1. One mathematician gave "odds" that there was only a 1:600 chance that the boxes of bones belonged to anyone else. This was based on the chance that the names of Christ's family would all be in the same vault.
-1:600 is not really impressive. Would you get on a plane that had 1:600 chance of crashing?
2. We know that there was incredible persecution of the early Christians. Would they risk such persecution if they knew Christ really didn't exist?
3. We also know that the Romans and Jews would have done anything to suppress Christianity. Is it likely that they would have built up a ossuary and put any bones in there in the hopes that they could refute Jesus's claims?
-Is there a chain of custody showing that this was never tampered with.
4. Why would a family from Galilee, and a poor one at that, be buried in Jerusalem, in such an impressive (read expensive) chamber?
5. How do we know that some misguided pilgrim didn't set this up at some point in the distant past?
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No slight intended if I missed anyone.
That was my first thought.
3. We also know that the Romans and Jews would have done anything to suppress Christianity. Is it likely that they would have built up a ossuary and put any bones in there in the hopes that they could refute Jesus's claims?
Very Nicely said on point #2.
On Point #3 the argument can be augmented that the cruxifixation is an historical fact. But throw that aside, lets say that Jesus wasn't crucified. Let say that after he was brutally beaten by the Romans, he went away quietly never to claim to be the Messiah again. As the apostles started spreading the news of the resurrection why wouldn't the Jewish authorities pull Jesus out of exile and display him on the steps of the temple to prove the apostles to be liars?
They aren't even certain that the name they have reads "Jesus." It could read "Hanun."