My view on this is, that Jesus is commenting on a specific verse in the Law, that the jewish scholars had expanded beyond its due application. The exception is mentioned only in the Gospel of Matthew which is the Gospel to the hebrew people. Now in their law they had one exception stated, and Jesus clarified that the exception was only included ("by Moses") for the hardness of their hearts, and it only relates to fornication which is sex before marriage. Now, a case of this exception clause is actually described in the beginning of the Gospel of Matthew, when Joseph finds out that his espousee Mary (whom God calls his "wife") seems to have had illicit sexual relations before the marriage. And the comment is, that "Joseph being a just man", while he yet did contemplate to "put her away".
So my answer is, that the exception clause is only regarding if the woman is not a virgin, and it is only viable before the fulfilment of the espousal (the marriage). After that, they are one flesh with no exceptions. Besides, it is only granted to jewish people, there is not exception discussed in the other gospels.
I had briefly thought this was also talking exclusively about lying about one's virginity based on the fact that word "forncation" was used, too. For we see fornication is primarily used to refer to sex outside of marriage (Which is true). What changed my mind on this point was a discovery of an extended meaning on the word "fornication" and by thinking about this logically. First, how does this law of exception on lying about virginity apply in a world like today? How often would this case come up? Not very often. But lets not let looking at logic alone to make our case here (Which then leads me into my other two points). Two, the word "fornication" is used as in reference to unfaithfulness in a marriage covenant with Israel in Ezekiel 16:26. It is claried in verse 8, God says to Israel,
"...Behold, thy time was the time of love; and I spread my skirt over thee, and covered thy nakedness: yea, I sware unto thee, and entered into a covenant with thee, saith the Lord GOD, and thou becamest mine." (Ezekiel 16:8).
26 "Thou hast also committed fornication with the Egyptians thy neighbours, great of flesh; and hast increased thy whoredoms, to provoke me to anger.
27 Behold, therefore I have stretched out my hand over thee, and have diminished thine ordinary food, and delivered thee unto the will of them that hate thee, the daughters of the Philistines, which are ashamed of thy lewd way.
28 Thou hast played the harlot also with the Assyrians, because thou wast unsatiable; yea, thou hast played the harlot with them, and yet couldest not be satisfied.
29 Thou hast moreover multiplied thy fornication in the land of Canaan unto Chaldea; and yet thou wast not satisfied herewith."
(Ezekiel 16:26-29).
Three, in Hosea 2, Hosea had told Gomer's family that he was no longer his wife. No doubt Hosea divorced Gomer because of her sexual misconduct with many men when they were married. Important Note: Many believe God told Hosea to marry a prostitute to begin with. This is wrong and it is not what the beginning of Hosea 1 says. Hosea married a wife of whoredoms (idolatry). Meaning, Hosea married a wife of a people of idolatry and he did not marry a harlot to begin with. She later become a harlot or prostitute, but he divorced her and the later bought her out of the sex slave trade (back in those days) and he became her loving friend and servant.
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