Commentaries:
Jamieson, Fausset, and Brown
Then Joseph her husband—Compare Matthew 1:20, "Mary, thy wife." Betrothal was, in Jewish law, valid marriage. In giving Mary up, therefore, Joseph had to take legal steps to effect the separation.
being a just man, and not willing to make her a public example—to expose her (see Deuteronomy 22:23-24)
was minded to put her away privily—that is, privately by giving her the required writing of divorcement (Deuteronomy 24:1), in presence of only two or three witnesses, and without cause assigned, instead of having her before a magistrate. That some communication had passed between him and his betrothed, directly or indirectly, on the subject, after she returned from her three months' visit to Elizabeth, can hardly be doubted. Nor does the purpose to divorce her necessarily imply disbelief, on Joseph's part, of the explanation given him. Even supposing him to have yielded to it some reverential assent—and the Evangelist seems to convey as much, by ascribing the proposal to screen her to the justice of his character—he might think it altogether unsuitable and incongruous in such circumstances to follow out the marriage.
Other Jamieson, Fausset, and Brown entries containing Matthew 1:19:
Joel 1:8
Matthew 1:18
Luke 1:56
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