Yevamot 4 - Looking for a permission to marry one's daughter

The logic about not marrying one's daughter could be completely reversed. Here is what a man trying to find the permission to do so could argue.

He will marry his daughter off to his brother (the Torah law allows marriage with the niece.) Then, when his brother dies, he gets to marry his daughter as his brother's wife or a "yevamah." True, there is a prohibition against marrying one's daughter, but it is overwritten by a positive commandment to marry a yevamah.

His source? Two verses: "You should not wear wool and linen together" and next to it, "You shall fringes on your garment." For your fringes (tzitzit), you can use wool and linen together. In fact, that is what they did in the Temple, making the priests' belts. This teaches us that "do" overwrites "don't do." 

He seems to have built his case? We answer that "do" overwrite "don't do" only for relatively light prohibitions, such as wearing wool and linen together. Marrying one's daughter - or any other similar ban - is more strict. So even the mitzvah of yibum does not help him turn the forbidden into permitted.

Art: Henri Rouart and his Daughter Helene by Edgar Degas

Yevamot 3 - Sleeping with one's daughter

Most people would agree that a man should not sleep with his daughter. However, this is not mentioned in the Torah directly. Instead, this prohibition is derived by connecting with another ban in two steps.

We are not talking about his legitimate daughter because she is "his wife's daughter," and it is indeed prohibited. Instead, we are talking about his out-of-the-wedlock daughter from his lover who is not his wife. Why can't he sleep with her? 

First, one should not marry a woman and her daughter because they are close relatives,  and it is a shame. Second, one should not sleep with his son or daughter's daughter because it is a shame. Since these two phrases include a similar word, "shame" or "heinnah" in Hebrew, we can combine the prohibitions and derive that sleeping with one's daughter, even born out of wedlock, is incest.

The teacher (Tanna) who taught this law loved involved logic. Since this law is a perfect example, the teacher has put one's daughter as the first in the list of the fifteen women who are automatically released from yibum or chalitzah.

Father and Daughter by Charles H. Moreau