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Hagar does not become Jerusalem below, but merely represents Jerusalem in Paul's analogy (Gal. 4:22-26) where Ishmael and Isaac are used to represent a work of the flesh (Ishmael from Hagar) vs. the promise (Isaac from Rachel)
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Paul clearly tells us when he is using symbols to communicate typology, "which things are symbolic" (Gal. 4:24)
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In any case, in Revelation 17 the symbol is the Harlot, not Babylon. It is what the Harlot represents which is tied to Babylon, not Jerusalem
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Pauls is making an application of the concept of those who were not close to God (e.g., Israel in apostasy) later coming close to God (e.g., Israel in her restoration) to the idea that, through Israel's stumble at the first coming, a similar thing has happened to the Gentiles.
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In the similar way in which Israel today is not in fellowship, but will be in the future, so too the Gentiles were not in fellowship in the past, but are now through Christ.
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Paul's use of Hosea's prophecy does not alter the original meaning: Hosea's passage was entirely about Israel being forsaken and restored. Hosea's meaning continues, just as it was given.
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Nothing is "reversed", Paul is taking a passage with a fixed meaning and using it in an application, much like a modern preacher.