Hume was born in Edinburgh and attended the university there. At first he considered a career in law, but came to have, in his words, "an insurmountable aversion to everthing but the pursuits of philosophy and general learning."
He did some self-study in France, where he also completed A Treatise of Human Nature at the age of 26. When published in England (1739-40) it received next to no attention. Hume famously wrote that it "fell dead-born from the press."
After a few years of service to various political and military figures, Hume returned to his studies. After deciding that the problem with the Treatise was style not content, he reworked some of the material for more popular consumption in An Enquiry Concerning Human Understanding. It was not extremely successful either, but more so than the Treatise.
However, between philosophical pursuits, Hume did achieve literary fame as an essayist and historian. Attention to his works grew after Immanuel Kant credited Hume with awakening him from "dogmatic slumber".
The Problem of Causation When one event causes another, most people think that we are aware of a connection between the two that makes the second event follow from the first. Hume challenged this belief, noting that whereas we do perceive the two events, we don't perceive any necessary connection between the two. And how else but perception could we gain knowledge of this mysterious connection? Hume denied that we could have any idea of causation other than the following: when we see that two events always occur together, we tend to form an expectation that when the first occurs, the second is soon to follow. This constant conjunction and the expectation thereof is all that we can know of causation, and all that our idea of causation can amount to. Such a lean conception robs causation of all its force and some later Humeans like Bertrand Russell have dismissed the notion of causation altogether as something akin to superstition. But this violates common sense, thereby creating the problem of causation -- what justifies our belief in a causal connection and what kind of connection could we have knowledge of? -- a problem which has no accepted solution. For relevant contemporary work, see Wesley Salmon's Hume and the Problem of Causation and Causality and Explanation.
The Problem of Induction We all think that the past is a reliable guide to the future. For example, physicists' laws of planetary orbit work for describing past planetary behavior, so we presume that they'll work for describing future planetary behavior as well. But how can we justify this presumption -- the principle of induction? Hume suggested two possible justifications and rejected them both. The first justification is that, as a matter of logical necessity, the future must resemble the past. But, Hume pointed out, we can conceive of a chaotic, erratic world where the future has nothing to do with the past -- or, more tamely, a world just like ours right up until the present, at which point things change completely. So there is nothing logically necessary about the principle of induction. The second justification, more modestly, appeals only to the past reliability of induction -- it's always worked before, so it will probably continue to work. But, Hume pointed out, this justification is using circular reasoning -- justifying induction by an appeal that requires induction to gain any force. Hume concluded that induction cannot be intellectually justified, but that since we are hard-wired by nature to believe it, there's no point in fighting it. This also violates common sense, and the problem of justifying induction is still with us. For relevant contemporary work, see Richard Swinburne's compilation The Justification of Induction.
The Bundle Theory of the Self We tend to think that we are the same person we are 5 years ago. Though we've changed in many respects, the same person is present as was present then. We might start thinking about which features can be changed without changing the underlying self. But Hume denies the distinction between the various features of a person and the mysterious self that bears those features. After all, Hume pointed out, when you start introspecting, you notice a bunch of thoughts and feelings and perceptions and such, but you never perceive any substance you could call the self. So as far as we can tell, Hume concluded, there's nothing to the self over and above a big, fleeting bundle of perceptions. Note in particular that, on Hume's view, there is nothing that these perceptions belong to. Hume further compares the soul to a commonwealth, which retains its identity not by virtue of some enduring core substance, but by being composed of many different related and constantly changing elements. Questions of personal identity then become a matter for arbitrary stipulation. (Note that in the Appendix to the Treatise Hume said mysteriously that he was dissastified with his account of the self and never returned to it!) For relevant contemporary work, see Derek Parfit's Reasons and Persons.
Practical Reason: Instrumentalism and Nihilism Most of us think that some behavior is more reasonable than others. There seems to be something unreasonable about, say, eating aluminum foil. But Hume denied that reason has any important role in motivating or discouraging behavior. After all, reason is just a sort of calculator of concepts and experience. What ultimately matters, Hume said, is how we feel about the behavior. His work begot the doctrine of instrumentalism, which states that an action is reasonable if and only if it serves the agent's goals and desires, whatever they be. Reason can enter the picture only as a lackey, informing the agent of useful facts concerning which actions will serve his goals and desires, but never deigning to tell the agent which goals and desires he should have. So, if you want to eat aluminum foil, reason will tell you where to find the stuff, and there's nothing unreasonable about eating it or even wanting to do so. Instrumentalism went on to become the orthodox view of practical reason in economics, rational choice theory, and some other social sciences. But, some commentators argue, Hume actually went a step further to nihilism and said there's nothing unreasonable about deliberately frustrating your own goals and desires ("I want to eat aluminum foil, so let me wire my mouth shut"). Such behavior would surely be highly irregular, granting reason no role at all, but it would not be contrary to reason, which is impotent to make judgments in this domain. For relevant contemporary work, see Jean Hampton's The Authority of Reason and David Schmidtz's Rational Choice and Moral Agency.
Moral Anti-Realism and Motivation Drawing on his attack on reason's role in judging behavior, Hume argued that immoral behavior is not immoral by being against reason. He first claims that moral beliefs are intrinsically motivating -- if you believe killing is wrong, you will be ipso facto motivated not to kill and to criticize killing and so on (moral internalism). He then reminds us that reason alone can motivate nothing -- reason discovers matters of fact and logic, and it depends on our desires and preferences whether apprehension of those truths will motivate us. Consequently, reason alone cannot yield moral beliefs. Hume proposed that morality ultimately rests upon sentiment, with reason only paving the way for our sensitive judgments by analysis of the moral matter in question. This argument against founding morality on reason is now one in the stable of moral anti-realist arguments; Humean philosopher John Mackie argued that, for moral facts to be real facts about the world and, at the same time, instrinsically motivating, they would have to be very weird facts. So we have every reason to disbelieve in them. For relevant contemporary work, see J. L. Mackie's Ethics: Inventing Right and Wrong, Mackie's Hume's Moral Theory, David Brink's Moral Realism and the Foundation of Ethics, and Michael Smith's The Moral Problem.
Free Will vs. Indeterminism Just about everyone has noticed the apparent conflict between free will and determinism -- if your actions were determined to happen billions of years ago, then how can they be up to you? But Hume noted another conflict, one that turned the problem of free will into a full-fledged dilemma: free will is incompatible with indeterminism. Imagine that your actions are not determined by what events came before. Then your actions are, it seems, completely random. Moreover, and most importantly for Hume, they are not determined by your character -- your desires, your preferences, your values, etc. How can we hold someone responsible for an action that did not result from his character? How can we hold someone responsible for an action that randomly occurred? Free will seems to require determinism, because otherwise, the agent and the action wouldn't be connected in the way required of freely chosen actions. So now, nearly everyone believes in free will, free will seems inconsistent with determinism, and free will seems to require determinism. (See also Compatibilism.) How can we resolve this dilemma?
The Is-Ought Problem Hume noted that many writers talk about what ought to be on the basis of statements about what is. But there seems to be a big difference between descriptive statements (what is) and prescriptive statements (what ought to be). Hume calls for writers to be on their guard against changing the subject like that, not without giving an explanation of how the ought-statements are supposed to follow from the is-statements. But how exactly can you derive an 'ought' from an 'is'? That question, prompted by Hume's small paragraph, has become one of the central questions of ethical theory, and Hume is usually assigned the position that such a derivation is impossible. A similar thesis was argued by G. E. Moore's 'open question argument', intended to refute any identification of moral properties with natural properties -- the so-called 'naturalistic fallacy'. Now any ethical theorist who wishes to give morality an objective grounding in more down-to-earth features of the world is fighting an uphill battle.
Utilitarianism Hume, along his fellow members of the Scottish Enlightenment, first advanced the idea that moral rules are justified by promoting the utility of the persons involved. Hume's role is not to be overstated, of course; it was his countryman Francis Hutcheson who coined the utilitarian slogan "greatest good for the greatest number". But it was from reading Hume's Treatise that Bentham first felt the force of a utilitarian system: he "felt as if scales had fallen from [his] eyes". But Hume's proto-utilitarianism is a peculiar one from our perspective. He doesn't think that the aggregation of cardinal units of utility provides a formula for arriving at moral truth. On the contrary, Hume thinks that moral principles aren't intellectually justifiable -- some rules appeal to us and others don't. But, he thinks, the reason that good moral principles appeal to us is that they promote our interests and those of our fellows, with whom we sympathize. Humans are hard-wired to approve of things that help society -- public utility. Hume used this insight to morally appraise things from social institutions and government policies to character traits and talents. The legacy of utilitarianism is too well-known to go into -- the theory is a mainstay of ethics and economics.
The Problem of Miracles One way to support a religion is by appeal to miracles. But Hume argued that, at minimum, miracles could never give religion much support. There are several arguments suggested by Hume's essay, all of which turn on his conception of a miracle: namely, a violation of the laws of nature by God. One argument claims that it's impossible to violate the laws of nature. Another claims that human testimony could never be reliable enough to countermand the evidence we have for the laws of nature. The weakest and most defensible claims that, due to the strong evidence we have for the laws of nature, any miracle claim is in trouble from the get-go, and needs strong supporting evidence to defeat our initial presumptions. In a slogan, extraordinary claims require extraordinary evidence. This point has been most applied to the question of the resurrection of Jesus, where Hume would no doubt ask, "Which is more likely -- that a man rose from the dead or that this testimony is mistaken in some way?" Or, more blandly, "Which is more likely -- that Uri Geller can really bend spoons with his mind or that there is some trick going on?" This argument is the backbone of the skeptic's movement and a live issue for historians of religion. For a critical and technical (Bayesian) analysis of Hume, see John Earman's Hume's Abject Failure -- the title of which gives you an idea of his assessment!
The Design Argument One of the oldest and most popular arguments for God's existence is the design argument -- that all the order and 'purpose' in the world bespeaks a divine origin. Hume gave the classic criticism of the design argument, and though the issue is far from dead, many are convinced that Hume killed the argument for good. All a century before Darwin! Here are some of his points. (1) For the design argument to work, it needs to be true that about the only time we see order and perceived purpose is when it results from design. But we see the stuff all the time, resulting from presumably mindless processes like generation and vegetation. Design accounts for only a tiny part of our experience with order and 'purpose'. (2) The design argument, even if it worked, could not support a robust theism; all you can hope for is the conclusion that the universe's configuration is the result of some morally ambiguous, possibly unintelligent agent or agents whose method bears some remote similarity to human design. (3) By the design argument's own principles, God's mental order and functionality needs explanation. Otherwise, we could leave the universe's order, etc. unexplained. (4) Often, what appears to be purpose, where it looks like object X has feature F in order to secure some outcome O, is better explained by a filtering process: that is, object X wouldn't be around did it not possess feature F, and outcome O is only interesting to us, a human projection of goals onto nature. This mechanical explanation of teleology anticipated natural selection. For relevant contemporary work, see J. C. A. Gaskin's Hume's Philosophy of Religion, and Richard Swinburne's The Existence of God; for a view from a philosopher of biology, see Elliott Sober's Philosophy of Biology, ch. 2.