Have sinned (hmarton). Constative aorist active indicative, "sinned," a timeless aorist. Without law (anomw). Old adverb "contrary to law," "unjustly," but here in ignorance of the Mosaic law (or of any law). Nowhere else in N.T. Shall also perish without law (anomw kai apolountai). Future middle indicative of apollumi, to destroy. This is a very important statement. The heathen who sin are lost, because they do not keep the law which they have, not because they do not have the Mosaic law or Christianity. Under law (en nomwi). In the sphere of the Mosaic law. By the law (dia nomou). The Jew has to stand or fall by the Mosaic law.