A. I suppose it depends on what kind of evidence you are looking for.
A lot of people demand physical, empirical evidence for God. But God Himself is not physical. By his nature, he cannot be measured. And empirical science can only deal with that which can be measured. Philosophically, God is "existence", and so asking the question "What is the evidence for God's existence" is somewhat like asking the question "What is the evidence for existences existence."
I also do not actually think that there is irrefutable evidence for the existence of God. Any evidence I could present, someone could say 'yes, but...'. Christians believe that god is like this deliberately, that God for some reason wants people to have faith in Him, and trust what they do not see. In deed, Jesus makes a really big deal out of faith, doing works for people with faith, not doing them for people who don't have it, scolding people who don't have it, praising those who do. For some reason Jesus never made it plainly and irrefutably obvious to everyone that he was the Messiah. I suspect that that reason is in keeping with why God does not reveal himself in a way that could not be rejected.
That said, I think there is plenty of evidence for the existence of God. I think it is suspect that the evidence for God is routinely thrown out by those who would deny his existence.
I will start with the weaker evidence to my mind;
I will skip over the whole argument from beauty thing. I think that arguing that God exists on the basis that there is so much beauty in the world begs the question why is there so much ugliness?
Argument from design- young earth creationists in particular seem to like this one. They will point to extraordinary animals; turtles with built in compasses, beetles with explosive compounds in their abdomens, giraffes with an intricate series of valves to allow blood to flow up and down it's neck according to need, wood peckers with tongues that begin by going down their throat, up around their brain, through a nostril, and out their beak... etc. The argument goes that these animals have irreducibly complex systems- systems that would fail if not all there at once so cannot be explained by the mechanism of evolution by natural selection. Microbiologists (notably Michael Behe) will point to the nature of the cell, of blood clotting, of flagellum, and point to the same logic of irreducibly complex systems. Physicists will describe the laws governing our universe, and the fact that if any of these laws were adjusted by the slightest degree, life would be impossible. And so they argue "Therefore there must have been an intelligent designer."
But the counterargument comes quickly that if conditions were not just so, there could be no one to ask the question, therefore they must have been so. And they propose the idea of a multi verse, wherein different universes are potentially popping in and out of existence, and we naturally live in the one suitable for life. In the end they tend to accuse us of believing in the "God of the gaps". They suggest that we believe in God simply because we have questions that cannot be answered by science yet, and we assume that they never will be. Then you get guys like Richard Dawkins who paint Christians as believing in God simply to explain the universe.
I think the 'unanswered questions' argument is fair, but I think it goes both ways. If we cannot allow for unanswered and seemingly unanswerable questions about science to be evidence for the existence of God, I would challenge that unanswered and seemingly unanswerable questions about God are not evidence against. Why doesn't God heal amputees? I don't know, but this does not mean He does not exist. In fact, I would expect that if God were real, there would be things about Him that we could not understand. If a religion successfully answered every question, I would suspect that it was man made.
Argument from Morality- I've already exhausted this one in previous posts. Much of morality, notably sexual morality and the concept of human rights- depends on the idea that humans have a dignity above that of animals. Catholics argue that morals are intrinsic- in something called 'natural law', and I think this is demonstrated clearly by the morals of non Christians. But for Catholics our morals are based in something and are consistent- atheists are left with the uncomfortable position that morals are subjective and decided democratically.
Argument from History- I would like to suggest that scripture is itself a type of evidence of the existence of God. It is interesting how the Bible gets treated by those who doubt it. They say "what evidence was there for the existence of Jesus outside of the Bible?". And Christians tend to say something about Flavius Jospehus, a Jewish historian who made a very vague and unimpressive reference to Jesus. But why would we reject scripture as historical documents? Unlike most historical documents, scriptures have been painstakingly copied and preserved for centuries. Many of the scriptures- Gospel of John, letters of Paul, Acts- claim to be written by people with first hand knowledge of what they are speaking about. Others- Gospel of Luke- claim to be well researched. I would like to suggest that scriptures are rejected as historical documents on the grounds that we reject their conclusions, therefore we cannot accept the documents. I think rather we should treat them like historical documents, and recognize that this is a form of evidence which should be admissible.
Perhaps the most convincing argument from history is the sudden emergence of the Christian movement 2000 years ago wherein people were killed for making the claim that Jesus rose from the dead.
Argument from miracles- At the moment, this is the argument I find most compelling. That's because miracles- at least the ones I refer to- are scientifically verifiable, and therefore provide the opportunity to disprove Catholicism, and yet they stand up to scrutiny! In my discussions with atheists, I keep hearing this argument regarding miracles; "Miracles are by definition impossible. If you rule out the impossible solutions, then whatever remains, however improbable, must be true. For every miracle there is other possible, though improbable, explanations. We must accept that explanation, and reject the miraculous one." In other words "Miracles are impossible, therefore miracles are impossible."
It is remarkable to me that I keep coming across this line of thinking again and again. I suspect that someone must be teaching it, because so many atheists seem to come to the same conclusion independently. If what we are discussing is whether miracles are possible, we cannot allow for a premise 'miracles are impossible.' I even had an atheist argue that Padre Pio's stigmata was not a miracle, because it could have been faked, or it could have been that 'contrary to the laws of nature, holes grew in his hands and in his feet in a way the emulates a crucified man.' Although that is extremely unlikely, an extremeliy unlikely thing is more likely than an impossible thing, therefore it must be the true explanation.
A parallel is drawn to believing in UFO's based on what evidence is presented, despite the fact that it is extremely unlikely that if intelligent alien life did exist it would be able to visit earth, and would focus all it's attention on Americans.
So let's all agree that the idea of alien life forms coming to earth is extremely unlikely, to such a degree that we would sooner dismiss all claims as being those of lunatics or liars or people with faulty memory. But supposing they produced evidence- say they produced a spacecraft with technology hitherto unknown on earth, that could do things that even the American military, though they could duplicate, could only do so with great difficulty. And let’s say there were some elements that they could not quite duplicate, but could make a fairly close replica of. From that evidence, which can be scientifically tested, we would have to eliminate the lunatic and liar theories, and develop some others. I think the reasonable theories to consider would be.
The Church has had to rule on the subject, and has its own reputation to uphold which would be dubious if it ever claimed a hoax to be authentic. Note it has not ruled on the Shroud, but did declare Padre Pio a saint. If Padre Pio can be demonstrated to be a fraudster, then we will know for certain that the Church is wrong! The Church cannot afford those risks… and so requires a certain level of scrutiny before authenticating something. So the very fact that the Church would examine a miracle like Pio's stigmata, and still feel compelled to stake it's reputation on canonizing him, is itself an indication of the strength of the evidence.
Conclusion- I return then to my original point, which is this- There is plenty of evidence for God, even a remarkable amount. I submit that the tendency to reject the evidence outright usually demonstrates that we are using our conclusion as a premise. It is my opinion that the evidence strongly points to the conclusion that Catholicism is correct, even if it leaves some questions unanswered.