Rebekka;
And my husband and I are people who came to faith through our intellects, through rationalization.
This opens you up to faith, but unless God revealed himself to you, through whatever ways and means, you may have belief, but not faith.
God's revelation can come to us in many ways, but it is his gift and unless we have that experience of God in our lives, we may have belief, through rationalization, but have yet to have faith.
Faith is what draws us forward in our relationship with God. We are moved toward the spiritual union with him, which St John of the Cross calls the spiritual marriage.
Without faith, you may be merely practicing religion and for many who are in this situation, religion eventually fails them and the quit. Happens to many Catholics who are baptised as infants and raised in the Church, but have no experience of Jesus in their lives.
Probability theory was a great influence on me when I left agnosticism for belief. Faith is a gift from God, but I was given it through intellect, and the intellectualist approach that my husband had towards his faith - unlike my charismatic catholic friends, who tried their best for years to bring me to the church.
As I said earlier, intellect and faith are not separate in that we need intellect to open ourselves to faith.
However, faith itself comes from God alone.
Choosing to believe in God is not faith, just belief and even the demons believe in God.
Its why some of the holiest of Saints were those who had the simplest intellects.
Their faith wasn't the result of their own rationalization, but the revelation of God himself to them.
Jim