God had intended from the beginning that God and man would commune together and that the Spirit of God would abide in us, guiding our thoughts by that same Spirit.  The intellect is to willingly yield to the Spirit so that it can know the truth by revelation. 

What happens when we are saved and what does that have to do with the intellect?

When we accept Jesus as our savior, our spirits are changed, but our minds and bodies remain to be changed.  We are to be transformed, literally transfigured, by renewing our minds.  We wait for the adoption, which is the redemption of our bodies, the manifestation of the sons of God. 

We can know things in our spirits without the intellect, but the understanding is not enlightened.  That's the reason that Paul, the apostle, gave for prophecy being better than the unknown tongue in the church service.  Prophecy enlightens the understanding.  Truth comes from God.  God's intent is that we also have an understanding of truth.  For this, we need the intellect.  The intellect, however, must be willing to take instruction from the Spirit of God.  That's why God gives us a new heart.

Our spirits had been dead to God until we were born again.  We were unable to communicate with the Holy One.  Being born again, our spirits are joined to God's Spirit, the Holy Spirit.  Only through Jesus Christ can you be born again.  Only those who have been born again can enter into further growth: being baptized in the Spirit, receiving the impartation of gifts of the Spirit through the laying on of hands, walking in the Spirit and producing the fruit of the Spirit.  These are all ways that God uses to make us spiritual.  Good works can only come from God.  When we direct our minds to the Holy Spirit, an inner work takes place.  To be fleshly minded is death, just as Paul the apostle said.  To direct our minds to the Spirit is life.  Failing to do so is death.  The human mind is deceptive and opposed to God.  By yielding to God, we gradually become less enslaved to the flesh, which is enslaved by the fall to Satan.  Our part is small but important.  We submit, that is yield to God.  It is only God who puts right thoughts into our hearts; He changes our hearts as we walk with Him and yield ourselves to Him.  It is His love, not our own, that flows out from us in compassion and mercy.  Without the Spirit, true good works would be impossible.  He does the work in and through us.  We cannot take any of the glory.  We become love slaves of God who is love, and we begin to show the family traits of our Father.