What does the Catholic Church believe about faith and reason?

Pope John Paul II said, “Faith and reason are like two wings on which the human spirit rises to the contemplation of truth; and God has placed in the human heart a desire to know the truth – in a word, to know himself – so that, by knowing and loving God, men and women may also come to the fullness of truth about themselves.”

What exactly is the Catholic perspective on the relationship of faith and reason? Is one greater than the other? Does one come before the other? And how does this apply to atheists?

Your quote comes from FIDES ET RATIO. Have you read it?

[quote=CCC]159 Faith and science: "Though faith is above reason, there can never be any real discrepancy between faith and reason. Since the same God who reveals mysteries and infuses faith has bestowed the light of reason on the human mind, God cannot deny himself, nor can truth ever contradict truth."37 "Consequently, methodical research in all branches of knowledge, provided it is carried out in a truly scientific manner and does not override moral laws, can never conflict with the faith, because the things of the world and the things of faith derive from the same God. The humble and persevering investigator of the secrets of nature is being led, as it were, by the hand of God in spite of himself, for it is God, the conserver of all things, who made them what they are."38
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I don’t know how this relates to atheists. Do any of them care what the Church teaches?

It may mean that atheists, through God’s mercy and grace, may come to believe by way of reason.

With God, all things are possible.

Excellent questions.

According to St. Augustine “faith precedes reason” in that faith seeks understanding.

HOWEVER, according to St. Thomas Aquinas, “natural reason precedes faith for faith presupposes natural knowledge, even as grace presupposes nature**.”**

A human being is a rational animal - an animal with an intellect and will, the soul.
It is into this soul that Faith is infused by Grace, as a gift (along with Hope and Charity).

A human is first reasoning, which is natural to his created being. When granted the Holy Spirit, Faith is now present in the soul, believing in the Mysteries of the Gospel, that they are true and good (and beautiful).

And being rational, the reason kicks in to think about and understand the Mysteries. It does not try to figure out IF they are True and Good. It instead tries to reason out all the implications of them, because it knows (believes) they are True. Reason works to try and know this new-found Love - the Lord.

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