To me it's always been a little bit ironic (I really do think) that this passage creates the same problem for me that Paul intends for it to solve for the Corinthians.
In these earliest days of the church, Christian people didn't have many of the sources of authority that we do. They have probably two, maybe three gospels to study, but no New Testament -- after all, the NT is going to include Paul's letter, which makes it tough for one to be around yet. If they're not Jewish, they don't have a familiarity with what we call the Old Testament, at least not to the degree that Paul does.
So when they come into the society of the early Roman Empire with their weird one-God and-his-Son-the-Messiah-and-a-kind-of-Spirit story, people who lean on religions with hundreds and maybe thousands of years of history of their own might be unimpressed. They might ask the questions my journalism professors always said should follow every statement that we didn't see or hear for ourselves. "Who says? Who are they? How do they know?"
Well, Paul tells the Corinthian church, here are some people who know that Jesus was crucified but he rose from the dead. They saw him! Then there's a list: Peter and the inner circle of disciples, a big group of about 500 people, then James and some other apostles, and so on. Down to Paul, who describes himself "as one untimely born" because he encountered the risen Christ after his ascension. If you don't want to believe Paul when he says Christ is risen, you can go talk to a bunch of people who saw him. They can't all be wrong.
And, I imagine, this may settle the issue for many of the Corinthians. At least, based on what Paul writes to them later, the issue doesn't seem to come up again.
Of course, for you and me, living today, Paul's words don't solve the problem at all. "Christ is risen!" is a fantastic claim. A man, dead on a cross, in a tomb for three days, rises and appears to his friends. Many people today refuse to believe it because, they point out, dead people don't get up. "After death" experiences almost always involve times of just minutes, not whole days, and we can bet nobody in first-century Judea had a defibrillator handy to kick-start Jesus' heart after he was in the tomb.
Since dead people don't rise, then Jesus didn't rise, they say, unless he wasn't really dead. And if he wasn't really dead, then what's the big deal about him anyway?
But we can't go see Paul's list of witnesses. None of them live today, nineteen hundred plus years later. And we can't get the kind of eyewitness testimony that he offers to his questioners. It doesn't seem fair, does it? It would seem, if things like eyewitness testimony that can support proof Jesus was who he said he was were so important, God would have provided the same kind of authorities for us to lean on as he did Paul and the early church. But he didn't.
Or did he?
Remember my journalism professors' questions? "Who says? Who are they? How do they know?" It was all part of an attitude of skepticism that was supposed to make us verify everything as much as possible and take nothing for granted. They also said, "If your mother says she loves you, check it out." If we'd been living in Paul's time, and we'd had the chance to question those eyewitnesses, the most we could have learned is that they all saw someone they knew to be the risen Christ. We could judge their credibility, of course. If a fellow who said he saw the risen Christ also said he was Emperor of Rome, we would wonder. But if a woman said she saw the risen Christ and she didn't make other wild claims, she's more credible.
Either way, though, whether or not we believe them is a decision we have to make. There's no proof, not of the kind we think of as certainty like DNA evidence or something. There's only testimony. There's only witness. And in the end, there's only faith -- a deliberate choice to see things a certain way and live like that way is real.
That way has to make some sense, of course. It's got to have some consistency, even if every little thing doesn't match up with every other little thing. It can't just be whatever someone dreams up.
Look, nobody's ever proved the reality of God to me. Nobody ever will. Folks can fuss about that, but mathematician Kurt Godel's incompleteness theorem suggests nobody can ever prove two plus two equals four either. We can believe it does, and we operate as if it does, because that's the way things usually work and because the world makes sense when we do.
Which poses the question for us Christians: Will we invest more time in trying to prove the gospel or in trying to live it? We're unlikely to succeed at either, but I have faith that the effort I put into the latter of those will be do more good than whatever I might try to do for the former.