The Lord now carries the commandment further inward, from the act of adultery to the desire from which it proceeds. For just as murder begins in anger, so adultery begins in lust. The Law restrained the body, but Christ reforms the heart. It is not the bodily act alone that defiles a man, but the consent of the will to unlawful desire. Even if no outward deed follows, the soul is already guilty when it delights in what is forbidden.

By speaking of the eye and the hand, the Lord does not command mutilation of the body, but teaches how resolutely occasions of sin must be removed. For the eye signifies delight, and the hand signifies action; and these are called “right” because they may be things dear and useful to us. Yet even what is dear must be cut away if it leads the soul into ruin. Nothing is so valuable that it should be preferred to the integrity of the heart.

This severity is not cruelty, but mercy. For it is better to part with what gives pleasure in time than to lose the whole man eternally. Thus the Lord shows that purity is not preserved by outward caution alone, but by inward discipline, whereby desire itself is restrained and ordered.

He then addresses divorce, which had been permitted because of the hardness of men’s hearts, but not approved as righteous. To dismiss one’s wife without just cause is not merely to end a union, but to expose her to sin, and to involve oneself and others in guilt. Marriage is not to be treated as a convenience of desire, but as a bond requiring fidelity of heart as well as body.

In all this, the Lord teaches that righteousness exceeding that of the scribes and Pharisees demands more than external conformity. It requires the purification of desire, the guarding of the inner eye, and a steadfast commitment to fidelity. Thus the Law is fulfilled, not when the body alone is restrained, but when the heart is healed and brought into harmony with God’s will.

Source: St. Augustine, On the Lord’s Sermon on the Mount,  Book I, Chapters 11-12