I copied this from another topic I made on this subject: Carrier said, primarily based on the inscription that Jayhawker Soule brought up, that we can be fairly certain that Nazareth existed during that time period (the first century).
Not too long back, they also found a house that dated to around the time of Jesus, in Nazareth. I haven't seen any work that has claimed this to be false.
There are a variety of other archeological discoveries that also place Nazareth in the first century. The only thing against Nazareth from that time period is written accounts outside the Gospels. However, there have been a variety of villages never mentioned in text that we have later discovered. It really is evidence of anything, except that Nazareth was a nowhere place.
The biggest thing for the existence of Nazareth is why would they create such a village? It serves no real purpose. It would have been easier just to place Jesus in Bethlehem (Luke and Matthew even jump through hoops to get Jesus born there). But we can see that the tradition for Jesus being born in Nazareth was so strong, that he had to be placed there.
As for population numbers, there are rough estimates. However, we see this to be true for many ancient villages. They just didn't keep population records, so we have to try to figure them out through archeological evidence.
and:
We do know that it was there. The tablet that Jayhawker provided is all of the evidence we need. What you are asking us to believe is that during a war, a city pops up. That simply is not a very plausible explanation.
The fact that Jesus was said to be of Nazareth is also clear evidence that Nazareth existed during that time. All of the evidence we have of Nazareth points to it being a village of no real importance. It was a village of a few hundred people. Really nothing to write about. However, we do see that there was a very strong tradition about Jesus being from there. So strong was this tradition that Matthew and Luke have to jump through hoops in order to get Jesus born in Bethlehem. And instead of just leaving him there, which would make sense, we see that they are forced to put Jesus back in Nazareth. The Gospel writers simply were not able to get Jesus out of Nazareth because the tradition was too strong. And really, if they could have, they would have. John is the best example of this. There we see negative remarks about Nazareth. There is no reason to doubt that Nazareth existed.
Add that to the archeological evidence dating from around the time (the house, pottery shards, graves, etc), there is more than enough evidence to be sure that Nazareth existed during that time.
James Randi is not a Bible Scholar. I respect him, but he really has no background in this. And really, he seems to be more dealing with the tourist trade there than anything.
The fact that Jesus is said to be from Nazareth is more than enough evidence to suggest that it was a real site. The reason being, it would be ridiculous to put Jesus there if he wasn't from there. Why not just stick with the idea that he was born in Bethlehem and stayed there? It would have been much easier to do that. However, the Gospel writers were forced to place Jesus in some obscure village because that is where it was accepted that he lived. More so, there is never any sources during that time that state that there was no Nazareth. And really, if someone wanted to attack the Jesus story, and there were plenty, that would have been a prime discussion point.
As for the last thing that Randi stated, it simply was ignorant. When speaking of synagogues in ancient times, before the rise of Rabbinical Judaism and the fall of the Temple in Jerusalem, synagogues were different from the idea we have of them today. Many times, it was just a gathering place for Jews. It wasn't necessarily a distinct location set off just for that. Many times there were in someone's home, or the like. Not finding a synagogue structure really means nothing in this aspect, as one should not expect to find such.
Really, I just have to say that I am disappointed by the lack of credible research that James Randi did here.