Question

I found a contradiction in my outlook.
 
On the one hand, it’s clear to me that a faith based on emotion in God or in the Torah is not enough, and a person has to challenge himself, ask questions, and examine with his intellect what the truth is.
 
 
On the other hand, there are parts of my life for which I have no intellectual proof at all, and I simply believe in them.
 
1. My intellect itself—the trust I place in my intellect, that it works well most of the time—is faith without any intellectual proof.
 
2. That there is valid objective morality. That there are things one ought to do and things one ought not do. My sense of obligation to this command is my faith in that command; I have no ability to prove it. It is a strong feeling.
 
3.
Free will—I simply feel that I choose; I have no proof that I choose.
 
 
So I’m trying to understand the place of feeling and of the concept of faith. I assume this is connected to understanding the concept of intuition.
 
Can you point me in the right direction?
Thank you.