Can someone verify if this is true:
Ibn Al-Arabi said, “Lineage is an expression referring to the mixture of fluids between a male and a female from a religious legal point of view. However, if this union (between male and female) occurs through disobedience (fornication) then the resulting child is not considered part of a person’s true lineage. That is why a daughter born from zina is not mentioned in Allah’s saying, ‘Prohibited to you (for marriage) are: your mothers and daughters’ (Surah 4:23) because she is not considered a daughter according to the most authentic teaching of our religion.. If there is no legal lineage then there is no legal relationship; for zina does not prohibit (from marriage) the daughter of the mother (you committed zina with) nor the mother of a woman (you committed zina with). […]I (Qurtubi) said: The scholars have differed on the permissibility of a man marrying his daughter who was the result of an adulterous relationship; or for that matter marrying his sister or granddaughter who was the result of zina. Some prohibited this type of relationship; among them was Ibn Al Qasim, which is also the saying of Abu Hanifa and his companions. Others however allowed this type of marriage such as Abdul Malik Al Maj’shun, which is also the saying of Al-Shafi’i. This was detailed in the explanation of Surah 4 (Al Nisa’).
Tafsir Al Qurtubi 25:54
Al Maududi seemed to have mentioned this and showed his disproval:
The prohibition about daughter also applies to the daughter of the son and the daughter of the daughter. There is, however, a difference of opinion in regard to a girl born of an illicit relationship. Imam Abu Hanifah, Imam Malik and lmam Ahmad-bin-Hanbal (may Allah bless them all) are of the opinion that she too is unlawful like the lawful daughter, but Imam Shafi 'i does not consider an illegitimate daughter unlawful. But the very idea is repugnant that one should marry a girl about whom one has the knowledge that she is of one's own seed.
Tafsir Al Maududi 4:23
If this is true, why did Imam Al Shafi'i permit it. On what basis from the Qur'an and Sunnah? Or was it simply ijtihad?