Unto whom is Baptism to be administered?
Baptism is not to be administered to any that are out of the visible church, and so strangers from the covenant of promise, till they profess their faith in Christ, and obedience to him,1 but infants descending from parents, either both, or but one of them, professing faith in Christ, and obedience to him, are in that respect within the covenant, and to be baptized.2
Scripture proofs
The Westminster Assembly's proof texts (KJV). The bracketed numbers in the answer above mark the clause each set of references supports; expand a row to read the verses.
1 Acts 2:38; Acts 8:36–37
Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Acts 8:36 And as they went on their way, they came unto a certain water: and the eunuch said, See, here is water; what doth hinder me to be baptized?
Acts 8:37 And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.
2 Gen. 17:7, 9; Gal. 3:9, 14; Col. 2:11–12; Acts 2:38–39; Rom. 4:11–12; Rom. 11:16; 1 Cor. 7:14; Matt. 28:19; Luke 18:15–16
Gen. 17:7 And I will establish my covenant between me and thee and thy seed after thee in their generations for an everlasting covenant, to be a God unto thee, and to thy seed after thee.
Gen. 17:9 And God said unto Abraham, Thou shalt keep my covenant therefore, thou, and thy seed after thee in their generations.
Gal. 3:9 So then they which be of faith are blessed with faithful Abraham.
Gal. 3:14 That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith.
Col. 2:11 In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ:
Col. 2:12 Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead.
Acts 2:38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Acts 2:39 For the promise is unto you, and to your children, and to all that are afar off, even as many as the LORD our God shall call.
Rom. 4:11 And he received the sign of circumcision, a seal of the righteousness of the faith which he had yet being uncircumcised: that he might be the father of all them that believe, though they be not circumcised; that righteousness might be imputed unto them also:
Rom. 4:12 And the father of circumcision to them who are not of the circumcision only, but who also walk in the steps of that faith of our father Abraham, which he had being yet uncircumcised.
For if the firstfruit be holy, the lump is also holy: and if the root be holy, so are the branches.
For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the husband: else were your children unclean; but now are they holy.
Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
Luke 18:15 And they brought unto him also infants, that he would touch them: but when his disciples saw it, they rebuked them.
Luke 18:16 But Jesus called them unto him, and said, Suffer little children to come unto me, and forbid them not: for of such is the kingdom of God.
This doctrine across the Standards
Where the Confession and the Westminster Shorter Catechism treat the same matter, so the question can be studied alongside its parallel statements.
In the Westminster Confession
XXVIII.1 Baptism is a sacrament of the New Testament, ordained by Jesus Christ, not only for the solemn admission …
Baptism is a sacrament of the New Testament, ordained by Jesus Christ, not only for the solemn admission of the party baptized into the visible Church, but also to be unto him a sign and seal of the covenant of grace, of his ingrafting into Christ, of regeneration, of remission of sins, and of his giving up unto God, through Jesus Christ, to walk in newness of life: which sacrament is, by Christ's own appointment, to be continued in his Church until the end of the world.
→ XXVIII.1 · Of BaptismXXVIII.2 The outward element to be used in this sacrament is water, wherewith the party is to be baptized …
The outward element to be used in this sacrament is water, wherewith the party is to be baptized in the name of the Father, and of the Son, and of the Holy Ghost, by a minister of the gospel lawfully called thereunto.
→ XXVIII.2 · Of BaptismXXVIII.3 Dipping of the person into the water is not necessary; but baptism is rightly administered by pouring or …
Dipping of the person into the water is not necessary; but baptism is rightly administered by pouring or sprinkling water upon the person.
→ XXVIII.3 · Of BaptismXXVIII.4 Not only those that do actually profess faith in and obedience unto Christ, but also the infants of …
Not only those that do actually profess faith in and obedience unto Christ, but also the infants of one or both believing parents are to be baptized.
→ XXVIII.4 · Of BaptismXXVIII.5 Although it be a great sin to contemn or neglect this ordinance, yet grace and salvation are not …
Although it be a great sin to contemn or neglect this ordinance, yet grace and salvation are not so inseparably annexed unto it, as that no person can be regenerated or saved without it, or that all that are baptized are undoubtedly regenerated.
→ XXVIII.5 · Of BaptismXXVIII.6 The efficacy of baptism is not tied to that moment of time wherein it is administered; yet, notwithstanding, …
The efficacy of baptism is not tied to that moment of time wherein it is administered; yet, notwithstanding, by the right use of this ordinance the grace promised is not only offered, but really exhibited and conferred by the Holy Ghost, to such (whether of age or infants) as that grace belongeth unto, according to the counsel of God's own will, in his appointed time.
→ XXVIII.6 · Of BaptismXXVIII.7 The sacrament of baptism is but once to be administered to any person.
The sacrament of baptism is but once to be administered to any person.
→ XXVIII.7 · Of BaptismIn the Westminster Shorter Catechism
Q.94 What is Baptism?
Baptism is a sacrament, wherein the washing with water in the name of the Father, and of the Son, and of the Holy Ghost, doth signify and seal our ingrafting into Christ, and partaking of the benefits of the covenant of grace, and our engagement to be the Lord's.
→ Open Q.94Q.95 To whom is Baptism to be administered?
Baptism is not to be administered to any that are out of the visible church, till they profess their faith in Christ, and obedience to him; but the infants of such as are members of the visible church are to be baptized.
→ Open Q.95