Kiddushin, Chapter Four, Mishnah Eight
In this mishnah we learn that parents are not believed if they say that their child is a mamzer.
1) If a man declares, this son of mine is a mamzer, he is not believed.
2) And even if both [the husband and wife] say about the fetus inside her, its a mamzer they are not believed.
3) Rabbi Judah says: they are believed.
Section one: There are two explanations given for why a father is not believed to say that his child is a mamzer. The first is that the father is related to the child and relatives may not testify. The second is that by saying that the child is a mamzer, the father is testifying against himself and halakhah does not allow self-incrimination.
Section two: Even if both parents say that their child is a mamzer, which means that they are saying that the child is not from the husband but from an adulterous affair, they are not believed.
Section three: Rabbi Judah disagrees with both of the previous clauses. In the Talmud Rabbi Judahs ruling is based on a midrash. That is to say his halakhah is not necessarily logical; rather it is based on his interpretation of Scripture.