Concise Bible Dictionary:

The idea conveyed in this term is of great importance from the fact of its application not only to man but to God, showing how God, in His government of the earth, is pleased to express His own sense of events taking place upon it. This does not clash with His omniscience. There are two senses in which repentance on the part of God is spoken of.
1. As to His own creation or appointment of objects that fail to answer to His glory. He repented that He had made man on the earth, and that He had set up Saul as king of Israel (Gen. 6:6-7; 1 Sam. 15:11,35).
2. As to punishment which He has threatened, or blessing He has promised. When Israel turned from their evil ways and sought God, He often repented of the punishment He had meditated (2 Sam. 24:16). On the other hand, the promises to bless Israel when in the land were made conditionally on their obedience, so that God would, if they did evil, turn from or repent of the good that He had said He would do, either to Israel or in fact to any nation (Jer. 18:8-10). He would alter the order of His dealings towards them, and as to Israel He said, “I am weary with repenting” (Jer. 15:6). In all this the responsibility of man is concerned, as well as the divine government.
But the unconditional promises of God, as made to Abraham, Isaac, and Jacob, are not subject to repentance. “The gifts and calling of God are without repentance” (Rom. 11:29). “God is not a man that he should lie; neither the son of man that he should repent: hath he said, and shall he not do it?” (Num. 23:19; 1 Sam. 15:29; Mal. 3:6). And this must hold good in regard to every purpose of His will.
As regards man, repentance is the necessary precursor of his experience of grace on the part of God. Two motives for repentance are presented in scripture: the goodness of God which leads to repentance (Rom. 2:4); and coming judgment, on account of which God now commands all men to repent (Acts 17:30-31); but it is distinctly of His grace and for His glory that this door of return to Him is granted (Acts 11:18) in that He has approached man in grace and by His glad tidings, consequent on His righteousness having been secured in the death of Christ. Hence God’s testimony is “repentance toward God, and faith toward our Lord Jesus Christ” (Acts 20:21).
Repentance has been described as “a change of mind Godward that leads to a judgment of self and one’s acts” (1 Kings 8:47; Ezek. 14:6; Matt. 3:2; Matt. 9:13; Luke 15:7; Acts 20:21; 2 Cor. 7:9-10; etc.). This would not be possible but for the thought of mercy in God. It is the goodness of God that leads to repentance (Rom. 2:4).
Repentance is also spoken of as a change of thought and action where there is no evil to repent of (2 Cor. 7:8).

From Anstey’s Doctrinal Definitions:

Repentance is to have a changed mind about a wrong course that we have been on, and to have passed our judgment on it. J. N. Darby's Translation footnote on Matthew 3:8 says, "Repentance denotes the moral judgment of the soul upon all the past, upon all that is in the flesh before God. It includes, but goes further than a changed mind." The Concise Bible Dictionary states, "Repentance has been described as 'a change of mind Godward that leads to a judgment of self and one's acts" (p. 658).
Confession is an act, but repentance is a process that should carry on throughout the believer's life after he is saved. Luke 15:7 says, "I say unto you, that thus there shall be joy in heaven for one repenting sinner." Note: it doesn’t say, "repented," but "repenting"—thus indicating that it is something that should continue on in a believer’s life. In fact, if we were to cease repenting about a wrong thing or a wrong course that we have been on, we would no longer be holding our judgment upon it, and thus turning back to it in heart. This does not mean that we are to go around moping and live in sorrow for wrongs that we have done, but rather, to go on our way rejoicing, holding a changed mind and a conviction of judgment against that particular thing or course. In 2 Corinthians 7:10, we have the principle of repentance stated. The Corinthians' repentance was "never to be repented of." That is, they were not to change their mind about their repentance, because in doing so they would be going back to their wrongs. Thus, the older we get and the longer we have been on the Christian path, the deeper our hatred should be of the sins that we have committed—but we are not to be occupied with those things; the believer’s normal occupation is Christ and His interests.
Repentance is produced in men by “the goodness of God” touching their hearts (Rom. 2:4). When the prodigal son thought on the goodness of his father, it led him to change his mind about his father, and to pass judgment on himself (Luke 15:17-19). Unfortunately, repentance is a word that has lost its Scriptural meaning in the minds of many today. Some of the confusion has resulted from the bad teaching that has been in the Christian profession for years. Some examples are:
•  Repentance is not penance. Penance is the effort of man to atone for his wrongs.
•  Repentance is not confession. Some mistakenly think that if they apologize for some wrong done, that they are repenting. However, it’s possible to make a confession, and not be truly repentant.
•  Repentance is not reformation. Reformation has more to do with an outward change, the turning over of a new leaf in an attempt to supplant bad habits with good ones. Although those things will spring from repentance, they are not repentance. God is not asking us to make solemn promises that we don’t have the power to keep.
•  Repentance is not penitence. Penitence is sorrow for sin. This might result in repentance, but sorrow itself is not repentance.
Repentance should seen in the sinner who comes to Christ for salvation and it should also be seen in a failing believer who gets restored to the Lord (Acts 20:21; Rev. 2:5, etc.). The KJV says that Judas “repented,” but it should say that he was “filled with remorse.” He was not repentant. True repentance has its fruits. These are tell-tale signs that a person will manifest. John the Baptist stated this to the unrepentant Pharisees who came to him. He said, “Bring forth therefore fruits meet [worthy] of repentance” (Matt. 3:8). Naomi illustrates the marks of true repentance.
She made a clean break with her former life in Moab. The goodness of God had worked in her heart when she heard that He had given His people bread. The result was that “she went forth out of the place where she was” (Ruth 1:6-7).
She got back to the point of her departure (Ruth 1:19). She went to “Bethlehem,” the very place from which she and her husband had come when they lived in the land of Israel. This illustrates the need of getting down to the root of our failure and judging it.
She manifested a spirit of genuine brokenness and humility. She said, “Call me not Naomi, call me Mara.” Mara means “bitter.” Thus, she indicated a bitterness of soul concerning her course (Ruth 1:20; Psa. 51:17).
She justified God in all that He had allowed to happen to her (Ruth 1:20).
She made a frank confession of her wrong. She said, “I went out ... ” (Ruth 1:21). She didn’t blame her husband or anybody else.
She gave full credit to the Lord for her restoration. She said, “The LORD hath brought me home again” (Ruth 1:21; Psa. 23:3).
She wanted to be among the Lord’s people (Ruth 1:22).
Scripture indicates that God Himself repents, but not, of course, in the same way in which failing men do. Since repentance means to have a changed mind, God can and does change His mind from time to time. But with God, repentance never has to do with passing judgment on Himself, because He never does anything wrong.
When it comes to God’s purposes, He never repents (Num. 23:19; 1 Sam. 15:29). But as to His ways with men, He does repent (Gen. 6:6-7; 1 Sam. 15:11). Oftentimes God’s repentance is in connection with, and contingent upon, man’s repentance. When God sees true repentance with men on whom He has pronounced a judgment, He may repent of it, and not execute the judgment (Ex. 32:14; Judg. 2:18; 1 Chron. 21:15; Psa. 90:13; 106:44-45; Jer. 18:8; Joel 2:13; Jonah 3:9-10). Such is the mercy of God.

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