In this excerpt from his work Outlines of Theology, former Princeton Seminary professor A. A. Hodge explains a bit about his understanding of baptism and why he believes Baptists are wrong:1
What is the design of baptism?
Its design is …
Primarily, to signify, seal, and convey to those to whom they belong the benefits of the covenant of grace. Thus - it symbolizes “the washing of regeneration,” “the renewing of the Holy Ghost,” which unites the believer to Christ, and so makes him a participant in Christ’s life and all other benefits.—1 Cor. 12:13; Gal. 3:27; Titus 3:5. (2.) Christ herein visibly seals his promises to those who receive it with faith, and invests them with the grace promised.
Its design was, secondarily, as springing from the former, (1) to be a visible sign of our covenant to be the Lord’s, i.e., to accept his salvation, and to consecrate ourselves to his service. (2) And, hence, to be a badge of our public profession, our separation from the world, and our initiation into the visible church. As a badge it marks us as belonging to the Lord, and consequently (a) distinguishes us from the world, (b) symbolizes our union with our fellow-Christians.—1 Cor. 12:13.
What is the emblematic import of baptism?
In every sacrament there is a visible sign representing an invisible grace. The sign represents the grace in virtue of Christ’s authoritatively appointing it thereto, but the selection by Christ of the particular sign is founded on its fitness as a natural emblem of the grace which he appoints it to represent.
Thus in the Lord’s supper the bread broken by the officiating minister, and the wine poured out, are natural emblems of the body of Christ broken, and his blood shed as a sacrifice for our sins. And in like manner in the sacrament of baptism the application of water to the person of the recipient is a natural emblem of the “washing of regeneration.”—Titus 3:5.
Hence we are said to be “born of water and of the Spirit,” John 3:5, i.e., regenerated by the Holy Spirit, of which new birth baptism with water is the emblem; and to be baptized “by one Spirit into one body,” i.e., the spiritual body of Christ; and to be “baptized into Christ,” so as “to have put on Christ,” Gal. 3:27; and to be “baptized into his death,” and to be “buried with him in baptism … so that we should walk with him in newness of life,” Rom. 6:3, 4, because the sacrament of baptism is the emblem of that spiritual regeneration which unites us both federally and spiritually to Christ, so that we have part with him both in his life and in his death, and as he died unto sin as a sacrifice, so we die unto sin in its ceasing to be the controlling principle of our natures; and as he rose again in the resumption of his natural life, we rise to the possession and exercise of a new spiritual life.
Baptist interpreters, on the other hand, insist that the Bible teaches that the outward sign in this sacrament, being the immersion of the whole body in water, is an emblem both of purification and of our death, burial, and resurrection with Christ. Dr. Carson says, p. 381:
“The immersion of the whole body is essential to baptism, not because nothing but immersion can be an emblem of purification, but because immersion is the thing commanded, and because that, without immersion, there is no emblem of death, burial, and resurrection, which are in the emblem equally with purification.”
He founds his assumption that the outward sign in the sacrament of baptism was designed to be an emblem of the death, burial, and resurrection of the believer in union with Christ, upon Rom. 6:3, 4, and Col. 2:12.
We object to this interpretation:
First, in neither of these passages does Paul say that our baptism in water is an emblem of our burial with Christ
He is evidently speaking of that spiritual baptism of which water baptism is the emblem; by which spiritual baptism we are caused to die unto sin, and live unto holiness, in which death and new life we are conformed unto the death and resurrection of Christ. We are said to be “baptized into Christ,” which is the work of the Spirit, not “into the name of Christ,” which is the phrase always used when speaking of ritual baptism.—Matt. 28:19; Acts 2:38; 19:5.
Second, to be “baptized into his death” is a phrase perfectly analogous to baptism “into repentance,” Matt. 3:11, and “into remission of sins,” Mark 1:4, and “into one body,” 1 Cor. 12:13, i.e., in order that, or to the effect that, we participate in the benefits of his death.
Third, the Baptist interpretation involves an utter confusion in reference to the emblem. Do they mean that the outward sign of immersion is an emblem of the death, burial, and resurrection of Christ, or of the spiritual death, burial, and resurrection of the believer? But the point of comparison in the passages themselves is plainly “not between our baptism and the burial and resurrection of Christ, but between our death to sin and rising to holiness, and the death and resurrection of the Redeemer.”
Fourth, Baptists agree with us that baptism with water is an emblem of spiritual purification, i.e., regeneration, but insist that it is also an emblem (in the mode of immersion) of the death of the believer to sin and his new life of holiness. But what is the distinction between regeneration and a death unto sin, and life unto holiness?
Fifth, Baptists agree with us that water baptism is an emblem of purification. But surely it is impossible that the same action should at the same time be an emblem of a washing, and of a burial and a resurrection. One idea may be associated with the other in consequence of their spiritual relations, but it is impossible that the same visible sign should be emblematical of both.
Sixth, our union with Christ through the Spirit, and the spiritual consequences thereof, are illustrated in Scripture by many various figures.
For example, the substitution of a heart of flesh for a heart of stone, Ezek. 36:26; the building of a house, Eph. 2:22; the ingrafting of a limb into a vine, John 15:5; the putting off of filthy garments, and the putting on of clean, Eph. 4:22–24; as a spiritual death, burial, and resurrection, and as a being planted in the likeness of his death, Rom. 6:3–5; as the application of a cleansing element to the body, Ezek. 36:25.
Now baptism with water represents all these, because it is an emblem of spiritual regeneration, of which all of these are analogical illustrations. Hence we are said to be “baptized into one body,” 1 Cor. 12:13, and by baptism to “have put on Christ,” Gal. 3:27. Yet it would be absurd to regard water baptism as a literal emblem of all these, and our Baptist brethren nave no scriptural warrant for assuming that the outward sign in this sacrament is an emblem of the one analogy more than of the other.
1 Archibald Alexander Hodge, Outlines of Theology (New York, NY: Hodder & Stoughton, 1878), 606–609 (ch. 42, questions 10-11).