Karl Barth and Thomas Aquinas were two theologians with two different emphases. Aquinas focused on logic and apologetics as a way to know God. Barth, an existentialist, rejected logic and focused on the spiritual. He saw God as unknowably transcendent. Aquinas was Aristotelian, Barth was Platonic.
When taken in isolation, neither of these views are correct. 1 Corinthians 1:18 says “the message of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God.” You cannot look at the gospel from a purely logical standpoint. “For it is written: ‘I will destroy the wisdom of the wise; the intelligence of the intelligent I will frustrate’ [Isaiah 29:14]. Where is the wise man? Where is the scholar? Has not God made foolish the wisdom of the world?” (v. 19-20).
Still we are commanded to worship God with all of our minds (Matthew 22:37). Throughout his ministry, the apostle Paul reasoned with the Jews and the Greeks (e.g. Acts 17:17). When in Athens he even used the culture, the altar to the unknown God and the poet, to preach the gospel (v. 22-31).
There is a place for reason and logic in a relationship with God. But you will miss God completely if you never look at the spiritual. After all, “God is spirit, and his worshipers must worship in spirit and in truth” (John 4:24). It is the Holy Spirit that guides us into all truth (John 16:13). God uses the Spirit to draw us near to himself. There is nothing physical or this-worldly about it. We must look at the things of God through spiritual eyes, just like you can’t see the wind, but only hear its sound (John 3:8).
But again, if you only look at the unseen (if that can be said), then you will miss what is logical. God then becomes so transcendent that he is unknowable, untouchable and unreachable. But this is not so. The Lord Jesus Christ came so that we can be one with him and one with God. And even before Christ, men of faith like Abraham communed with God and he was called God’s friend (James 2:23). Surely God is not so transcendent as to be unknowable by men. God appeals to our hearing, if only the hearing of our hearts. He appeals to our minds and our logic. He can be found, because we are told to seek and we shall find (Matthew 7:7). Therefore, there must be a balance between our logical and spiritual seekings after God.
All my life I have tended to lean more towards the logical explanation of things, and my writing shows it. Thomas Aquinas spent years of his life working and writing. His great work was his Summa Theologica. Yet it was left unfinished. His reply to the urgings to complete his magnum opus is profound: “I can do no more; such things have been revealed to me that all I have written seems as straw, and I now await the end of my life.” He had finally met the transcendent, and logic no longer mattered.