Francis Turretin, the Reformed theologian of the seventeenth century, carefully distinguishes the Reformed view of infant faith from Lutheran and Anabaptist claims. Anabaptists denied any faith to infants so that they could justify their refusal to baptize them. Lutherans affirmed (rightly) that covenant infants were believers, but made no distinction between that sort of faith that is in infants and that which is possible for those who have matured cognitively and been taught verbally. In Turretin’s terminology, while infants do not possess “actual faith,” they do possess “seminal or radical and habitual faith” (Institutes, 15.14.2, vol 2, p. 583). Actual faith would include a profession of knowledge, intellectual acts, or hearing and meditating upon the word (15.14.3, vol 2, p. 584). Thus, Turretin understands Hebrews 11.6 to refer to actual faith and writes:

When the apostle says, “Without faith, it is impossible to please God,” he speaks of adults, various example of whom he in the same place commemorates and whom alone the proposed description of faith suits (Hebrews 11.1). Now it is different with infants who please God on account of the satisfaction of Christ bestowed upon them and imputed by God to obtain the remission of their sins, even if they themselves do not apprehend it and cannot apprehend it by a defect of age (15.14.7, vol 2, p. 585).

[Note in 2010: calling youth a “defect” bothers me.]

Nevertheless, while Christian infants don’t have or need adult faith in order to be saved, there is some change inaugurated in elect children within the covenant which grows and flowers over time–one which involves the beginning of faith at an infant level: “Although infants do not have actual faith, the seed or root of faith cannot be denied to them, which is ingenerated in them from early age and in its own time goes forth in act (human instrumentation being applied from without and a greater efficacy of the Holy Spirit within)” (15.14.13, vol 2, p. 586). [Note in 2010: as a Lutheran commenter mentioned on the original post, I don’t know why the Reformed have made such a big deal about Lutherans being wrong.  Since both Reformed and Lutherans believe infants are justified by it, why not just call it faith?)

While Turretin’s major work was a massive three-volume theology that dealt with opposing views, his nephew, Benedict Pictet, publicized his positions in a much shorter and simpler Christian Theology. Pictet deals with the possibility of infant faith under his discussion of infant baptism. (pp 418-420). He divides baptized infants into four classes.

1. Those who grow up unbelieving and impenitent. For these “baptism sets forth nothing and seals nothing.”
2. Those who grow up unbelieving and impenitent until they are thirty or forty years old. For these, “baptism does not disclose or put forth its efficacy before they are actually converted.” (I have no idea why Pictet is so specific about the age. If I was forced to guess I might throw out the possibility that Pictet thinks that someone who is rebellious at the age of twenty may merely be a backslidden rather than a confirmed unbeliever. But again, I am guessing.)
3. Those who grow up as believers. In these, “while reason unfolds itself, piety and faith are discovered, corresponding with the good instruction of their parents. For such covenant children growing up believing, “we may say, that baptism has been efficacious, that God has forgiven their original sin, and given them such a measure of the Spirit, as renders them capable of embracing the offers of the gospel, when reason begins to dawn upon their minds.”
4. Those who die in infancy. In the case of such infants, “we cannot doubt but that baptism … is a public and authoritative declaration on the part of God, that he has forgiven them original sin, and granted them title to life; since infants cannot be saved without forgiveness of sins and sanctification.”

It is in regard to his third class that Pictet elaborates on the possibility of infant faith. It is clear from his discussion that he regards these children, not as converted in youth, but as brought into a saving relationship with Christ while yet infants. He writes:

But should anyone say, he cannot comprehend the operations of the Holy Ghost in these cases; we reply that the thing ought not to be denied, merely because we do not comprehend it. It is not more difficult to conceive the idea of the Holy Spirit restoring the faculties of the infant, and rendering them capable of receiving evangelical objects, as soon as reason shall dawn, than it is to conceive the idea of original sin, which is nothing else but the depravation of those faculties, inclining them to objects of sense. If we can conceive of the principle of evil before any act of it, why not the principle of good before any act of the same? If Adam had not sinned, his descendants would have been naturally innocent; and why cannot it be conceived, that the Holy Spirit places infants, who are born sinful, in some state of regeneration? The cause of our corruption is the proneness of the soul to follow the motions of the body: why then should we not conceive, that the Holy Spirit prevents the soul from following those motions, and gives it the power of directing them aright?

(Readers should note: I doubt that this account of the nature of original sin, as “the proneness of the soul to follow the motions of the body,” is correct.)

While Pictet thinks these considerations are relevant to infant baptism, he doesn’t think that the regeneration of elect infants invariably occurs at the time of baptism. He replies to such ideas that

they may obtain all spiritual blessings from the very moment of their birth, but that these may be confirmed in baptism, which is the seal, pledge, or earnest of them; the infant, indeed, knows not what is taking place, but when he arrives at years of discretion, then he recognizes it, and from the knowledge of it, possesses every motive to holiness. Some infants are regenerated in the womb, and before baptism, others in baptism, others after: we assign no particular period.