What is the significance of other sources of Islamic legislation besides the Qur’an and the Prophetic Sunnah, and how can those who deny them be convinced of this?

The agreed-upon sources of Islamic legislation are the Qur'an, the Sunnah, scholarly consensus (Ijma'), and analogical reasoning (Qiyas) (with the exception of the Zahiris). As for the disputed sources, they are many, and understanding their proofs requires learning the principles of Islamic jurisprudence (Usul al-Fiqh). Among the proofs for the authoritative nature of Ijma' is the Almighty's saying: "And whoever opposes the Messenger after guidance has become clear to him and follows other than the way of the believers – We will turn him to what he has turned to and admit him to Hell, and what an evil destination!" (Quran 4:115). The proof for the authoritative nature of Ijtihad (independent juristic reasoning) is the hadith: "If a judge makes Ijtihad and is correct, he will have two rewards; and if he makes Ijtihad and is mistaken, he will have one reward." As for Istihsan (juristic preference), it is the deviation of the ruling of an issue from its analogues due to a specific evidence from the Qur'an and Sunnah, which aligns with the Almighty's saying: "O you who have believed, obey Allah and obey the Messenger" (Quran 4:59). As for the Istihsan that Al-Shafi'i rejected, it is that which is not based on a legal proof.