We run into that same dilemma with all of history more than a few centuries old. We do have the evidence of the martyrdoms in both the writings of the early church and Roman histories. We also have the evidence of higher textual criticism, which just seems to have the right amount of mix of correlation and differentiation. Early writings cannot prove miracles, but they can serve evidence that those that first said they witnessed miracles believed enough to die for their story.
It is only evidence. That is all we can hope for. That is why I do not like the word “proof”. I could not even prove the existence of Julius Caesar, at least by modern standards, or the extension of Judaism from the present day into the past before the Diaspora.
Peter Kreeft expanded this by adding a fourth option, which he also addressed. That is, that Jesus claimed divinity, but did so in a mystical sense, perhaps influence by Eastern mysticism. I think it also is worth saying that anyone could add more possibilities, and we should be open to answering those. We cannot assume there are only three (or four) possibilities. For instance, one possibility is that Jesus never made any such claim, and was not killed for making such a claim.
TBH, I haven’t read Kreeft in a long time. (Come to think of it, the last time I remember doing so – which was about a dozen years ago – was at the request of a Protestant friend. So how do you like them bananas?)
i agree that talk of any proof in history is very problematic. I like to use the example of trying to prove I had eggs for breakfast last Tuesday.
I think if we get very technical and strip out all philosophical assumptions of science it is very hard to prove just about anything that isn’t completely pre-defined by man.
I think though with regards to Christianity and historical examples of early Christian martyrdom, given what we know, it would be extraordinary if such examples did not exist.
We see that the explosive spread of Christianity was spear-headed by eye-witnesses and that the figure of Jesus Christ was the message. That message was to follow in the footsteps of Jesus who gave his life to God and who would rise followers from death if they likewise gave their lives to God.
Reading the leaders of the early Christian movement, they all gave adulation to Jesus while humbly regarding themselves as unworthy even though specifying they would be willing to die for the message of Jesus.
The martyrdom of these early Christians would be exactly what we would expect given their Theology, the extraordinary immediate widespread growth of Christianity amongst the oppressed, the cruelty of the Roman state and the willingness of subsequent generations to glorify and undertake martyrdom.
As mentioned above, it would require more explanation if there were not Christian references of such behaviour from the initial generation of eye-witness Christians.