Karl Barth's rejection of infant baptism (paedobaptism) in his doctrine of baptism (CD IV/4) is infamous. Barth was a professor and pastor within the Swiss Reformed church, and the Reformed tradition has strongly affirmed the baptism of infants from its earliest days (c.f John Calvin's Institutes 4.16), and had persecuted the Anabaptists for rejecting infant baptism. So Barth was not a Baptist like the American baptists that originated from English baptists in late 17th century that had adopted some elements of Calvin's theology (c.f. Second London Baptist Confession). Barth admired the baptists he was glad that the American baptist tradition was strong, but he himself was firmly within the Reformed church tradition.

An important point of differentiation between Barth's rejection of infant baptism from that of the baptists, is that Barth firmly rejected rebaptism (or multiple baptisms) and many Baptist churches frequently perform multiple rebaptisms (even of adults who had been previously baptized as an adult). In 1965, when Barth was 79 years old, he wrote a famous letter explaining why he refused to be rebaptised. Barth explained that he was baptized as an infant, and although it was a disorderly baptism (because was not asked whether he wanted to be baptized), it was nevertheless a valid baptism that should not be replaced by another baptism.

Karl Barth's rejection of infant baptism received its most important definition in the Church Dogmatics IV/4 fragment, which was an unfinished part volume of his ethical conclusion to the "Doctrine of Reconciliation" (CD IV) published in 1967. Barth had already criticized infant baptism in his 1948 lectures on The Teaching of the Church Regarding Baptism, but it wasn't until 1967 that this criticism took an official dwelling in Barth's most mature theological work (the Church Dogmatics), and included a more thoroughly desacramentalization. 

Eberhard Jüngel's Five Point Summary of Barth's Doctrine of Baptism

What is Karl Barth's doctrine of baptism? Eberhard Jüngel has summarized Barth's doctrine of baptism in five points based on Barth's The Teaching of the Church Regarding Baptism (a translation of these five points are available in W. Travis McMacken's The Sign of the Gospel: Toward an Evangelical Doctrine of Infant Baptism after Karl Barth):

Barth's Doctrine of Baptism according to Jüngel (via McMaken):

First, "Baptism has a portraying, attesting and—in the sense of attestation—imitating, symbolic, signifying function." It is an image of the salvation history that occurs between God and humanity in Jesus Christ, and not itself that which it attests.

Second, the power of baptism does not reside within baptism itself or within the faith of the one being baptized. Rather, it resides within Jesus Christ. Jüngel clarifies this notion in five subpoints, the sum of which is that baptism has the necessity of a command, but that baptism is not a necessary or indispensable means of salvation.

Third, "baptism is an exclusively cognitive event" that "seals" or reinforces subjectively the truth of the objective reality it attests. It is not a causal or generative event creating that reality.

Fourth, the administration of baptism ought to be characterized by responsibility, both on the side of the church and on the side of the baptizand. Although the power of baptism cannot be questioned because that power is located in Jesus Christ, deficient baptismal order can lead to subjective questioning of baptism's meaning. Baptismal order must be reformed for this reason, and that means—among other things—the abrogation of infant baptism.

Fifth and finally, baptism's effectiveness resides neither within its administrator nor its receiver, but within Jesus Christ. Baptism possesses the character of an eschatological sign that determines and equips the one who has been baptized. [1]

McMacken provides this helpful analysis of Jüngel's five points:

This much is clear from Jüngel's explication: in this essay, Barth takes an approach similar to Schleiermacher's with reference to the inherent tension in Calvin's legacy on the doctrine of baptism. Barth wants to maintain that baptism is an instrument of Christ and the Holy Spirit employed for the strengthening of our faith, which Barth casts as "cognitive" here in a way that is perhaps more reductive than Calvin would have liked. Like Schleiermacher, Barth maintains that faith is necessary for baptism to be effective even if it is valid when faith is absent, although Barth jumbles the terminology a bit because he ties baptism's objective aspect, the question of efface, to the operation of Christ and the Holy Spirit rather than to the confluence of ritual and faith: "Baptism without the willingness and readiness of the baptized is true, effectual and effective baptism, but it is not correct; it is not done in obedience, it is not administered according to proper order, and therefore it is necessarily clouded baptism." Thus while infant baptism is valid, or complete in a formal or objective sense, it is improper insofar as it is deficient in the subjective sense of being irresponsible—this "willingness" and "readiness" is not present in the baptizand. [2]

Conclusion

W. Travis McMaken's The Sign of the Gospel book is an excellent resource for responding Karl Barth's criticism of the Reformed Doctrine of Baptism that retains the important critics that Barth contributed to the doctrine of baptism, yet does not exclude infants from baptism. I am a Presbyterian, which is a reformed tradition that has always performed infant baptism, so Barth's criticisms forces me to admire the baptists and understand baptist traditions in a much more positive attitude. I'm also sharing Barth's doctrine of baptism (even though I have disagreements with it) because Barth is a valuable teacher of baptists too, who may likewise be aided by Barth's indispensible contributions to theology. 

(Note: This article was originally published on July 22, 2014 but was rewritten on July 18, 2019.)

Sources:

1. W. Travis McMaken, The Sign of the Gospel: Toward an Evangelical Doctrine of Infant Baptism after Karl Barth, pp. 32-33

2. McMaken. Ibid. p. 34.