Historians most famously see Humean philosophy as a thoroughgoing form of skepticism, but many commentators have argued that the element of naturalism has no less importance in Hume's philosophy. Hume scholarship has tended to oscillate over time between those who emphasize the sceptical side of Hume (such as Reid, Greene, and the logical positivists), and those who emphasize the naturalist side (such as Don Garrett, Norman Kemp Smith, Kerri Skinner, Barry Stroud, and Galen Strawson).

Hume was heavily influenced by empiricists John Locke and George Berkeley, along with various Francophone writers such as Pierre Bayle, and various figures on the Anglophone intellectual landscape such as Isaac Newton, Samuel Clarke, Francis Hutcheson, and Joseph Butler.

Life
Hume was born on 26 April 1711 (Old style) in Edinburgh. From time to time throughout his life, he was to spend time at his family home at Ninewells by Chirnside, Berwickshire. He was sent by his family to the University of Edinburgh at the unusually early age of twelve (fourteen would have been more normal). At first he considered a career in law, but came to have, in his words, "an insurmountable aversion to everything but the pursuits of Philosophy and general Learning; and while (my family) fanceyed I was poring over Voet and Vinnius, Cicero and Vergil were the Authors which I was secretly devouring." He had little respect for professors, telling a friend in 1735 "there is nothing to be learned from a Professor, which is not to be met with in Books."

At the age of eighteen, in 1729, Hume made a philosophical discovery that opened up to him "a new scene of thought". He did not recount what this was, but it seems likely to have been his theory of causality - that our beliefs about cause and effect depend on sentiment, custom and habit, and not upon reason or abstract, timeless, general Laws of Nature.

In 1734, after a few months in commerce in Bristol, he retreated to do self-study and conduct thought experiments on himself at La Fleche in Anjou, France. During his four years there, he laid out his life plan, as he wrote in My Own Life, resolving "to make a very rigid frugality supply my deficiency of fortune, to maintain unimpaired my independency, and to regard every object as contemptible except the improvements of my talents in literature." While there, he completed A Treatise of Human Nature at the age of twenty-six.

Although many scholars today consider the Treatise to be Hume's most important work and one of the most important books in the history of philosophy, the public in Great Britain did not at first agree. Hume himself described the (lack of) public reaction to the publication of the Treatise in 1739–40 by writing that it "fell dead-born from the press, without reaching such distinction as even to excite a murmur among the zealots. But being naturally of a cheerful and sanguine temper, I soon recovered from the blow and prosecuted with great ardour my studies in the country".

There he wrote An Abstract Of A book lately published; Entituled, A Treatise Of human nature, &c. Wherein The chief argument of that Book is farther illustrated and Explained. Without revealing his authorship, he aimed to make his larger work more intelligible by shortening it. Even this advertisement failed to enliven interest in the Treatise.

After the publication of Essays Moral and Political, in 1744 he applied for the Chair of Ethics and Pneumatics (psychology) at Edinburgh University but was rejected. During the Jacobite Rebellion of 1745 he tutored the Marquise of Annandale. It was then that he started his great historical work The History of Great Britain which would take fifteen years and run to over a million words, to be published in six volumes in the period 1754 to 1762. In 1748 he served, in uniform, for three years as Secretary to General St Clair writing his Philosophical Essays concerning Human Understanding later published as An Enquiry concerning Human Understanding.This did not prove much more successful than the Treatise.

Hume was charged with heresy but he was defended by his young clerical friends who argued that as an atheist he lay outside the jurisdiction of the Church. Despite his acquittal, and, possibly, due to the opposition of Thomas Reid of Aberdeen who, that year, launched a telling Christian critique of his metaphysics, Hume failed to gain the Chair of Philosophy at Glasgow. It was in 1752, as he wrote in My Own Life, that "the Faculty of Advocates chose me their Librarian, an office from which I received little or no emolument, but which gave me the command of a large library." It was this resource that enabled him to continue his historical research for his History.

Hume achieved great literary fame as an essayist and historian. His enormous History of Great Britain from the Saxon kingdoms to the Glorious Revolution was a best-seller in its day. In it, Hume presented political man as a creature of habit, with a disposition to submit quietly to established government unless confronted by uncertain circumstances. In his view, only religious difference could deflect men from their everyday lives to think about political matters.

Hume's early essay Of Superstition and Religion laid the foundations for nearly all secular thinking about the history of religion. Critics of religion during Hume's time needed to express themselves cautiously. Less than 15 years before Hume was born, 18-year-old college student Thomas Aikenhead was put on trial for saying openly that he thought Christianity was nonsense, was convicted and hanged for blasphemy. Hume followed the common practice of expressing his views obliquely, through characters in dialogues. Hume did not acknowledge authorship of Treatise until the year of his death, in 1776.

His essays Of Suicide, and Of the Immortality of the Soul and his Dialogues Concerning Natural Religion were held from publication until after his death (published 1778 and 1779, respectively), and they still bore neither author's nor publisher's name. So masterful was Hume in disguising his own views that debate continues to this day over whether Hume was actually a deist or an atheist. Regardless, in his own time Hume's alleged atheism caused him to be passed over for many positions.

There is an old (and probably false) story about David Hume and his supposed atheism. In the story, Hume falls off his horse into a pool of mud and is slipping in it, when an old and pious lady walks past. When she sees the renowned atheist flapping about for his life, she walks to the edge and looks at him. Hume urges the lady to pass him a stick to pull him out, but she refuses unless he declare his devotion to God Almighty. Hume accedes and the lady helps him out.

From 1763 to 1765 Hume was Secretary to Lord Hertford in Paris, where he was admired by Voltaire and lionised by the ladies in society. He made friends with and, later, fell out with Rousseau. He wrote of his Paris life "I really wish often for the plain roughness of the The Poker Club of Edinburgh . . . to correct and qualify so much luciousness." For a year from 1767, Hume held the appointment of Under Secretary of State for the Northern Department. In 1768 he settled in Edinburgh. Attention to Hume's philosophical works grew after the German philosopher Immanuel Kant credited Hume with awakening him from "dogmatic slumbers" (circa 1770) and from then onwards he gained the recognition that he had craved all his life.

James Boswell visited Hume a few weeks before his death. Hume told him that he sincerely believed it a "most unreasonable fancy" that there might be life after death. Hume wrote his own epitaph:"Born 1711, Died [----]. Leaving it to posterity to add the rest." It is engraved with the year of his death 1776 on the "simple Roman tomb" which he prescribed, and which stands, as he wished it, on the Eastern slope of the Calton Hill overlooking his home in the New Town of Edinburgh at No. 1 St David’s Street.

Legacy
Though Hume wrote in the 18th century, his work seems still uncommonly relevant in the philosophical disputes of today compared to that of his contemporaries. A summary of some of Hume's most influential work in philosophy might include the following:

Ideas and impressions
Hume believes that all human knowledge comes to us through our senses. Our perceptions, as he called them, can be divided into two categories: ideas and impressions. He defines these terms thus in his An Enquiry Concerning Human Understanding: "By the term impression, then, I mean all our more lively perceptions, when we hear, or see, or feel, or love, or hate, or desire, or will. And impressions are distinguished from ideas, which are the less lively perceptions, of which we are conscious, when we reflect on any of those sensations or movements above mentioned."

He further specifies ideas, saying, "It seems a proposition, which will not admit of much dispute, that all our ideas are nothing but copies of our impressions, or, in other words, that it is impossible for us to think of anything, which we have not antecedently felt, either by our external or internal senses." This forms an important aspect of Hume's skepticism, for he says that we cannot be certain a thing, such as God, a soul, or a self, exists unless we can point out the impression from which the idea of the thing is derived.

The problem of causation
When one event continually follows after another, most people think that a connection between the two events makes the second event follow from the first (post hoc ergo propter hoc). Hume challenged this belief in the first book of his Treatise of Human Nature and later in his Enquiry Concerning Human Understanding. He noted that although we do perceive the one event following the other, we do not perceive any necessary connection between the two. And according to his skeptical epistemology, we can only trust the knowledge that we acquire from our perceptions.

Hume asserted that our idea of causation consists of little more than expectation for certain events to result after other events that precede them. 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 defies common sense, thereby creating the problem of causation – what justifies our belief in a causal connection and what kind of connection can we have knowledge of? – a problem which has no accepted solution.

Hume held that we (and other animals) have an instinctive belief in causation based on the development of habits in our nervous system, a belief that we cannot eliminate, but which we cannot prove true through any argument, deductive or inductive, just as is the case with regard to our belief in the reality of the external world.

The problem of induction
Most of us think that the past acts as a reliable guide to the future. For example, physicists' laws of planetary orbits work for describing past planetary behavior, so we presume that they will 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 states 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 nothing makes the principle of induction logically necessary.

The second justification, more modestly, appeals only to the past reliability of induction – it has always worked before, so it will probably continue to work. But, Hume pointed out, this justification uses circular reasoning, justifying induction by an appeal that requires induction to gain any force.

The bundle theory of the self
We tend to think that we are the same person we were five years ago. Though we've changed in many respects, the same person appears present as was present then. We might start thinking about which features can be changed without changing the underlying self. Hume, however, denies that there is a distinction between the various features of a person and the mysterious self that supposedly 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 concludes, there is nothing to the self over and above a big, fleeting bundle of perceptions.

Note in particular that, on Hume's view, these perceptions do not belong to anything. Rather, Hume 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 yet constantly changing elements. The question of personal identity then becomes a matter of characterizing the loose cohesion of one's personal experience. (Note that in the Appendix to the Treatise, Hume said mysteriously that he was dissatisfied with his account of the self, and yet he never returned to the issue!)

Practical reason: instrumentalism and nihilism
Most of us find some behaviors more reasonable than others. Eating aluminum foil, for example, seems to have something unreasonable about it. 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 is now associated with 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 (unless, of course, one has a stronger desire for health or the appearance of sensibility).

Today, however, many commentators argue that 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 important to make judgments in this domain.

Sentiment based ethical theory
Hume first discusses ethics in A Treatise of Human Nature. He later extracts and expounds upon the ideas he proposed there in a shorter essay entitled An Enquiry Concerning the Principles of Morals. Hume's approach in the Enquiry is fundamentally an empirical one. Instead of telling us how morality ought to operate, he proports to tell us how we do actually make moral judgments.

After providing us with various examples, he comes to the conclusion that most if not all of the behaviors we approve of increase public utility. Does this then mean that we make moral judgments on self-interest alone? Unlike his fellow empiricist Thomas Hobbes, Hume argues that this is not in fact the case. In addition to considerations of self-interest, he asserts, we are swayed by our sympathies for our fellow men. Hume also defends this sentiment based theory of morality by claiming that we could never make moral judgments based on reason alone.

Our reason deals with facts and draws conclusions from them, but, all else being equal, it could not lead us to choose one option over the other; only our natural sentiments can do this. This argument against founding morality on reason is now one in the stable of moral anti-realist arguments. As Humean philosopher John Mackie put it, for sheer facts about the world to be intrinsically motivating as far as morality goes, they would have to be very weird facts. Thus we have every reason not to believe in them.

Free will versus determinism
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. Hume's view is that human behavior, like everything else, is caused, and therefore holding people responsible for their actions should focus on rewarding them or punishing them in such a way that they will try to do what is morally desirable and will try to avoid doing what is morally reprehensible. (See also Compatibilism.)

The is-ought problem
Hume noted that many writers talk about what ought to be on the basis of statements about what is (is-ought problem). 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 in this way 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. (Others interpret Hume as saying not that one cannot go from a factual statement to an ethical statement, but that one cannot do so without going through human nature, that is, without paying attention to human sentiments.) Hume is probably one of the first writers to make the distinction between normative (what ought to be) and positive (what is) statements, which is so prevalent in social science and moral philosophy. G. E. Moore defended a similar position with his "open question argument", intending to refute any identification of moral properties with natural properties—the so-called "naturalistic fallacy".

Utilitarianism
It was probably Hume who, along with his fellow members of the Scottish Enlightenment, first advanced the idea that the explanation of moral principles is to be sought in the utility they tend to promote. Hume's role is not to be overstated, of course; it was his countryman Francis Hutcheson who coined the utilitarian slogan "greatest happiness for the greatest numbers". But it was from reading Hume's Treatise that Jeremy Bentham first felt the force of a utilitarian system: he "felt as if scales had fallen from [his] eyes". Nevertheless, 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 was a moral sentimentalist and, as such, thought that moral principles could not be intellectually justified. Some principles simply appeal to us and others don't; and the reason why utilitarian moral principles do 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 explain how we evaluate a wide array of phenomena, ranging from social institutions and government policies to character traits and talents.

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 start, 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 is somewhat similar to Occam's Razor. This argument is the backbone of the skeptic's movement and a live issue for historians of religion.

The design argument
One of the oldest and most popular arguments for the existence of God 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 in Dialogues Concerning Natural Religion and An Enquiry Concerning Human Understanding and though the issue is far from dead, many are convinced that Hume killed the argument for good. Here are some of his points:

1. For the design argument to be feasible, it must be true that order and purpose are observed only when they result from design. But order is observed regularly, resulting from presumably mindless processes like snowflake or crystal generation. Design accounts for only a tiny part of our experience with order and 'purpose'.
2. Furthermore, the design argument is based on an incomplete analogy: because of our experience with objects, we can recognise human-designed ones, comparing for example a pile of stones and a brick wall. But in order to point to a designed Universe, we would need to have an experience of a range of different universes. As we only experience one, the analogy cannot be applied.
3. Even if the design argument is completely successful, it could not (in and of itself) establish a robust theism; one could easily reach the conclusion that the universe's configuration is the result of some morally ambiguous, possibly unintelligent agent or agents whose method bears only a remote similarity to human design.
4. If a well-ordered natural world requires a special designer, then God's mind (being so well-ordered) also requires a special designer. And then this designer would likewise need a designer, and so on ad infinitum. We could respond by resting content with an inexplicably self-ordered divine mind; but then why not rest content with an inexplicably self-ordered natural world?
5. 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 as a human projection of goals onto nature. This mechanical explanation of teleology anticipated natural selection. (see also Anthropic principle)

Conservatism and political theory
Many regard David Hume as a political conservative, sometimes calling him the first conservative philosopher. He expressed suspicion of attempts to reform society in ways that departed from long-established custom, and he counselled people not to resist their governments except in cases of the most egregious tyranny. However, he resisted aligning himself with either of Britain's two political parties, the Whigs and the Tories, and he believed that we should try to balance our demands for liberty with the need for strong authority, without sacrificing either.

He supported liberty of the press, and was sympathetic to democracy, when suitably constrained. It has been argued that he was a major inspiration for James Madison's writings, and the Federalist No. 10 in particular. He was also, in general, an optimist about social progress, believing that, thanks to the economic development that comes with the expansion of trade, societies progress from a state of "barbarism" to one of "civilisation". Civilised societies are open, peaceful and sociable, and their citizens are as a result much happier. It is therefore not fair to characterise him, as Leslie Stephen did, as favouring "that stagnation which is the natural ideal of a skeptic". (Leslie Stephen, History of English Thought in the Eighteenth Century, 2 vols. (London: Smith, Elder and Co., 1876), vol. 2, 185.)

Although strongly pragmatic, Hume produced an essay titled Idea of a Perfect Commonwealth, where he detailed what any reforms should seek to achieve. Strong features for the time included a strict separation of powers, decentralisation, extending the franchise to anyone who held property of value and limiting the power of the clergy. The Swiss militia system was proposed as the best form of protection. Elections were to take place on an annual basis and representatives were to be unpaid, which was aimed at keeping the interests of constituents in the minds of politicians.

Contributions to economic thought
Through his discussions on politics, Hume developed many ideas that are prevalent in the field of economics. This includes ideas on private property, inflation, and foreign trade.

Hume's idea on private property is special—private property was not a natural right, but is justified since it is a limited good. If all goods were unlimited and available freely, then private property would not be justified, but instead becomes an “idle ceremonial”. Hume also believed in unequal distribution of property, since perfect equality would destroy the ideas of thrift and industry, which leads to impoverishment.

Hume did not believe that foreign trade produced specie, but considered trade a stimulus for a country’s economic growth. He did not consider the volume of world trade as fixed because countries can feed off their neighbor’s wealth, being part of a “prosperous community”. The fall in foreign demand is not that fatal, because in the long run, a country cannot preserve a leading trading position.

Hume was among the first to develop automatic price-specie flow, an idea that contrasts the mercantile system. Simply put, when a country increases its in-flow of gold, this in-flow of gold will result in price inflation, and then price inflation will force out countries from trading that would have traded before the inflation. This results in a decrease of the in-flow of gold in the long-run.

Hume also proposed a theory of beneficial inflation. He believed that increasing the money supply would raise production in the short run. This phenomenon was caused by a gap between the increase in the money supply and that of the price level. The result is that prices will not rise at first and may not rise at all. This theory was later developed by John Maynard Keynes.