A slightly late post from near the end of one of my classes
At long last, we arrive at the locus classicus for natural law in Scripture, Romans 1-2. The first inklings of a connection to natural law starts with Paul's use of natural revelation in 1:18-23. Verse 20 in particular affirms that various truths about God are understood by means of creation itself. At minimum, something of the divine power and essential superiority can be discerned from the world God has made. Verse 21 then employs a kind of natural law logic: they knew God, but they did not give Him due honor as God. In this way they became fools and worshipped created images. This implies that they ought have been able to infer from what creation reveals about God that He alone ought to be worshipped and ought not to be worshipped alongside, beneath, or by means of created forms. This permits the inference from the order of creation itself that the nations are under divine wrath for their many crimes of idolatry.
Verses 28-32 are interesting inasmuch as they show the distorting effect of idolatry on what man thinks about other aspects of what nature teaches. The best of the philosophers and other pagan sources could always have told you that promiscuity, greed, malice, hubris, rebellion, callousness, and homesexual relations were immoral according to nature or at least chafed against it (though most of them would have gotten at least one or more of these wrong to a greater or lesser degree). Yet even these men were often willing to concede the legitimacy in some sense of the cults and myths of the gods used at large, and these cults and myths always helped to blind the masses of ordinary people from the truth of nature. Worshipping anything less than the true God skews our vision of the natural order, so that whatever perfections are present in the created objects of worship may be overemphasized, while whatever perfections those objects of worship lack may be neglected or abandoned altogether. Moreover, since these idols and imposters are not the living God who speaks His law and holds the world accountable, but rather fictions (at best) or rebellious spirits (at worst), they do not tend to correct vices at all but rather ignore or even encourage them. At the same time, as can be seen in the philosophers, the truth of these matters remains available to those who are willing to seek it out, which renders the mass of humanity without excuse.
It is worth noting the context of these statements, however. Paul is setting the context for the Gospel he preaches. The seriousness of the human plight when left in a post-Fall world to natural revelation alone can be hard to see from within the fallen order. Like with drug addiction, the severity of the condition is only quite as vivid as Paul renders it after it has been left behind. The pagans were never quite so ignorant as to miss than humanity had something deeply wrong and that even their own conception of how the world is may be quite flawed. Yet apart from the retrospective clarity disclosed by the quite radical solution in the Gospel of Christ, both the depths of human depravity and the heights of God's intended human righteousness are drastically obscured.
Moving into chapter two, we can see more clearly that though Paul speaks of a condition applying to the pagan nations, the account he provides is at least specific to the vantage point of Israel. Many pagans had ideas of divine judgment and eternal recompense, but the ultimate eschatological character of the coming crisis Paul describes is distinctively Jewish (especially as we see in "to the Jew first, and also to the Greek"). Here ambiguities arise. Paul speaks of people sinning and perishing "without the law," and he mentions Gentiles who are a law unto themselves because they do by nature what the law says, and they show it is written on their hearts. Who are these figures? Many have taken then as general pagan Gentiles, displaying the natural law written into their consciences. Others have taken them as Gentile Christians, who have the law written in their hearts in the sense prophesied by Jeremiah and by it by the power of the Spirit, which will come into account when God judges through Jesus Christ.
The debate on this issue is no small one and hard to settle. I have often gone back and forth, but at present I am somewhat inclined to the more traditional view of Gentiles obeying natural law for a couple of reasons. For one, I find at least somewhat persuasive the argument in Fulford and Haines that the language here is actually connected to Aristotle rather than Jeremiah. We certainly know that Paul used and knew of Greek philosphers and poets, and it is quite intriuging that "a law to himself," "do the work of the law," and "accusing and excusing" all appear in Aristotle. This, however, is not the strongest point. What seems much stronger is how Paul concludes his description of the function of this inner law: "their conscience also bearing witness, while their conflicting thoughts accuse or even excuse them." This language does not seem to match how Paul normally speaks of believers, putting accusation and excusal side-by-side. When Paul (and, incidentally, the author of Hebrews) speaks of the believer's conscience, it is almost always as good, pure, and testifying in a positive way (except its function in the discussion of stronger/weaker brethren, which seems of little relevance to the subject matter of this passage). This is epecially noteworthy since Paul has to qualify with "or even excuse," giving accusation a more stable place in the description. Leading with accusation as the main function of a conscience makes sense if referring to Gentiles who in some general sense act as people whose conscience partially guides them to the natural law, while still leaving them sinners on the whole, but seems much less fitting as a way to talk about believing Gentiles living by the Spirit.
As a final note, the passage as it ends highlights the function of special revelation, specifically in the form of divine law, as hypothetically serving to enlighten and illuminate, but before and apart from Christ actually only being able to intensify condemnation, since all in fact are deeply sinful. This is probably worth noting for use of natural law and divine law in political matters, though the proper implications of this I am not quite prepared to unpack here.