6 ideas
Once one notices that Christian children grow up Christian and Jewish children grow up Jewish, belief taken on authority (taqlid) loses its hold, because its cause is plainly upbringing, not truth. Such belief cannot be mended afterward: a naive believer who knows he is naive is no longer naive, so the only way forward is to rebuild knowledge from what cannot be doubted.
Real knowledge is knowledge where no room for error remains, so firmly that if someone turned a stick into a snake to prove that ten is less than three, you would marvel at the trick but not doubt the arithmetic. Any belief that could be shaken by a strong enough challenge fails this test, and this sets the standard against which every other source of knowledge is then measured.
The senses are overruled by reason: the eye sees a shadow as still and a star as coin-sized, and reason corrects both. By the same pattern, reason might be overruled by a higher faculty, just as dream-certainties feel true until waking shows them false. The doubter has no position outside reason from which to rule out a wider waking that would expose his present certainties.
At the height of his Baghdad career, torn between worldly ambition and leaving for the spiritual path, al-Ghazali found his tongue would not move to teach. He then lost his appetite, and his physicians said the illness was in his heart, not his body. The breakdown resolved only when he gave up his post and wealth and left, showing that an unresolved decision can bring on bodily collapse.
His skepticism ended not by proof or ordered argument but by 'a light which God cast into the breast,' which restored trust in self-evident first principles. Doubt about the grounds of reasoning cannot be settled by more reasoning, since any proof would rest on the very grounds being questioned. The way out has to come from outside the chain of proof.
Knowing the definition, causes, and conditions of drunkenness is different from being drunk, and a physician who is ill can know health while lacking it. Sufi knowledge is of this experiential kind (dhawq, 'taste'): it is reached only by changing one's state through practice, not by study, so a scholar can master everything written about it and still be outside it.