It is “mantiq” - arguments are not true or false - they are strong or weak and are constructed to be “valid”.
I meant that philosophical methods can be used help finding our way in discussions. I did not claim proof as you have stated above. Logic is important for telling us when something is really a contradiction. It also allows us to analyse each others arguments to see if they are constructed validly or if we are drawing the correct conclusion from a given set of premises … it puts rules forth for a fruitful discussion to take place. The logic tools can also show - especially from inductive reasoning - what is more likely to be the case. So initially we are concerned with what is or is not possible - and secondly what is more or less likely within the things that are possible.
We both see certain tensions in matters within our faith - for example let’s say the Qur’an does not specifically say that Jesus (AS) is alive, whereas it does say that all beings will die. The hadith however say he (AS) was taken and shall descend literally. The Qur’an says he has Ascended - and the meaning taken by different people for this term are either spiritually ascended or literally. For the person who believes in the literal ascension he has to explain the point about all being will die … the person who believes in the metaphorical understanding only will in most cases claim that the hadith is wrong.
This does not boil down to the interpretation of scholars - rather it is directly associated with accepting or rejecting one aspect of scripture.