This post is part of my year long study of Calvin's Institutes of the Christian Religion. To facilitate this course of study, I am following along with Princeton University's "A Year with the Institutes", which also includes an audio reading of the text.
Calvin's Institutes - 1.7.4-5
Calvin: "Profane men think that religion rests only on opinion, and, therefore, that they may not believe foolishly, or on slight grounds, desire and insist to have it proved by reason that Moses and the prophets were divinely inspired. But I answer, that the testimony of the Spirit is superior to reason. For as God alone can properly bear witness to his own words, so these words will not obtain full credit in the hearts of men, until they are sealed by the inward testimony of the Spirit. The same Spirit, therefore, who spoke by the mouth of the prophets, must penetrate our hearts, in order to convince us that they faithfully delivered the message with which they were divinely entrusted."
And this:
"Let it therefore be held as fixed, that those who are inwardly taught by the Holy Spirit acquiesce implicitly in Scripture; that Scripture, carrying its own evidence along with it, deigns not to submit to proofs and arguments, but owes the full conviction with which we ought to receive it to the testimony of the Spirit. Enlightened by him, we no longer believe, either on our own Judgment or that of others, that the Scriptures are from God; but, in a way superior to human Judgment, feel perfectly assured—as much so as if we beheld the divine image visibly impressed on it—that it came to us, by the instrumentality of men, from the very mouth of God. We ask not for proofs or probabilities on which to rest our Judgment, but we subject our intellect and Judgment to it as too transcendent for us to estimate."
Calvin is telling us that the elect, those who are regenerated by the Holy Spirit, have the greatest proof of all, the testimony of the indwelling Holy Spirit.
Certainly this is no proof to the unregenerate, but Scripture also makes it clear that God has hidden these things from the "wise".