Moreover the Mosaic law pertaining to divorce applies only to valid marriages and not to mere cohabitants. Deuteronomy links the bill of divorce to proper marriages and I can not find any evidence to link a bill of divorce to unmarried couples… . One simply could not divorce someone who is not one’s spouse. A certificate of divorce is not needed if an unmarried couple is just breaking up.
On this point, I fully agree with you. There’s no such thing as a divorce unless there has first been a marriage. The passage in Deuteronomy that has been quoted on this thread lays down rules about the correct procedure to be followed in the case of divorce, but that’s all. There is no suggestion that divorce is wrong in itself or ought to be avoided. As far as I’m aware, that basic stance remains unchanged throughout the OT, though I’m not claiming to have made a study of the subject and I’m open to correction, as always.
In the NT, we find a change. In the two passages from Matthew that @rcwitness is examining on this thread, Jesus is explicitly enacting an amendment to the Law of Moses: “It has been said … but I am telling you …” in the first passage, with its echo in the later passage, “Moses allowed you … but I say …”
Jesus is proclaiming the indissolubility of marriage, though allowing an exemption from his new law in the case of
porneia. What exactly he means by this term is the question we are focussing on here, under the label “Matthew’s exception clause”. The point I wished to make about the translation issues is that it cannot be conclusively proved that Jesus can only be referring to legally married couples, since the Greek words translated as “wife” and “divorce” do not have such a narrow range of meanings in the original Greek as they do in English. He
may be referring to legally married couples, in which case he is exempting cases of
porneia meaning adultery, or he
may be referring to couples whose marriage is invalid for whatever reason, such as incest, in which case the English word “divorce” would be inappropriate, as you point out. “Separation” would perhaps be a better word to use in this case.