This exercise is not about “certain” (P ~ 1), it’s about “doubt” (P ~ 1⁄2).
Concerning your question, I can say following:
1) Birth records/absence of such.
2) Place of burial/absence of such.
3) Mention of Achilles in the independent sources/lack of such for Julius Caesar (if some reliable Egyptian historian describes the century between 100 BC and 0 BC as the “epoch of a perfect stability of Roman Empire”, it would speak against both coup-d’etat by Julius and coup-d’etat by Brutus, which is part of the legend of Julius)
4) Evidence about reliability of Homer (can legend of Odyssey be some sort of political satire in disguise?)/Evidence about unreliability of historians describing Julius Caesar.
5) Social evidence: some person respected by me starts to believe in it.
I believe I would start taking existence of Achilles/non-existence of Julius Caesar seriously after those things: P ~ 1⁄2.
About “certainty”: I think large amount of independent Arabian/Egyptian/whatever books will do the trick.
Would it take all of those to cause you to doubt your current belief? The purpose is to figure out how strong of evidence you need to doubt your current belief, and use that as a measuring tool for how strongly you believe...
This exercise is not about “certain” (P ~ 1), it’s about “doubt” (P ~ 1⁄2).
Concerning your question, I can say following:
1) Birth records/absence of such.
2) Place of burial/absence of such.
3) Mention of Achilles in the independent sources/lack of such for Julius Caesar (if some reliable Egyptian historian describes the century between 100 BC and 0 BC as the “epoch of a perfect stability of Roman Empire”, it would speak against both coup-d’etat by Julius and coup-d’etat by Brutus, which is part of the legend of Julius)
4) Evidence about reliability of Homer (can legend of Odyssey be some sort of political satire in disguise?)/Evidence about unreliability of historians describing Julius Caesar.
5) Social evidence: some person respected by me starts to believe in it.
I believe I would start taking existence of Achilles/non-existence of Julius Caesar seriously after those things: P ~ 1⁄2.
About “certainty”: I think large amount of independent Arabian/Egyptian/whatever books will do the trick.
Would it take all of those to cause you to doubt your current belief? The purpose is to figure out how strong of evidence you need to doubt your current belief, and use that as a measuring tool for how strongly you believe...