Romans 2:12 For as many as have sinned without law will also perish without law, and as many as have sinned in the law will be judged by the law 13 (for not the hearers of the law are just in the sight of God, but the doers of the law will be justified; 14 for when Gentiles, who do not have the law, by nature do the things in the law, these, although not having the law, are a law to themselves, 15 who show the work of the law written in their hearts, their conscience also bearing witness, and between themselves their thoughts accusing or else excusing them) 16 in the day when God will judge the secrets of men by Jesus Christ, according to my gospel.

Paul explains why the Gentile can be condemned without the law. Their conscience (which is the work of the law written in their hearts) is enough to condemn them – or, theoretically this law on the heart is enough to justify them.

Many pagan authors of Paul’s day referred to the “unwritten law” within man. They thought of it as something that pointed man to the right way. Though it is not embodied in written laws, it is in some ways more important than the written law.

In theory, a man might be justified (“excused”) by obeying his conscience. Unfortunately, every man has violated his conscience (God’s internal revelation to man), just as every man has violated God’s written revelation.
This is why we need a savior.