What do Paul's letters and Hebrews say about Abraham's children, compared with Jewish rules?

"He who had embraced the promises was about to sacrifice his one and only son"

"The promise to Abraham is not limited to physical descendants but extends to all who share in the faith of Abraham."

"in Isaac shall seed be called to thee."

"he lived in tents, as did Isaac and Jacob, who were heirs with him of the same promise."

"This promise is subsequently inherited by Isaac, Abraham's son by his wife Sarah , while Isaac's half-brother Ishmael is also promised that he will be the founder of a great nation."

"The promise of the Messiah was made to Abraham and Sarah, and they believed the promise. Yet they died having never received it, only seeing it in faith ."

"And through your offspring all nations of the earth will be blessed, because you have obeyed My voice."

"dwelling in tents with Isaac and Jacob, the heirs with him of the same promise"

"As far as Abraham was concerned, Isaac was as good as dead and it was from the dead that he received him back, in a manner that prefigured the resurrection of Jesus."

"By faith Isaac blessed Jacob and Esau concerning things to come. "

"Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ."

"That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith."

"Know ye therefore that they which are of faith, the same are the children of Abraham."

"And this I say, [that] the covenant, that was confirmed before of God in Christ, the law, which was four hundred and thirty years after, cannot disannul, that it should make the promise of none effect."

"For if the inheritance [be] of the law, [it is] no more of promise: but God gave [it] to Abraham by promise."

"And as for Ishmael, I have heard thee: Behold, I have blessed him, and will make him fruitful, and will multiply him exceedingly; twelve princes shall he beget, and I will make him a great nation. But my covenant will I establish with Isaac, which Sarah shall bear unto thee at this set time in the next year"

"R. Eliyahu from Vilna notes that the implication here is that Ishmael was alive since Esau went to him to take a wife from his daughters."

"It teaches you that Ishmael had betrothed her, but he died and her brother Nebajoth gave her [in marriage] to Esau."

"Our father Abraham was at the time that he was circumcized 99 years old, as it is written "And Abraham was ninety years old and nine, when he was circumcized in the flesh of his foreskin" . And he died at the age of 175 years"

"Sarah died at age 127 years, Isaac died at age 180 years"

"Paul’s interpretation in Galatians, which we may call “genealogical allegory,” resembles that of Dorshei Rashumot on several counts and differs significantly from Alexandrian allegories."

"Γινώσκετε ἄρα ὅτι οἱ ἐκ πίστεως, οὗτοι ⸂υἱοί εἰσιν⸃ Ἀβραάμ."

"כִּ֣י לֹ֤א יִירַשׁ֙ בֶּן־הָאָמָ֣ה הַזֹּ֔את עִם־בְּנִ֖י עִם־יִצְחָֽק׃"

"He does so among the Galatians – who were of non-Jewish origin (as they were not descendants of Isaac “according to the flesh”)."

"Paul’s allegory has often been presented as the binary opposite of midrash."

"τῷ δὲ Ἀβραὰμ ἐρρέθησαν αἱ ἐπαγγελίαι καὶ τῷ σπέρματι αὐτοῦ· οὐ λέγει· Καὶ τοῖς σπέρμασιν, ὡς ἐπὶ πολλῶν, ἀλλ’ ὡς ἐφ’ ἑνός· Καὶ τῷ σπέρματί σου, ὅς ἐστιν Χριστός."

"כִּ֣י בְיִצְחָ֔ק יִקָּרֵ֥א לְךָ֖ זָֽרַע׃"

"This is in agreement with the main thrust of the Hagar allegory, that is with Paul’s argument that even the non-Jewish Christians become descendants of Isaac in a spiritual sense."

"Qumran literature, Paul, and the Tannaim travail to build sacred communities based on a reworking of scriptural constructs, such as “Israel” or the “seed of Abraham.”"

"διαθήκην προκεκυρωμένην ὑπὸ τοῦ ⸀θεοῦ ὁ μετὰ ⸂τετρακόσια καὶ τριάκοντα ἔτη⸃ γεγονὼς νόμος οὐκ ἀκυροῖ, εἰς τὸ καταργῆσαι τὴν ἐπαγγελίαν."

"וְגַ֥ם אֶת־בֶּן־הָאָמָ֖ה לְג֣וֹי אֲשִׂימֶ֑נּוּ כִּ֥י זַרְעֲךָ֖ הֽוּא׃"

"Hagar is identified as a mountain called Sinai that corresponds to the Jewish temple-state of Jerusalem."

"Paul interprets scripture with view to incorporate gentiles into a community by generating reading practices that allow them to see themselves as being addressed directly by Jewish scriptures and to understand how they must live in order to be included in eschatological redemption."

"εἰ γὰρ ἐκ νόμου ἡ κληρονομία, οὐκέτι ἐξ ἐπαγγελίας· τῷ δὲ Ἀβραὰμ δι’ ἐπαγγελίας κεχάρισται ὁ θεός."

"וַיֵּ֧רַע הַדָּבָ֛ר מְאֹ֖ד בְּעֵינֵ֣י אַבְרָהָ֑ם עַ֖ל אוֹדֹ֥ת בְּנֽוֹ׃"

"ἵνα εἰς τὰ ἔθνη ἡ εὐλογία τοῦ Ἀβραὰμ γένηται ἐν ⸂Χριστῷ Ἰησοῦ⸃"

"וַתֵּ֨רֶא שָׂרָ֜ה אֶֽת־בֶּן־הָגָ֧ר הַמִּצְרִ֛ית אֲשֶׁר־יָלְדָ֥ה לְאַבְרָהָ֖ם מְצַחֵֽק׃"

"Paul uses the Abrahamic matriarchal allegory to argue in favour of the gentiles’ status as children of the promise, heirs of Abraham, and born of the free woman."

"Paul uses Old Testament Scripture to support his own view."

"Paul insists that physical identity markers are contrary to the gospel of Christ (for gentiles) and are indistinguishable from the Galatians’ former cultic life."