Commentaries:
Barnes' Notes
For neither they themselves who are circumcised - The Jewish teachers, or perhaps all Jews. It was true in general that the Jews did not wholly and entirely obey the Law of Moses, but it is probable that the apostle refers particularly here to the judaizing teachers in Galatia.
Keep the law - The Law of Moses, or the Law of God. Paul' s idea is, that if they were circumcised they brought themselves under obligation to keep the whole law of God; see the note at Galatians 5:3. But they did not do it.
(1) No person perfectly observes the whole law of God.
(2) The Jewish nation as such were very far from doing it.
(3) It is probable that these persons did not pretend even to keep the whole Law of Moses.
Paul insists on it that if they were circumcised, and depended on that for salvation, they were under obligation to keep the whole law. But they did not. Probably they did not offer sacrifice, or join in any of the numerous observances of the Jewish nation, except some of the more prominent, such as circumcision. This, says Paul, is inconsistent in the highest degree; and they thus show their insincerity and hypocrisy.
That they may glory in your flesh - In having you as converts, and in persuading you to be circumcised, that they may show their zeal for the Law, and thus escape persecution. The phrase "in your flesh" here, is equivalent to "in your circumcision;" making use of your circumcision to promote their own importance, and to save themselves from persecution.
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