Divorce and remarriage

My answer to a question on Facebook:

A valid divorce means the spouse is no longer married. They are single again. So valid divorce implies the legitimacy of remarriage. The only obstacle to remarriage is if one is already married. That would be adulterous. If, however, one is no longer married in the eyes of God, then there's no impediment to remarriage. It's a fresh start, like getting married the first time since divorce resets your marital status to single.

By valid divorce, I mean cases where there are biblical grounds for divorce (e.g. desertion, infidelity). The effect of a valid divorce is to cause the divorcé/divorcée to revert to their premarital status. They revert to the condition they were in before they got married in the first place.

This is partly an issue of theological method. Do we expect the Bible to spell out all the implications. Do we just act on what the Bible says, and if it doesn't say certain things, we don't act on that? Jesus makes some pithy statements about divorce. There's a lot he leaves unstated. Are we supposed to stop with what he explicitly teaches, or consider the logical implications? Do we expect a trail of bread crumbs? Jesus frequently criticizes the religious leaders for failing to consider the rationale for certain biblical laws. By robotically obeying the law, they sometime subvert the original purpose of the law. So we do need to think about the logical implications of Biblical ethics. Likewise, the commands and prohibitions of Scripture usually deal with typical situations, not extreme or exceptional situations. They don't address every conceivable circumstance.