[Zeeshan]

From this website we have Anselm & Aquinas proofs.

St. Anselm’s Ontological Argument

St. Anselm, the Catholic archbishop of Canterbury and a Doctor of the Church, first formulated the Ontological Argument. This philosophical argument is perhaps the strangest and most hotly debated of the proofs. The argument has attracted the attentions of such notable philosophers as Immanuel Kant (who attacked St. Anselm’s proof) and G.W.F Hegel (who defended Anselm’s proof).

The proof is most notable because it alone claims to prove the existence of God by relying independently on human reason without the need for perception or evidence. The proof itself relies on the defined concept of God as a perfect being. St. Anselm’s proof is summarized here:

God exists in our understanding. This means that the concept of God resides as an idea in our minds.
God is a possible being, and might exist in reality. He is possible because the concept of God does not bear internal contradictions.
If something exists exclusively in our understanding and might have existed in reality then it might have been greater. This simply means that something that exists in reality is perfect (or great). Something that is only a concept in our minds could be greater by actually existing.
Suppose (theoretically) that God only exists in our understanding and not in reality.
If this were true, then it would be possible for God to be greater then he is (follows from premise #3).
This would mean that God is a being in which a greater is possible.
This is absurd because God, a being in which none greater is possible, is a being in which a greater is possible. Herein lies the contradiction.
Thus it follows that it is false for God to only exist in our understanding.
Hence God exists in reality as well as our understanding.
Study the above proof carefully. It is an intriguing proof because it states that God, a perfect being, must exist in all possible circumstances in order to satisfy the definition of his perfection. A God that can exist in only some circumstances, but fails to exist in others is a less than perfect being.

St. Thomas Aquinas’ Cosmological Argument

The great Catholic thinker, philosopher and theologian St. Thomas Aquinas summarized his cosmological argument in the Summa Theologia. In this theological masterpiece, St. Thomas writes five "ways" that we can know God exists. His first three ways deal with the cosmological argument:

St. Aquinas argues that there are things in the world in motion (this simply means that things are changing) and that whatever is in motion must have been put in motion by another thing in motion. Aquinas holds that, "whatever is in motion must be put in motion by another," and that, "this cannot go on to infinity, because then there would be no first mover." Hence St. Thomas argues that in order to eliminate the infinite chain of motions, there must be a first mover and source of all motion, God.
The second way is very similar to the first. It argues that," In the world of sense we find there is an order of efficient causes. There is no case known (neither is it, indeed, possible) in which a thing is found to be the efficient cause of itself; for so it would be prior to itself, which is impossible." By this he means that any thing, circumstance or event cannot change itself, but can only change something else (concept of efficient cause). Since there is a string of causes in which the string cannot be infinite (see premise #1), then all causes must attribute themselves to a first cause: God.
The third way also argues using the notion of a chain of causes. St. Thomas notes that things in our world owe their existence to something else in the world. Aquinas calls this the way of "possibility and necessity," meaning that all things made possible, necessarily attribute their existence to some pre-existing thing. Only God can be the source of all things since he is a being having its own necessity and does not need a pre-existing thing to cause him to exist. All things existing can trace themselves in a chain back to God.
A second shorter version of the cosmological argument can be formulated as:

Every being (that exists or ever did exist) is either a dependent being or a self-existent being.
Not every being can be a dependent being.
So there exists a self-existent being.
Finally, a third rendition of the cosmological argument (extracted from the book Philosophy for Dummies by Dr. Tom Morris):

1. The existence of something is intelligible only if it has an explanation.
2. The existence of the universe is thus either:
a. unintelligible or
b. has an explanation
3. No rational person should accept premise (2a) by definition of rationality
4. A rational person should accept (2b), that the universe has some explanation for its being.
5. There are only three kinds of explanations:
a. Scientific: physical conditions plus relevant laws yield the Event explained.
b. Personal: Explanations that cite desires, beliefs, powers and intentions of some personal agent.
c. Essential: The essence of the thing to be explained necessitates its existence or qualities (for example, if you ask why a triangle has 3 sides, I would respond that it is the essence and necessity for a triangle to have 3 sides by its definition.
6. The explanation for the existence of the whole universe can’t be scientific because there can’t be initial physical conditions and laws independent of what is to be explained. Event the Big Bang theory fails to explain the existence of the universe because modern science cannot explain where the original Big Bang singularity came from. The universe as a sum total of all natural conditions and laws cannot be explained unless we have an Archimidean reference point outside the system.
7. The explanation for the existence of the universe can’t be essential because the universe cannot exist necessarily. This is because, it could have been possible for the universe not to have existed (if the Big Bang had been slightly different it is possible for large-scale structures to not have existed). Thus the universe is not something the must necessarily or essentially exists.
8. Thus a rational person should believe that the universe has a personal explanation.
9. No personal agent but God could create the entire universe.
10. A rational person should believe that there is a God.
The Teleological Argument

The teleological argument, or argument from design, is also summarized by St. Thomas Aquinas in the Summa Theologica. Here is the extract from the Summa:

"The fifth way is taken from the governance of the world. We see that things that lack intelligence, such as natural bodies, act for an end, and this is evident from their acting always, or nearly always, in the same way, so as to obtain the best result. Hence it is plain that not fortuitously, but designedly, do they achieve their end. Now whatever lacks intelligence cannot move towards an end, unless it be directed by some being endowed with knowledge and intelligence; as the arrow is shot to its mark by the archer. Therefore some intelligent being exists by whom all natural things are directed to their end; and this being we call God."

Perhaps this is the most common form of reasoning behind the existence of God. The average theist will argue for the existence of God with the teleological argument.

Conclusion

Of course, these three proofs have their share of proponents and opponents. The proofs do not definitively prove the existence of God because they can be argued. Even the greatest truth can be masked behind a veil of innocent ignorance or blindness of pride. It is faith that provides the bedrock for belief in God and the cornerstone for ultimate happiness. Nevertheless, these three proofs can help show that Christianity is a rational religion, as well as an endlessly controversial one.