Assalamualaikum, I have apprehension in judging the veracity of hadith, (e.g the probability calculator) after reading verse 4:65: "But no, by your Lord, they can have no faith, until they make you judge in all disputes between them, and find in themselves no resistance against your decisions, and accept (them) with full submission" because what if a hadith was accurate although poorly transmitted and I chose not to follow it because in my limited understanding the alternative seemed better?
Alaikumassalam wa rahmatullah,
The problem is that it can be a matter of life and death. For example, by relying on low-quality hadiths, scholars ignored the text of the Quran and concluded that stoning adulterers was the punishment recommended by the Prophet , as I discuss here. We also have contradictory hadiths, such as an “authentic” one that says only bad people listen to music, and another “authentic” one where we see the Prophet listening to music and approving of it. We need a way to judge which of these authentic ones is superior. As it happens, the one approving of music is five times more authentic, as I discuss here.
So our goal in having high standards for which hadiths we accept is that we want to follow the real Prophet and to avoid following teachings falsely attributed to him, including many teachings that make him look like a bad or cruel person (as in the stoning of adulterers). A person who truly loves the Prophet will hate to see anything immoral or illogical attributed to him.
In general we have two kinds of scholars, hadith scholars who love to increase the number of authentic hadiths as much as they can (as al-Albani, may God have mercy on him) without too much concern for how these hadiths would affect our understanding and practice of Islam. Then we have fiqh scholars, scholars of Islamic law or jurisprudence, who have the difficult task of making sense of all the contradictory hadiths and finding how they will affect our understanding and practice of Islam. Scholars of fiqh have much higher standards for the hadiths they accept and in their books of legal theory (usul al-fiqh) they have very lengthy discussions on probability theory; the number of chains a hadith needs for a hadith to be considered authentic beyond doubt. Some scholars require four authentic chains (something that’s extremely rare), others say there is no set number of necessary chains, we just have to use our own hunches until our heart is content that a hadith is truly authentic.
So the issue is rather complicated, and personally I have a fiqhi approach to hadith. I see all hadiths as probabilities, not certainties, and I use probability theory to find out which ones are the most authentic.
Also note that great scholars like Imam Malik were happy to reject authentic hadiths when they had additional evidence from non-hadith sources (the opinion of the scholars of Medina, which they had inherited from the Companions without hadiths). Imam al-Shafi`i preferred an authentic hadith on how the athan should be said, which Imam Malik considered ridiculous since the athan had been said differently in Medina since the time of the Prophet . Imam al-Bukhari himself rejected perfectly authentic hadiths when he considered their contents to be ridiculous, as in a hadith that claimed something would happen within 200 years that never happened. See Dr. Jonathan Brown’s study (PDF): How We Know Early Ḥadīth Critics Did Matn Criticism and Why It’s So Hard to Find.