How on earth do you prove that X did Y because of Z with facts? [Auto]biographies, letters, interviews of friends, family members and companion, diaries, recor

How on earth do you prove that X did Y because of Z with facts? [Auto]biographies, letters, interviews of friends, family members and companion, diaries, records about the books they lent from the library, intelligence records ... we know quite a lot about the motivations of well-researched important personalities. It would of course still not be a proof of mathematical rigor but such sources would definitely lend a lot of credibility if they are itself reliable.