In his comments on 2 Corinthians 3, the old Princeton biblical scholar and systematic theologian Charles Hodge observed the following on Paul and the law:
Every reader of the New Testament must be struck with the fact that the apostle often speaks of the Mosaic law as he does of the moral law considered as a covenant of works; that is, presenting the promise of life on the condition of perfect obedience. He represents it as saying, Do this and live; as requiring works, and not faith, as the condition of acceptance.
Remarkably, what struck Hodge and "every reader" as obvious back then is lost on most people today even among Hodge's Reformed descendants.
The background of Hodge's statement above is that the precise character of a covenant of works resides in the imposition of an obligation to personal and perfect (or entire) obedience to its specified stipulations. The Mosaic law imposes such an obligation; therefore---at the very least---it embodies a works principle within its broader covenanted administration. The key point here as I will discuss further is personal over against mediated or substitutionary performance of the covenantal stipulations. Granted, the Mosaic covenant in its typological priestly embodiment of mediation (the ceremonial law) must be viewed as an administration of the covenant of grace. Nevertheless, the Mosaic law more narrowly considered embodies what can only be described best as a works principle. This is what other and I mean by "republication" of the covenant of works in Moses. (pp. 259-260)And as an enticement to get the book and read the whole thing, here is the conclusion to Dr. Baugh's essay:
In conclusion, this examination of Galatians 5:1-6 has shown that Paul presents here two mutually exclusive ways of eschatological righteousness and justification. The one comes by faith in Christ's substitutionary mediation as our Surety, which is bestowed on us by divine grace apart from personal fulfillment of the law's demands. The other that the Galatians were seeking through their circumcision moved them into a closed system of obligation to personal, perfect obedience to the law as it embodied a principle of the republished covenant of works.
The Mosaic law itself did not originate the notion of personal obedience de novo, since it recapitulated a more fundamental creational principle of righteousness through obedience to the Creator's covenant stipulations. Further, the Mosaic law did not introduce a new way of salvation through a covenant of works, but it did embody this principle for pedagogical and typological functions in the history of redemption. But Paul does not elaborate on these sorts of essential qualifications n Galatians 5:1-6. Rather this passage is his urgent testimony to avoid even placing one foot on the path to a righteousness based on personal law-keeping whether mixed with supposed divine grace or Christ's mediation or not. The two are not compatible, as Paul makes abundantly clear. (pp.279-280) [bold emphasis added]