Though the linked article stated that one only needs to believe that induction has a non-super-exponentially small chance of working and that a single large ordinal is well-ordered, but it did really justify this. It spoke nothing about why belief in one’s percepts and reasoning skills is needed.
You seemed to think that not taking some assumptions could lead to better beliefs, and it wasn’t clear to me how strong your “could” was.
You seem to accept induction, so I’ll refer you to http://lesswrong.com/lw/gyf/you_only_need_faith_in_two_things/
Though the linked article stated that one only needs to believe that induction has a non-super-exponentially small chance of working and that a single large ordinal is well-ordered, but it did really justify this. It spoke nothing about why belief in one’s percepts and reasoning skills is needed.