¶ … Saint Paul's Epistle to the Galatians, Paul is continuing the overall castigation of the Galatian churches which is the overarching subject of the letter as a whole. Indeed, Paul's fierce tone in Galatians is the first thing that strikes the reader: Longenecker (2003) describes Galatians as "teem[ing] with impassioned fervor unequalled in any other Pauline letter" (p.64). The subject is the "backsliding" (so to speak) of the individual congregations in Galatia: Paul indicates at Galatians 4:8 that they had previously been Gentiles, and the third chapter will make repeated reference (as we shall see) to Paul's ministry among them, but it seems that more recently they were accepting missionaries from a Jewish sect that was not Christian in any sense that Paul is prepared to recognize: they have attempted to convert the Galatian congregations begins with Paul's question (presumably rhetorical) of whether the churches have been subject to some kind of witchcraft: "O foolish Galatians, who hath bewitched you, that ye should not obey the truth, before whose eyes Jesus Christ hath been evidently set forth, crucified among you?" ?(Gal. 3:1). Paul is couching this in such a rhetorically aggressive position precisely because he himself had witnessed the Spirit work miracles among the Galatian churches: "He therefore that ministereth to you the Spirit, and worketh miracles among you, doeth he it by the works of the law, or by...

3:5). Paul's implication here is that true Christianity insists on the latter, the "hearing of faith" which had been credited with the "miracles" of Paul's own ministry -- the insistence on Mosaic law is credited, throughout the epistle to the Galatians, to the outside agitation of the rival Jewish sect who has been preaching in the region. A memorable example of the "works of the law" referenced here in 3:5 will come later in Galatians chapter 6, in which Paul addresses the issue of circumcision: required by mosaic law, but dispensed with in Paul's Christianity.
For now, Paul is content to outline the doctrinal differences between himself and this recent set of false preachers -- if they have tried to lure the Galatians into following the behavioral practices of Leviticus with reference to the Abraham of Scripture, Paul makes it clear here that spiritual affinity with Abraham (and with the God of Abraham, and of Christ) is attained through "faith" contrasted to doing the works according to Mosaic law:

Know ye therefore that they which are of faith, the same are the children of Abraham. And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed. So then they which be of faith are blessed with faithful Abraham. (Gal. 3:7-9)

This is presumably the same faithas…