To be “of two minds” means that a person has a mixture of two opposing points of view that compete for dominance.
When used in a spiritual sense it can refer to a mixture of faith and doubt or it can refer to a mixture of right desire and wrong desire. For example in James 1 he says, “a double minded man is unstable in all his ways” in the context of faith. In James 4 he says, “Draw near to God and He will draw near to you. Cleanse your hands, you sinners; and purify your hearts you double minded.”
Purification consists of a single minded approach to temptation and sin: The lower nature still speaks and still gets tempted, but the sanctified person has his mind set to follow God and resist the flesh.
When a person is born again they gain the life of God, after which they have a dual nature. The sin nature is not removed; it remains in the believer. However, after conversion a person’s sin nature can be resisted because they now have the divine nature within them. Thus, in Christ, a person can be free from sin’s dominance. A born again person has the ability to resist sin and walk in newness of life and to do God’s will. This is not an automatic or completed work at conversion however. A believer still must be taught and transformed by God in order to be single minded. A person must come to see how frail they are and how desperate is their need for God.
Generally speaking, a new Christian will have some immediate victory but will then discover persistent wrong desires in them. This results in a battle between the 2 natures within them. Usually the process of becoming single minded involves failure, confession, contrition and repentance. Eventually, through many trials, a person learns how to avoid sin. The peace that such single mindedness brings is profound.
When monastics speak of the mystical pathway they characterize it as a progression from purgation to illumination to union. The process of “purgation” is vast and includes many elements, but one of the main elements is the move from double mindedness to being single minded.