One short sentence, and it is the hinge of the whole allegory. Paul has spent vv. 21-27 building two lines out of Abraham’s household — the slave woman’s son born κατὰ σάρκα, the free woman’s son born διʼ ἐπαγγελίας — and then capped it with Isaiah 54:1 on the barren woman with many children. Now he turns from the figure to the people in front of him: ὑμεῖς δέ — you, for your part.

Three decisions carry the verse.

1. The fronted pronoun. Greek does not need ὑμεῖς with a 2nd-plural verb. Its presence is contrastive: over against Hagar’s slave-children who are still in bondage (v. 25), you stand on the other side of the ledger.
2. κατὰ Ἰσαάκ. Not ‘like Isaac’ in the sense of loose resemblance, and not ‘descended from Isaac.’ κατά + accusative names a measuring standard (the same construction Paul has just used twice for κατὰ σάρκα, vv. 23, 29). Isaac is the pattern by which the Galatians’ status is scored.
3. ἐπαγγελίας τέκνα. Both words are marked: the genitive is anarthrous and stands before its noun, which throws the weight on ‘promise,’ and τέκνα rather than υἱοί keeps the birth-language of ὠδίνω (v. 19) and γεννάω (vv. 23, 29) audible.

The theological point is the indicative mood. Paul does not urge the Galatians to become promise-children. He tells them they already are — which is exactly why turning back to the στοιχεῖα (v. 9) or to circumcision is a return to a line they have left.

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The nominative pronoun is redundant morphologically — ἐστέ already encodes second plural — so its presence is marked. Greek uses an expressed nominative for contrast or topicalization, and here both are in play: it topicalizes the addressees and sets them over against the ἐκ τῆς παιδίσκης line just described.

The same construction recurs six verses earlier and later in the letter’s rhythm: cf. ὑμεῖς δέ at Gal 5:13, and the parallel ἡμεῖς δέ constructions. Compare also the corpus policy already fixed for ἐγώ expressed with a finite verb (Phil 4:11) — the pronoun is rendered visibly rather than absorbed.

δέ is mildly contrastive rather than strongly adversative; Paul is not correcting a misapprehension but drawing the inference from the citation. English ‘but you’ or ‘now you, for your part’ both work; the wooden tier keeps ‘but.’

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Vocative masculine plural, Paul’s standard direct address in Galatians at the points of highest pressure (1:11; 3:15; 4:12, 31; 5:11, 13; 6:1, 18). Its placement here, in the middle of a hard argument about who belongs to which mother, is pastoral: the people he is about to reclassify are family.

Per the standing glossary decision and §3, the masculine plural is rendered ‘brothers’ as it stands. The Galatian assemblies were certainly mixed-sex, and the grammatical form is the ordinary Greek default for a mixed group — that is data about the language, not about the composition of the room. The referent is noted; the rendering is not neutralized.

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κατά + accusative with a personal name. Three construals have been defended:

• Norm / pattern: ‘after the manner of Isaac,’ i.e. Isaac is the standard by which their sonship is measured. This matches Paul’s own use of κατά + acc. three times in the immediate context (κατὰ σάρκα, vv. 23, 29; κατὰ πνεῦμα, v. 29), where the preposition unambiguously names the mode or standard of begetting.
• Correspondence / typology: ‘corresponding to Isaac,’ making Isaac the τύπος and the Galatians the antitype. This is a shading of the first rather than a separate reading.
• Descent: ‘descended from Isaac.’ This is excluded — descent in this chapter is consistently marked by ἐκ + genitive (ἐκ τῆς παιδίσκης, ἐκ τῆς ἐλευθέρας, vv. 22-23, 30-31), and Paul had that construction ready to hand.

So: the same preposition that measured the slave-son by the flesh now measures the Galatians by Isaac. ‘In line with Isaac’ carries the standard-sense without either flattening to a vague ‘like’ or overreaching to genealogy.

Ἰσαάκ is indeclinable in the LXX and NT (transliterating יִצְחָק); the accusative is supplied by the preposition, not by morphology. This is his only appearance by name in Galatians — vv. 22-23 speak only of ‘one son’ and ‘the other’ — which makes the naming here deliberate.

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ἐπαγγελία is the load-bearing noun of Galatians 3-4 (3:14, 16, 17, 18, 21, 22, 29; 4:23, 28). In classical Greek it is an announcement or an offer; in Paul it is fixed on the specific divine pledge to Abraham, and it functions as the antonym of νόμος as a mode of inheritance (3:18). Rendered ‘promise’ throughout for concordance.

Two grammatical features are marked:

• Anarthrous. No article on ἐπαγγελίας. The genitive is qualitative — children characterized by promise, belonging to the promise-category — not ‘the children of the promise’ as a definite designation. English can render it ‘children of promise,’ which preserves the qualitative force.
• Fronted. The genitive precedes its head noun, the reverse of Greek’s usual order. Fronting a dependent genitive is emphatic (compare τῆς ὑμῶν δεήσεως, Phil 1:19, already noted in the glossary). The stress falls on promise: whatever else the Galatians are, this is the register they belong to.

τέκνα, not υἱοί. Paul had just used υἱοί of the same people (4:6-7) and will use υἱός of both Abrahamic sons (4:30). The switch to τέκνα here and at v. 31 keeps the maternal, birth-giving frame of the allegory in view — the two mothers, the Isaiah 54:1 barren woman, Paul’s own ὠδίνω at 4:19. Per the standing glossary entry, τέκνον is relational and affectionate rather than juridical, and ‘child’ is retained so that the inheritance-language of υἱός is not silently imported.

The genitive itself is best classified as a genitive of source or of quality — the two are hard to separate here, and both LXX and Pauline usage of this construction (τέκνα ὀργῆς, Eph 2:3; τέκνα φωτός, Eph 5:8) blend origin with character. No need to resolve it.

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NA28 reads ὑμεῖς δέ … ἐστέ (second person), with strong and early support: 𝔓⁴⁶, B, D*, F, G, 33, and the Latin and Syriac tradition.

A well-attested variant reads ἡμεῖς δέ … ἐσμέν (first person plural, ‘we are’): ℵ, A, C, D², K, L, P, Ψ, 062, 81, 104, 326, 1241, and the bulk of the Byzantine minuscules, with some Coptic support.

Nothing doctrinal turns on it — Paul includes himself among the promise-children at v. 31 either way. But the second person sharpens the rhetoric: he is telling them what they already are, immediately before quoting ‘cast out the slave woman’ at them.

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John Chrysostom (Homilies on Galatians, on 4:28) presses precisely the κατά: the Galatians’ relation to Isaac is not of blood but of the manner of birth. Isaac was born against nature, by promise, from a barren womb; so, he argues, are they — born not by ordinary generation but by the word of God. He draws out that this makes the argument a fortiori against the Judaizers: those insisting on physical descent are standing in Ishmael’s line, not Isaac’s.

Jerome (Commentary on Galatians, bk. 2) reads κατὰ Ἰσαάκ as secundum Isaac, taking Isaac as the figura whose pattern the Gentile believers fill out, and connects it directly to the Isaiah citation just quoted — the desolate woman’s children are the promise-children.

Augustine (Expositio ad Galatas) makes the same move and adds the pastoral edge Paul himself supplies at v. 29: if you are in Isaac’s line, expect Ishmael’s treatment.

What is worth noting is that none of the Greek or Latin commentators takes κατὰ Ἰσαάκ genealogically. The pattern-reading is the unanimous ancient construal, and it lines up with the preposition’s use three times in the surrounding verses.

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The verse is the application of the allegory, and the mood matters. ἐστέ is present indicative — a state of affairs, not a target. This is the same logic as 4:6-7 (‘because you are sons, God sent the Spirit… so you are no longer a slave but a son’) and it governs how the imperatives of chs. 5-6 work: obligation follows from status already conferred, not the reverse.

It also completes the argument begun at 3:29 (‘if you are Christ’s, then you are Abraham’s seed, heirs according to promise’). Between 3:29 and 4:28 Paul has run the seed-language through the slave/free allegory, and the conclusion is identical: promise, not law, not flesh, is what constitutes the line.

One restraint is worth naming. Paul does not say the Galatians replace Isaac’s descendants; he says they are measured by Isaac. The κατά keeps the relation typological rather than substitutionary, and the argument’s target throughout is a way of reckoning inheritance, not an ethnic people (§5). The following verse (v. 29) does introduce persecution language, but the two lines there are defined by mode of begetting — σάρξ against πνεῦμα — not by ethnicity.

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