This post is adapted from Andrew Fuller: Holy Faith, Worthy Gospel, World Mission by John Piper.
Natural Inability and Moral Inability
In his most famous work, The Gospel Worthy of All Acceptation, Andrew Fuller piles text upon text in which unbelievers are addressed with the duty to believe. These are his final court of appeal against the High Calvinists, who use their professed logic to move from biblical premises to unbiblical conclusions.
But he finds Jonathan Edwards very helpful in answering the High Calvinist objection on another level. Remember, the objection is that “it is absurd and cruel to require of any man what is beyond his power to perform.” In other words, a man’s inability to believe removes his responsibility to believe (and our duty to command people to believe). In response to this objection, Fuller brings forward the distinction between moral inability and natural inability. This was the key insight which he learned from Jonathan Edwards, and he gives him credit for it on the third page of The Gospel Worthy.
The distinction is this: Natural inability is owing to the lack of “rational faculties, bodily powers, or external advantages”; but moral inability is owing to the lack of inclination because of an averse will. Natural inability does in fact remove obligation. Fuller cites Romans 2:12 as a pointer to this truth: “For all who have sinned without the law will also perish without the law, and all who have sinned under the law will be judged by the law.” In other words, there is a correlation between what you will be held accountable for and what you had natural access to.
But moral inability does not excuse. It does not remove obligation. And this is the kind of inability the Bible is speaking about when it says, “The natural person does not accept the things of the Spirit of God, for they are folly to him, and he is not able to understand them because they are spiritually discerned” (1 Cor. 2:14; cf. Rom. 8:8). Fuller writes:
There is an essential difference between an ability which is independent of the inclination, and one that is owing to nothing else. It is just as impossible, no doubt, for any person to do that which he has no mind to do, as to perform that which surpasses his natural powers; and hence it is that the same terms are used in one case as in the other. 
In other words, it is just as impossible for you to choose to do what you have no inclination to do as it is to do what you have no physical ability to do. But the inability owing to physical hindrances excuses, while the inability owing to a rebellious will does not. This kind of reasoning was not Fuller’s main reason for rejecting High Calvinism and Arminianism. Scripture was. But Edwards’s categories helped him make more sense of what Fuller saw there.
The Practical Upshot: World Evangelization
The all-important conclusion from all this exegetical, doctrinal, theological labor and controversy was the enormously practical implication for evangelism and world missions:
I believe it is the duty of every minister of Christ plainly and faithfully to preach the gospel to all who will hear it; and, as I believe the inability of men to [do] spiritual things to be wholly of the moral, and therefore of the criminal kind—and that it is their duty to love the Lord Jesus Christ, and trust in him for salvation, though they do not; I therefore believe free and solemn addresses, invitations, calls, and warnings to them, to be not only consistent, but directly adapted as means, in the hand of the Spirit of God, to bring them to Christ. I consider it as part of my duty that I could not omit without being guilty of the blood of souls.
Fuller’s engagement at this level of intellectual rigor, as a pastor and a family man, may seem misplaced. The price was high in his church and in his family. But the fruit for the world was incalculably great. No one else was on the horizon to strike a blow against the church-destroying, evangelism-hindering, missions-killing doctrine of High Calvinism. Fuller did it, and the theological platform was laid for the launching of the greatest missionary movement in the world.