Jamieson, Fausset and Brown on Galatians 3:21

21. "Is the law (which involves a mediator) against the promises of God (which are without a mediator, and rest on God alone and immediately)? God forbid."

life--The law, as an externally prescribed rule, can never internally impart spiritual life to men naturally dead in sin, and change the disposition. If the law had been a law capable of giving life, "verily (in very reality, and not in the mere fancy of legalists) righteousness would have been by the law (for where life is, there righteousness, its condition, must also be)." But the law does not pretend to give life, and therefore not righteousness; so there is no opposition between the law and the promise. Righteousness can only come through the promise to Abraham, and through its fulfilment in the Gospel of grace.