Then you'd be in disagreement with the vast, vast majority of historians. Historical evidence is not empirical evidence. We cannot replay the events and say, "Okay, Caesar, cross the Rubicon again, so we can make sure this actually could have happened."
And that isn't what is required. But we *do* require some sort of evidence backing up the written story. That is why, for example, Herodotus is seen as rather unreliable.
We can, and do, point to the changes in societies as a result of the historical events and can point to physical aspects of those changes. Typically, the said his event is a good hypothesis for the observed effects.
Do you know any epistemologists who define knowledge this way?
Justified true belief is justified through testing.
There's no similarity there. The process of reasoning in mathematics is purely rational, while the natural sciences are empirical.
That's debatable, but you miss the point. When two mathematicians disagree about whether some result has been proven, there is a resolution procedure to say, at least, who is incorrect.
In the sciences, there is also a dispute resolution procedure: observation made of a situation where the disputed idea gives different results. At the very least, we can tell who is wrong.
You use logical reasoning, i.e. rational evidence.
Reasoning alone, with no observations to back it up, fails to say *anything* aside from whatever axioms are chosen. It cannot, for example, say whether the basic assumptions are true or not.
Far too much of philosophy is based on 'obviously true' ideas that can be shown to be false or which carry no actual meaning. It becomes an exercise of rearranging prejudices as opposed to actually finding knowledge.