I don't know how far back in time this is referencing. But, it may defend on the time and circumstance, for example, if during an early settlement period and depending on the cultural background, a marriage was often a verbal agreement. The marriage may exist in a simple Bible recording. I frequently butt my head up against a society wanting "proof" of a legal marriage when no proof exists except that a man and a woman took up living together as a married couple. Common law marriage.
If a man has a wife and other baby mothers, then the facts are pretty obvious, the babies born outside of wedlock are illegitimate issue. If it's a case of bigamy, I believe the law generally recognizes the first marriage as legitimate and the others illegitimate.
I would just take it case by case recognizing the time and circumstance.