Without the deeds of the law - Without works as a meritorious ground of justification. The apostle, of course, does not mean that Christianity does not produce good works, or that they who are justified will not obey the Law, and be holy; but that no righteousness of their own will be the ground of their justification. They are sinners; and as such can have no claim to be treated as righteous. God has devised a plan by which, they may be pardoned and saved; and that is by faith alone. Barnes Notes

Of works -The Law which commands works, and on which the Jews relied. If this were complied with, and they were thereby justified, they would have had ground of self-confidence, or boasting, as being justified by their own merits. But a plan which led to this, which ended in boasting, and self-satisfaction, and pride, could not be true. Barnes Notes

By what doctrine? Now the doctrine of works has this condition attached to it, that is, if you do, and the doctrine of faith has this condition, that is, if you believe. Geneva

Side Note

Seeing there is one God -the apostle alludes to Zechariah 14:8, where the prophet foretells the progress of the gospel, under the image of living waters going out from Jerusalem. And the Lord shall be king over all the earth, and in that day there shall be one Lord, and his name one; to show, that under the gospel dispensation, all nations shall be regarded by God as his people, that he will be acknowledged and worshipped by all nations, and that in the affair of their justification and salvation, he will observe one rule. Benson

Zechariah 14:8-9 And it shall be in that day — when the light shall not be clear, nor dark, that is, during the whole of the fore-mentioned period; living waters shall go out from Jerusalem — The enlightening, quickening, and saving truths of Christianity, accompanied by the power of the Holy Spirit, shall proceed from the church of Christ, the true spiritual Jerusalem; half of them toward the former sea — The eastern sea; and half of them toward the hinder sea — The western sea. They shall spread themselves eastward and westward, and on all sides; and even the sea, whether on the east or west, shall not be able to obstruct their progress; but, having watered and refreshed, enlightened, renewed, and cheered the continent, they shall make their way into the islands, and diffuse their renovating and gladdening influence even over them. In summer and in winter shall it be — Perpetually, without intermission; these waters shall never dry up, be obstructed in their course, or lose their healing, fructifying, and refreshing virtue. In other words, 'the gospel, attended by the influences of the Holy Spirit, having begun its progress from Jerusalem, shall continue its course on every side, amidst all those changes of which summer and winter are an emblem: so that nothing shall totally impede its progress, till the Lord shall become King over all the earth, not only in right but in fact; till neither idols, false religion, nor antichristian power, shall remain as his rivals; till all princes shall submit to and serve him; and all the earth shall agree in one object and way of worship, and unite in submission and obedience to one Lord.' Benson quoting Scott