism is not real, but only personal; that is, all the covenanted people of God, whether they be adults or infants, provided the infants be born of parents who are themselves in the covenant, or if one of their parents be among the covenanted people of God, both because ablution in the blood of Christ has been promised to them; and because by the Spirit of Christ they are engrafted into the body of Christ.
8. Because this baptism is an initiatory sacrament, it must be frequently repeated; because it is a sacrament of the New Testament, it must not be changed, but will continue to the end of the world; and because it is a sign confirming the promise, and sealing it, it is unwisely asserted that, through it, grace is conferred; that is, by some other act of conferring than that which is done through typifying and sealing: For grace cannot be immediately conferred by water.