The following story illustrates how we can convincingly offer proof of something (like the Deity of Christ, the resurrection of Christ, or the authority of Scripture) and still it ultimately takes the ministry of the Holy Spirit to persuade men of it:
John Warwick Montgomery, an evangelical apologist, tells the story of a man named Charlie, whose wife tried to rouse him from bed to go to work. Charlie would not get out of bed and said, “I can’t go to work today because I am dead.”
His wife said, “Charlie, that’s the most ridiculous excuse you’ve ever given to avoid work. You’re perfectly well. Now, get out of that bed and go to work.”
He continued to protest, saying, “I can’t. I’m dead.”
No matter how Charlie’s wife reasoned, she was unable to convince her husband that he was alive and well. So she called the doctor, and the doctor came and checked all his vital signs and said, “Charlie, you’re alive and well. Now you need to get out of bed and go to work.”
Charlie said, “I’m sorry, Doctor. Your instruments are wrong. I’m dead, and I know it.”
The doctor thought about how to convince Charlie that he was alive, and finally he said, “Charlie, when a person dies, the heart stops beating, and when the heart stops beating, it no longer pushes blood through the blood vessels. Dead people don’t bleed.” The doctor took Charlie to the coroner’s office, where he poked a needle into the cadavers to prove to Charlie that dead people do not bleed. Afterward the doctor said, “Now, Charlie, do you believe me that dead people don’t bleed?”
Charlie said, “Yes, you’ve proven it to me.” The doctor said, “Come here, Charlie. Give me your finger,” and the doctor pricked Charlie’s thumb with a pin, and Charlie’s thumb began to bleed. “So, what do you think now, Charlie?”
Charlie looked at his bleeding thumb and said, “Well, I’ll be! Dead men bleed after all.”
That is what John Calvin meant about the difference between proof and persuasion. Proof may be compelling, but because of hardness of heart people will not submit to it.
[Sproul, R. C. (2011-03-02). 1&2 Peter: St Andrew's Expositional Commentary (p. 119). Good News Publishers/Crossway Books. Kindle Edition]