Is it permissible for a man to attribute a child born as a result of his adultery with an unmarried woman to himself?

The scholars have agreed that the fundamental principle for establishing lineage is the marital bed (existing marriage). They differed, however, on whether a child born of adultery can be attributed to the adulterer, holding two opinions:

The first: The child born of adultery is not attributed to the adulterer, even if he claims him. This is the opinion of the majority of scholars, who cite the hadith (definition): "The child is for the bed, and for the adulterer is the stone."

The second: The adulterer's child can be attributed to him if he claims him. This is the opinion of some of the early generations (Salaf) and was chosen by Ibn Taymiyyah and Ibn al-Qayyim. They argue that the child is generated from his fluid, and that the aforementioned hadith is specific to cases where a marital bed exists, and that the Lawgiver desires the preservation of lineages.

Both opinions are considered valid, and the matter is open to scholarly interpretation (ijtihad (definition)). Each case is examined to achieve the benefit of preserving the child.