The original question is “Can God Be Proven?”
The complex answer is “maybe, depends on what you mean by “proven.”” The simple answer is “yes.”
If you mean by “proven” you mean “positivistically (scientifically) proven,” then the answer is no. God cannot be measured. Therefore, God, if extant, is outside of the ability of science and positivistic reason to describe.
Not everything that exists can be positivistically measured, so the mere lack of a positivistic proof is insufficient to disprove the existence of God. For example, abstract concepts like we are discussing here exist, but they cannot be measured. (If they did not exist, we would not be talking about them.) So the question becomes, is there some rational argument that compels the existence of God?
So, if you mean by “proven” a rational argument or set of arguments that compels an affirmative answer, then “yes,” God’s existence can be proven.
I’ve seen a lot of vague references to Aquinas’ proofs and how they’re not convincing or even “laughable” - but no rationale why.
Let’s address just one: The proof of first cause. Everything has a cause. You were caused by your parents. You can keep going back and back until you reach the Big Bang. However, the Big Bang must have had a cause. Even the world’s leading physicist, an atheist himself, has said, “What is it that breathes fire into the equations and makes a universe for them to describe?” Stephen Hawking
The only way to break the chain of causation is to arrive at a first point that is 1) unchanging, 2) capable of creation “ex nihilo” (from nothing) and 3) capable of creating a creation that itself can change. That first cause must be outside of time, for time itself had a beginning. And the chain of causation must be broken, because infinite causation is both meaningless and contrary to scientific observation (the Big Bang).
We call that first cause “God” by definition. Yes, you could call the first cause “gizmo” or “Zeus” if you want. However, humor me for a brief moment.
Jesus claimed to be God, explicitly. Scripture tells us that “in the beginning there was the Word” and that “the Word became flesh.” This passage refers directly to Jesus. Thus, scripture tells us that Jesus was “in the beginning” and, accordingly, we can derive that Jesus effectively claimed to be the first cause. A person claimed to be the first cause.
So, Jesus was one of 1) a liar, 2) a lunatic, or 3) actually God.
We can exclude liar and lunatic given His wisdom, genteless, self-sacrifice, the fact that He had nothing to gain, and the behavior of His clearly devoted followers (not the ones who screwed up and didn’t follow His teachings). We call them saints. We can also look to the endurance of His church despite the corruption of individuals up to and including popes, despite schizms, despite plagues, and everything else that has come at the Church in 2000 years.
Therefore, not only does God exist, but Jesus is God.
From here we can know a little bit more about the nature of God, because Jesus revealed some of His nature to us. We know that God is three persons in one entity - Father, Son, and Holy Spirit. We know God is Love. We know God is Just. We know God is merciful. We know that God created us, loves us, and will judge us based on our actions and our love for Him though his mercy.
I’ve been very brief of necessity. Because of this, there are gaps in the way I expressed the arguments, but these gaps can be filled.
Also, there are limits to reason. At a certain point faith must take over. For example, we are called to have a relationship with God, and reason can only help us a very little in this department. However, I can at least prove through rational argument that God exists and prove something about his nature.
The bottom line is that there is a Truth and, if so, the Truth can be ascertainable and put to the test. Jesus and His Church will meet any rational test. Of course, you can mock it, but you will find no other institution as inherently rational as the Catholic Church - because faith and reason go hand in hand when you are dealing with the Truth.