The word apeitheo relates to unbelief and disobedience both. It is important for us as classical Protestants to distinguish them, but is equally important for us to refuse to separate them. Far too many tight Protestants, zealous for what they believe to be the truth, are willing to sacrifice sola Scriptura on the altar of sola fide. But of course, God doesn’t want that, and He doesn’t want it to go the other way either. The relationship of faith and obedience, and also of unbelief and disobedience, is less like the relationship of ham and eggs, or salt and pepper, than it is like the relationship of height to breadth. If it is heresy to think so, then a lot of Bible translators need to be brought up on charges.
In the AV, apeitheo is rendered as believe not.
“He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him” (John 3:36).
“But the Jews which believed not, moved with envy, took unto them certain lewd fellows of the baser sort, and gathered a company, and set all the city on an uproar, and assaulted the house of Jason, and sought to bring them out to the people” (Acts 17:5).
“But when divers were hardened, and believed not, but spake evil of that way before the multitude, he departed from them, and separated the disciples, disputing daily in the school of one Tyrannus” (Acts 19:9).
“For as ye in times past have not believed God, yet have now obtained mercy through their unbelief: Even so have these also now not believed, that through your mercy they also may obtain mercy” (Rom. 11:30-31).
“That I may be delivered from them that do not believe in Judaea; and that my service which I have for Jerusalem may be accepted of the saints” (Rom. 15:31).
“And to whom sware he that they should not enter into his rest, but to them that believed not?” (Heb. 3:18).
“By faith the harlot Rahab perished not with them that believed not, when she had received the spies with peace” (Heb. 11:31).
So there you have it. Lack of assent to propositions, right? No, the same word is also rendered as disobedient.
“But to Israel he saith, All day long I have stretched forth my hands unto a disobedient and gainsaying people”(Rom. 10:21).
“Unto you therefore which believe he is precious: but unto them which be disobedient, the stone which the builders disallowed, the same is made the head of the corner, And a stone of stumbling, and a rock of offence, even to them which stumble at the word, being disobedient: whereunto also they were appointed” (1 Pet. 2:7-8).
“Which sometime were disobedient, when once the longsuffering of God waited in the days of Noah, while the ark was a preparing, wherein few, that is, eight souls were saved by water” (1 Pet. 3:20).
Some other scoundrel translated it as “obey not.”
“But unto them that are contentious, and do not obey the truth, but obey unrighteousness, indignation and wrath” (Rom. 2:8).
“Likewise, ye wives, be in subjection to your own husbands; that, if any obey not the word, they also may without the word be won by the conversation of the wives” (1 Pet. 3:1).
“For the time is come that judgment must begin at the house of God: and if it first begin at us, what shall the end be of them that obey not the gospel of God?” (1 Pet. 4:17).
This last rendering is especially troubling, because everyone knows you can’t obey or disobey the gospel, right? You have to think thoughts about it, and that’s it, correct?
But then in the nick of time, our translators veered back into propositionalist orthodoxy, and the word is rendered as unbelieving.
“But the unbelieving Jews stirred up the Gentiles, and made their minds evil affected against the brethren” (Acts 14:2).
We live in troubled times so I should note for the record that some of my comments above are facetious. But not all of them.