It is irrelevant that Tacitus and Josephus were not alive during the crucifixion of Jesus. Most of the famous ancient world historians were not alive during the events that they experienced. He wrote about it just a short 30 years after the fact. Most histories of the time were written hundreds of years after the event. Plutarch wrote about Alexander the Great 300 years after the fact. that does not make his history any less accurate. Herodotus wrote Histories, which recounted the battles of Marathon, Thermopolyae, and Salamis were written 40 years after. That does not make them any less accurate.

Bear in mind that Josephus was a historian. He compiled primary documents into a history. This is what historians do, they search through primary sources and compile knowledge into volumes.

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