John Calvin Commentary 1 John 5:13

"These things have I written unto you, that ye may know that ye have eternal life, [even] unto you that believe on the name of the Son of God." — 1 John 5:13 (ASV)

These things have I written unto you. As there ought to be daily progress in faith, he says that he wrote to those who had already believed, so that they might believe more firmly and with greater certainty, and thus enjoy fuller confidence regarding eternal life. The purpose of doctrine, then, is not only to initiate the ignorant into the knowledge of Christ but also to confirm more and more those who have already been taught. Therefore, it is fitting for us to diligently attend to the duty of learning, so that our faith may increase throughout the whole course of our lives. For there are still many remnants of unbelief in us, and our faith is so weak that what we believe is not yet truly believed unless there is fuller confirmation.

But we ought to observe the way in which faith is confirmed, namely, by having the office and power of Christ explained to us. For the Apostle says that he wrote these things—namely, that eternal life is to be sought nowhere else but in Christ—so that those who were already believers might believe, that is, make progress in believing. It is therefore the duty of a godly teacher, in order to confirm disciples in the faith, to extol the grace of Christ as much as possible, so that, being satisfied with it, we may seek nothing else.

Since the Papists obscure this truth in various ways and downplay it, they show sufficiently by this very fact that they have no true concern for the right doctrine of faith; indeed, for this reason, their schools should be more shunned than all the Scyllas and Charybdises in the world, for hardly anyone can enter them without the certain shipwreck of their faith.

The Apostle further teaches in this passage that Christ is the unique object of faith, and that to the faith we have in his name is connected the hope of salvation. For in this case, the goal of believing is that we become the children and heirs of God.