What is meant by a “reprobate mind” as spoken of in the Book of Romans?
What Paul means by “a reprobate mind” is a mind that has rejected all revelation from God and now has reached a point that it cannot understand the things of God. In the context of Romans one Paul mentions that there is truth available to all humanity from creation. If a person looks at creation he should surmise that God exists, and that He is both omnipotent and a wise God. Should he live up to the knowledge that he does have, God will make sure he gets more knowledge until he hears what he needs to hear to be saved.
However, the tendency of humanity, as all history shows, is to reduce the things he sees in creation into something he wants to worship. The tendency is to worship the created not the Creator. Therefore, society begins with idolatry, moves down to heterosexual immorality, and lastly culminates in homosexual immorality. Finally, God gives them up to a reprobate mind. People do not have a reprobate mind because God decreed them to from the beginning, but because they rejected the truth of God. After a period of time, God then decrees them to a reprobate mind. They cease to have the capacity to understand any further spiritual truth through creation or otherwise.