Let's understand what logic means: The study of the principles of correct reasoning. It is thinking that aims at a conclusion. It can be subject to errors and these errors can be studied to great advantage when someone is trying to foist something over on us like proving that which cannot be proved.
Today's aggressive atheists like to point out that God cannot be found through science and conventional logic, or by looking for God in the deep recesses of the universe. As believers, that doesn't bother us because we know they're right. God can't be found using those tools.
Belief that does not rest on logical proof or material existence.
God can only be known through God's own revelation of himself. The proof of God's existence is in the realm of faith, not in the realm of science. Belief in God is a matter if faith, not in the realm of science. It's a faith issue. God reveals himself to us.
It is even more common to speak of faith in God as if this were a specially compelling reason for belief and moreover, one beyond logical criticism. Faith however, is merely determination to believe and no kind of reason. (Vol 6, P 107).
Our God has also been taken away from us. For us, however, that removal of God did not occur in a single moment of violent defeat. It rather happened over a period of centuries as the steady and relentless advances in knowledge altered forever our ability to believe in the God content that stood at the heart of our sacred tradition. "Why Christianity must Change or Die", P. 29 (1998)
We cannot park our brains at the door of our places of worship in order to accept as real the words that were used to interpret God in years past but that can no longer today illumine our understanding of God. (P 18.)...we already know that we can only know God by his spiritual revelation of himself, not by studying science.
Spiritual means not tangible or material.
***That won't come through science, it will only come through the Holy Spirit.
Argument about the existence of God is rare (in 1966) for religious beliefs are effectively supported in our society by means that are not principally rational. (Vol 6, P107).