I guess it depends on what is meant by "prove" and what is meant by "Jesus" and what is meant by "evidence" and what is meant by "existed".
I think what we can prove is that the Gospel narratives are entirely post-First Jewish-Roman War literary inventions, and that the Jesus character in those stories is derived entirely from scriptures and the letters of Paul. The personality, associates, and teachings of Jesus in the Gospel of Mark are all based on Paul as described in the collection of letters ascribed to him.
Thus, it is proven that the Jesus of the Gospel of Mark is someone who "never existed". That is something that can be proven. That Jesus is not based on the life of any real-world Jesus. And it can be proven that every other story about Jesus is derived from the Gospel of Mark. Thus we can prove that all "Gospel Jesuses" are really just fictional characters and that nothing about the Jesus of the Gospels is based on anything real. None of the events described in the Gospels really happened, and none of the teaching relayed as coming from Jesus really came from a person called Jesus.
Whether you think that has been proven or not, all of that is theoretically provable, and my book basically makes the case that it has been proven, though I will say that I don't go into detail on every single sentence and every single word of every Gospel. I provide over a dozen examples with some lists that highlight dozens more examples, but, yes its true you can still find sentences among the Gospels that I haven't shown explicitly come from some known literary source. So I guess one could always say that some phrase whose provenance hasn't been traced to scripture or an epistle may have "been real words of Jesus". But anyway.
So once we've proven that the Jesus of the Gospels is a fictional literary invention, there really isn't anything left, because the Christian Jesus is the character described in the Gospels. It's like saying that maybe Harry Potter is real, but he wasn't a boy, he wasn't named Harry Potter, he wasn't a wizard, he never went to Hogwarts, etc. "He" was actually a little girl who lived in Africa and died when she was 10 years old. I mean at that point its all just nonsense.
So we can prove that the Jesus of the Gospels isn't based on the life of a real person, and we can prove that Jews in the 1st century were engaged in interpreting scripture in ways that conceived of eternal heavenly beings who had all of the attributes of Jesus, and that we find no examples of Jews ever worshiping a real living person as a powerful being the way he is described in the earliest writings about him, and that the earliest writings about Jesus are not consistent with descriptions of a real person. The earliest writings about Jesus share many consistencies with writings about other "mythical" Jewish figures, such as Enoch, Melchizedek, Isaac, etc.
The best model for how a real person would be become worshiped by Jews is far less reasonable than models for how the worship of a heavenly messiah would have developed.
And the key issue really is that all historicist arguments go back to claiming that the Gospels are the documents that provide the evidence that Jesus was real. Once it is proven that those documents actually don't provide any evidence for Jesus, there is nothing to base claims of his existence on.
@Kenneth:
I guess it depends on what is meant by "prove" and what is meant by "Jesus" and what is meant by "evidence" and what is meant by "existed".
I think what we can prove is that the Gospel narratives are entirely post-First Jewish-Roman War literary inventions, and that the Jesus character in those stories is derived entirely from scriptures and the letters of Paul. The personality, associates, and teachings of Jesus in the Gospel of Mark are all based on Paul as described in the collection of letters ascribed to him.
Thus, it is proven that the Jesus of the Gospel of Mark is someone who "never existed". That is something that can be proven. That Jesus is not based on the life of any real-world Jesus. And it can be proven that every other story about Jesus is derived from the Gospel of Mark. Thus we can prove that all "Gospel Jesuses" are really just fictional characters and that nothing about the Jesus of the Gospels is based on anything real. None of the events described in the Gospels really happened, and none of the teaching relayed as coming from Jesus really came from a person called Jesus.
Whether you think that has been proven or not, all of that is theoretically provable, and my book basically makes the case that it has been proven, though I will say that I don't go into detail on every single sentence and every single word of every Gospel. I provide over a dozen examples with some lists that highlight dozens more examples, but, yes its true you can still find sentences among the Gospels that I haven't shown explicitly come from some known literary source. So I guess one could always say that some phrase whose provenance hasn't been traced to scripture or an epistle may have "been real words of Jesus". But anyway.
So once we've proven that the Jesus of the Gospels is a fictional literary invention, there really isn't anything left, because the Christian Jesus is the character described in the Gospels. It's like saying that maybe Harry Potter is real, but he wasn't a boy, he wasn't named Harry Potter, he wasn't a wizard, he never went to Hogwarts, etc. "He" was actually a little girl who lived in Africa and died when she was 10 years old. I mean at that point its all just nonsense.
So we can prove that the Jesus of the Gospels isn't based on the life of a real person, and we can prove that Jews in the 1st century were engaged in interpreting scripture in ways that conceived of eternal heavenly beings who had all of the attributes of Jesus, and that we find no examples of Jews ever worshiping a real living person as a powerful being the way he is described in the earliest writings about him, and that the earliest writings about Jesus are not consistent with descriptions of a real person. The earliest writings about Jesus share many consistencies with writings about other "mythical" Jewish figures, such as Enoch, Melchizedek, Isaac, etc.
The best model for how a real person would be become worshiped by Jews is far less reasonable than models for how the worship of a heavenly messiah would have developed.
And the key issue really is that all historicist arguments go back to claiming that the Gospels are the documents that provide the evidence that Jesus was real. Once it is proven that those documents actually don't provide any evidence for Jesus, there is nothing to base claims of his existence on.