After the crusades, Christianity took a turn for the better. During the 12 century, because of a renewed emphasis on education, there arose several prominent thinkers who argued that reason can be used to answer questions of the Christian faith. No Christian thinker was more influential during this time period than Thomas Aquinas.
What Augustine was to the early church, Aquinas was to the Medieval church. He believed that reason plays a huge part in faith--especially when arguing for the existence of God. Below is a passage taken from R.C. Sproul's book, The Consequences of Ideas.
PROOFS OF GOD'S EXISTENCE
The first proof Thomas offers is the proof from motion. He begins with the evidence for motion in the world. Borrowing heavily from Aristotle, Thomas argues that whatever is moved is moved by another (based on what we call the law of inertia)...Whatever is moved must be moved by some prior actuality. But this change cannot regress to infinity, because in that case the motion could never begin. Therefore, Thomas concludes, there must be a first mover, and everyone understands this to be God.
Thomas's second proof is the proof from efficient cause. The law of causality asserts that every effect must have an antecedent cause. This is not the same thing as saying that every thing must have a cause...If every thing must have a cause, then God himself would require a cause. The law of causality refers only to effects and is an extension of the law of noncontradiction. The law is formally true, because it is true by definition. An effect is defined as that which is produced by a cause. A effect cannot be an effect unless it has a cause. Likewise, a cause (properly speaking) is by definition that which produces an effect...An uncaused (self-existent) being violates no rule of reason; an uncaused effect, however, is irrational and absurd.
Thomas Aquinas's third proof of God's existence is the proof from necessary being. Although this is usually thought of as part of the cosmological argument, it is more properly called 'ontological,' because it is an argument from being...If anything exists now, then something must have the power of being within itself, that is, something must have necessary being. This being, whose being is both logically and ontologically necessary, is God.
Thomas's fourth proof is the proof from degrees of perfection, in which he borrows heavily from Augustine. This is an argument from the comparative. We are aware of degrees of the good, the true, and the noble. But something can be deemed good or true only against some maximum norm or standard...There must also be some thing which is to all beings the cause of their being, goodness, and every other perfection, and this we call God.
Thomas's fifth and final proof of God's existence proceeds from the evidence of order in the universe. This is a form of the so-called teleological argument. The term teleological comes from the Greek telos, which means 'end, purpose, or goal.'
In nature we observe things that lack intelligence but function in an orderly and purposive way. They act in predictable ways to achieve certain ends or functions...One cannot have purpose accidentally, nor can one have unintentional intentionality. In its simplest form the teleological argument rests on the evidence of design in the universe...Design demands a designer.
Sproul, R.C. The Consequences of Ideas. Wheaton: Crossway Books. 2000. 70-74.