Short answers, pulled from the story.
David Hume is best known for his system of empiricism, philosophical scepticism, and his problem of induction, which argues that causal reasoning cannot be rationally justified and rests instead on habit and custom. He also identified the is-ought problem, known as Hume's Law, and argued that passions rather than reason govern human behaviour.
David Hume was born on the 7th of May 1711 in a tenement on the north side of Edinburgh's Lawnmarket, Scotland. He was born David Home and changed the spelling of his surname in 1734 because "Home" was not widely recognised in England.
Scholars today consider A Treatise of Human Nature (1739-40), completed when Hume was twenty-eight, to be his most philosophically important work and one of the most significant books in Western philosophy. Hume himself preferred his later Enquiry Concerning the Principles of Morals (1751), calling it "incomparably the best" of all his writings.
Hume's religious views have been described variously as agnostic, irreligious, or weakly deistic. His contemporaries suspected him of atheism, and the Church of Scotland considered charging him with heresy. All his works were placed on the Catholic Church's Index Librorum Prohibitorum in 1761.
Hume's problem of induction holds that there is no rational justification for inferring that the future will resemble the past. Both demonstrative reasoning and probable reasoning fail to justify this inference; demonstrative reasoning cannot prove it, and probable reasoning would be circular. Hume argued that natural instinct and habit, not reason, explain why humans make inductive inferences.
In An Enquiry Concerning Human Understanding, Hume argued that a wise person should weigh the evidence for a miracle against the uniform weight of human experience, which almost always favours the contrary. He defined a miracle as a transgression of a law of nature and concluded that the accumulated evidence of consistent natural laws will nearly always outweigh any eyewitness testimony.