Question

Hello Rabbi,
I wanted to ask what you think is the place of simple faith, and what is the place of investigation, in the service of God. Should we conduct ourselves only through intellectual inquiry, or is there also room for ungrounded faith? Is it even possible to conduct oneself only through intellectual inquiry? After all, we’ve seen that no matter how much we want otherwise, the analytic is empty. That is, even if we are rational people, we need axioms to which we can apply the principles of logic—and it would seem that this is where simple, ungrounded faith comes in, no? (As I understand it, the definition of axioms is that they are ungrounded.)
In addition, in your opinion, I’d be glad if the Rabbi could explain what the sages through the generations seem to have thought. I understand that this is a dispute among the medieval authorities (Rishonim), but I haven’t managed to get down to its finer points. Are there medieval authorities who are at opposite ends? That is, who really think that one can proceed only through intellectual inquiry, or only through simple faith without inquiry? Or are they all speaking along some spectrum? Of course, there’s no need right now for a full survey of the views of the medieval authorities, but perhaps two or three key positions in the topic, if that’s not too much.
Thank you very much!