Calvin on Evidences and Establishing the Authority of Scripture

Presuppositional apologetics is simply Reformed apologetics. There is nothing new under the sun:

Yet they who strive to build up firm faith in Scripture through disputations are doing things backwards. For my part, although I do not excel either in great dexterity or eloquence, if I were struggling against the most crafty sort of despisers of God, who seek to appear shrewd and witty in disparaging Scripture, I am confident it would not be difficult for me to silence their clamorous voices. And if it were a useful labor to refute their cavils, I would with no great trouble shatter the boasts they mutter in their lurking places. But even if anyone clears God's Sacred Word from man's evil speaking, he will not at once imprint upon their hearts that certainty which piety requires. Since for unbelieving men religion seems to stand by opinion alone, they, in order not to believe anything foolishly or lightly, both wish and demand rational proof that Moses and the prophets spoke divinely. But I reply: the testimony of the Spirit is more excellent than all reason. For as God alone is a fit witness of himself in his Word, so also the Word will not find acceptance in men's hearts before it is sealed by the inward testimony of the Spirit. The same Spirit, therefore, who has spoken through the mouths of the prophets must penetrate into our hearts to persuade us that they faithfully proclaimed what had been divinely commanded. Isaiah very aptly expresses this connection in these words: "My Spirit which is in you, and the words that I have put in your mouth, and the mouths of your offspring, shal never fail" [Isa. 59:21p.]. Some good folk are annoyed that a clear proof is not ready at hand when the impious, unpunished, murmur against God's Word. As if the Spirit were not called both "seal" and "guarantee" [II Cor. 1:22] for confirming the faith of the godly; because until he illumines their minds, they ever waver among many doubts! (The Institutes, Book I, Ch. VII, Sec. 4b)

Dr. Donald Barnhouse on the Organic Inspiration of Scripture

I came across this passage in Dr. Barnhouse's The Invisible War which I found insightful in describing the doctrine of Verbal-Plenary inspiration to those who are unfamiliar. He writes:

"It is objected by some that the marks of human personality upon the writings of the various human authors indicate that the Bible is a human book. We would answer this with an analogy. The angel who announced to Mary that she would become the mother of the Messiah, heard the Virgin ask, "How shall this be, seeing that I know not a man?" The answer came: "The Holy Spirit shall come upon thee, and the power of the Highest shall overshadow thee; therefore also that holy thing which shall be born of thee shall be called the Son of God" (Luke 1:35). So the baby was born. He was the second Person of the Trinity, the Son of God. But He was not a Chinese baby, nor a Negro baby, nor a Nordic Aryan; He was a Jewish baby. The greatest glory of Israel was this: "of whom as concerning the flesh Christ came, who is over all, God blessed for ever" (Romans 9:5).

Just as the Holy Spirit came upon the womb of Mary, so He came upon the brain of a Moses, a David, an Isaiah, a Paul, a John, and the rest of the writers of the divine library. The power of the Highest overshadowed them, therefore that holy thing which was born of their minds is called the Holy Bible, the Word of God. The writings of Luke will, of course, have the vocabulary of Luke, and the works of Paul will bear the stamp of Paul's mind. However, this is only in the same manner that the Lord Jesus Christ might have had eyes like His mother's, or hair that was the same color and texture as hers. He did not inherit her sins, because the Holy Spirit had come upon her. If we ask how this could be, the answer is that God says so. And the writings of the men of the Book did not inherit the errors of their carnal minds, because the writings were conceived by the Holy Spirit and born out of their personalities without partaking of their fallen nature. If we ask how this could be, again the answer is that God says so." (Barnhouse, The Invisible War Pg. 6)

This analogy, while not claiming to give a comprehensive vision of how the Spirit works in inspiration, is helpful in giving us a tangible example that we can relate to. Inspiration is analogous to the incarnation. Just as Jesus took a human nature onto His divine nature, so the Holy Spirit can use finite men in the writing of God's inerrant Word. There is no necessary problem with either of those truths, although our minds cannot completely comprehend either mystery.