Thoughts on the Law-Gospel Antithesis...

A few things to keep in mind going into the new year... The law, as Paul says, is spiritual (Rom. 7:14). Yet nonetheless, that spiritual law can only direct and tell us our duty while also condemning us for our failures. It provides us no power to obey, thus no way to avoid condemnation. We lack the power or true goodness in ourselves for the required perfect obedience because by nature we are sinners. This is true before regeneration as well as after (WCF 16.5). Lacking the righteousness of the law, we are in need of another righteousness, one not conditioned on our law-keeping.

Looking at John 1:17, the apostle writes, "The law came through Moses; grace and truth came through Jesus Christ." (John 1:17) It is the gospel which supplies to sinners what the law demands and cannot itself give. Salvation offered to the OT saints was obtained in the promise of righteousness through faith given to Abraham by God, not through their obedience to the law given under Moses. God, when forgiving the Israelites again and again, did so for the sake of his promise to Abraham not the law given to Moses. The law under Moses served to remind the Jews of their duty and sin, their condemnation under the law, and the need for forgiveness and righteousness.

The law-gospel antithesis operated and existed in the OT. Under the covenant given through Moses one of the purposes of the law was to bring a despair to the Jews because of their sin and so drive them to look to the promised mercy of God in Christ. Under Moses that covenant of grace mercy was not given through law-commands (though they attended it), but,

it was administered by promises, prophecies, sacrifices, circumcision, the paschal lamb, and other types and ordinances delivered to the people of the Jews, all foresignifying Christ to come; which were, for that time, sufficient and efficacious, through the operation of the Spirit, to instruct and build up the elect in faith in the promised Messiah, by whom they had full remission of sins, and eternal salvation... (WCF 7.5)

All these types and promises lacked in themselves the actual grace to be communicated, but rather pointed to Christ, the substance of the gospel promise. The moral law as found in the Ten Commandments as well as the ceremonial laws were not given in order to remove sin and impart righteousness.

The same law-gospel antithesis exists in the NT. 

But now apart from the Law the righteousness of God has been manifested, being witnessed by the Law and the Prophets, even the righteousness of God through faith in Jesus Christ for all those who believe... (Romans 3:21-22)

Therefore there is now no condemnation for those who are in Christ Jesus. For the law of the Spirit of life in Christ Jesus has set you free from the law of sin and of death. For what the Law could not do, weak as it was through the flesh, God did: sending His own Son in the likeness of sinful flesh and as an offering for sin, He condemned sin in the flesh, so that the requirement of the Law might be fulfilled in us, who do not walk according to the flesh but according to the Spirit. (Romans 8:1-4)

 Dr. Michael Horton writes in The Christian Faith, "The law’s imperatives tell us what must be done; the gospel’s indicatives tell us what God has done..." And,
"The promises of the law depend upon the condition of works,” Calvin notes, “while the gospel promises are free and dependent solely upon God’s mercy.” 

[*condition of works - do this and live **God's mercy - believe and live]

John Calvin expands on the doctrine,

For this reason, the promises offered in the law would all be null and ineffectual, did not God in his goodness send the gospel to our aid, since the condition on which they depend, and under which only they are to be performed--viz. the fulfillment of the law, will never be accomplished [i.e. by us]. Still, however the aid which the Lord gives consists not in leaving part of justification to be obtained by works, and in supplying part out of his indulgence, but in giving us Christ as in himself alone the fulfillment of righteousness. For the Apostle, after premising that he and the other Jews, aware that "a man is not justified by the works of the law," had "believed in Jesus Christ," adds as the reason, not that they might be assisted to make up the sum of righteousness by faith in Christ, but that they "might be justified by the faith of Christ, and not by the works of the law," (Gal. 2:16). If believers withdraw from the law to faith, that in the latter they may find the justification which they see is not in the former, they certainly disclaim justification by the law. Therefore, whoso will, let him amplify the rewards which are said to await the observer of the law, provided he at the same time understand, that owing to our depravity, we derive no benefit from them until we have obtained another righteousness by faith. Thus David after making mention of the reward which the Lord has prepared for his servants (Ps. 25 almost throughout), immediately descends to an acknowledgment of sins, by which the reward is made void. In Psalm 19, also, he loudly extols the benefits of the law; but immediately exclaims, "Who can understand his errors? cleanse thou me from secret faults," (Ps. 19:12). This passage perfectly accords with the former, when, after saying, "the paths of the Lord are mercy and truth unto such as keep his covenant and his testimonies," he adds, "For thy name's sake, O Lord, pardon mine iniquity: for it is great," (Ps. 25:10, 11). Thus, too, we ought to acknowledge that the favor of God is offered to us in the law, provided by our works we can deserve it; but that it never actually reaches us through any such desert. Institutes 3.17.2  [emphasis and bracketed comment added]

"For the law was given through Moses; grace and truth came through Jesus Christ." (John 1:17)