Comments by "Michael Wright" (@michaelwright2986) on "28 Historical Figures Mentioned in the New Testament" video.
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It depends a bit on the depth of the records. In the case of WW2, I'd trust a recent historian more than a near contemporary one because of event-specific reasons like distance from the partisanship of the conflict and the release of once secret records over time; but that is a special modern event with a huge quantity of evidence, and one whose conflicts still affect us. In the case of these extra-biblical references, we might assume that Roman historians had access to some sort of primary source or secondary sources they trusted (and they wouldn't have trusted the traditions of Christians). Outside of Christianity, Jesus of Nazareth wasn't a big deal, just another religious enthusiast and trouble-maker who got crucified like thousands of others, and are not mentioned in the records.
There's also oral history, which is a very large can of wriggly worms, especially as it is often important in identifying and, hopefully, compensating for some of the wrongs of colonisation. But I think most people would give some credence to oral history over a 50-100 year span, while expecting some details to get forgotten or mistaken, and some episodes to be either invented, or heavily re-imagined. Like, for instance, the Gospels. Which is why tracing extra-biblical references is important for sticking in, as it were, survey points to locate the whole narratives.
Matt will doubtless answer for himself, but I'm sticking my oar in, too, for what it's worth.
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