Faith is knowing that is not confirmed or "proven" by what is seen outside oneself (externally); in other words, faith is a knowing that is not confirmed by what you observe with the senses, for once you receive an external confirmation, then it is no longer faith. Faith is a knowing that is rooted internally; it comes when the interior self hears in silence or sees in darkness (meaning, without the senses) - this interior hearing is the voice of God, His Word, and the interior seeing is His Light...it is when the Spirit reveals within you a truth that was otherwise not known by logical reasoning or was not previously confirmed by the physical senses.
So then faith comes by hearing, and hearing, by the word of God (Romans 10.17). This speaks of the interior nature of hearing the voice of God - of hearing and knowing his word or his will. It is in the heart (the inner room), "for with the heart one believes unto righteousness."
So, faith is not believing with the intellect; for with this type of belief, there is always opportunity for doubt. However, faith is KNOWING that is not rooted in reasoning or the physical senses. It is true knowing - spiritual and interior.