An enquiry concerning human understanding

After his three-volume Treatise of Human Nature dropped like a rock to the bottom of the pool of British philosophic writing, Hume set out to write a briefer, more accessible version -- the Enquiry concerning Human Understanding. One of the early points it makes is that most endeavors to write about the nature of thought are hopeless and nearly impossible to understand. With that disclaimer, Hume sets out to contradict himself by writing lucidly about, while candidly acknowledging the severe limits of, this topic. He uses logic to show that most human understanding falls into two categories: a very small group of innate truths deducible by logic, like every triangle has three sides, and a much larger group -- nearly everything we "know" -- which is based on reality-based observation. This latter group always has, at a fundamental level, an element of probabilistic assumption: Things customarily happened this way before, so they probably will again. Thus almost everything we (think we) know about the world is based on empirical experience, not pure logic. So . . .how did he figure this all out?