Objective evidence for the existence of Jesus Christ?

[Pyrrho]

I don't deny him, I just say he has not met his burden. I don't need to make a positive claim "he didn't exist" any more than I need to say that about Sauron.

To be consistent you would have to be fairly skeptical about the existence of any individual who ever lived in the ancient world, and such extreme caution about Homer or Jesus or Socrates or anyone else---when there are reasons to think some facts can be more ascertained than others, at least in terms of probability---requires further justification than simply saying, "People sometimes write fiction."
...

Your examples are quite a bit different from each other.  I will address them in chronological order.  Generally speaking, the more recent the person, the more evidence that there should be.  And generally speaking, the more important the person, the more evidence there should be.

In the case of Homer, I would not be confident that he was as described, but we can be sure that someone wrote The Illiad and someone wrote The Odyssey, or some group of people did.  But whether they were written by someone named "Homer" or not is not really known.  We don't have any proper documentation on that, but given the era in which he lived, that is hardly surprising.  So Homer is, at best, semi-mythical.  There is no real confidence that he actually existed, but he might have.  I am nearly a pure agnostic on Homer.

In the case of Socrates, we have the testimony of three contemporaries (Plato, Xenophon, and Aristophanes), which puts him in an entirely different class than Homer.  We can be reasonably sure that he existed, and lived in Athens, and was a philosopher who inspired a play by one (which is not complimentary, and makes fun of him), and many of the writings of the others, and Socrates likely said some of the things in some of their writings (though not all of things which Plato puts into the mouth of Socrates).  What adds to the value of the testimony is that they do not attribute miraculous properties to Socrates.  So we have a rough idea about him, and can be reasonably certain he existed.

With Jesus, we are in a different situation still.  He is supposed to be supremely important, and yet we have nothing written during his lifetime.  And unlike the case of Socrates, the earliest writings are all propaganda pieces for a religion, in which miraculous things are attributed to him, which detracts from their value as testimony.  And we also have known cases of fraud, in which Christians have tried to alter texts to support the claim that Jesus existed, which further detracts from any trust one might have otherwise had in writings purporting to support his existence.  Some of the stories (in the Bible) seem like they are adapted from seeing magicians, but this does not tell us whether they are based on a particular one, or on having seen various magicians and making Jesus fit the type.  So we really have no good reason to believe that the stories of Jesus are really based on a particular person, and is, at the very best, semi-mythical, though given his supposed importance, one would expect better documentation if he were real.  I am inclined to think he did not exist at all, but, of course, such a thing isn't likely to ever be provable.  He might have existed, though certainly not as described, and we really don't have any good reason to believe he existed at all.

As for the fact that most people, who have addressed the question, believe Jesus existed, most who enter into the question do not do so without bias, as they generally start out with the belief he existed and conclude, after looking at the evidence, what they already believed before looking at the evidence.  I find this very unconvincing, and am not inclined to alter my opinion based on the opinions of others.


So, I would say that one of the three existed, and the others are uncertain at best, and likely did not exist at all.  Of course, one cannot prove they did not exist, at least not based on any evidence I have seen.


Edited to add:

I forgot to mention the fact that the oldest writings of Christianity are the most vague, and the later ones are more detailed, which strongly suggests that the details are all fiction.  This is obscured to many readers of the Bible, who falsely assume that the books of the New Testament appear in the order in which they are written.  But even most Christian scholars say that that is wrong, and that the earliest writings are ones that lack detail, just as I say.