Hume.
Born in Edinburgh 1711 Calvinist family. Goes to edinburg University; expected to become lawyer, but becomes philosopher. Goes to France and in his 20's writes A Treatise of Human Nature, which "fell dead-born from the press". The ruse of his own review fails. Moves away from Calvinism and Edimburgh University denies him a position in Pneumatology and Ethics.
1748 publishes First Enquiry and later the Second Enquiry.
1752 turned down at University of Glasgow
1757 A Natural History of Religion argues Christianty arises from negative emotions, e.g. a desire to flatter.
1756-61 the massive History of England, which gains him great repute.
1763 goes to Paris as assistant to the ambassador. Liked because of his wit.
1776 dies in Edimburgh after deciding to publish the Dialogues on Natural Religion postumously.

As Newton provided a science of nature, H. wants to provide a science of human nature (he calls it "moral science").
The First Enquiry about understanding; the Second Enquiry about ethics (passions). Here we study just the First Enquiry.

First Enquiry.

Sec. I: Of the different species of philosophy (read)

Sec. II: the origin of ideas.
Perceptions divided into impressions and ideas. Former more lively, vivid than the latter (feeling of heat vs. memory of heat): the difference between impressions and ideas is of degree, not kind. All ideas ultimately reducible to impressions (ex. golden mountain).
Problems:

Remembered hunger not faint hunger
Missing shade of blue and why H. dismisses it as bizarre case.

Impressions come from sensation and reflection (reflection is the source of secondary impressions, e.g., hope or fear caused by impressions of sensation, e.g., pleasure, pain).
H. not interested in tracing causes of sensory impressions.
Importance of justifying philosophical terms by finding the ideas and ultimately the impressions they originate from.

Sec. III: laws of association of ideas.
1) Resemblance (idea of picture/idea of thing depicted)
2)Spatio-temporal contiguity (idea of a room/idea of next room)
3)Cause-effect (Idea of pain/idea of wound)
Note: laws of association and Newton's gravitation; minds and Newton's space.

Secs. IV-V: induction.
First, H. partitions knowledge into knowledge of Relations of ideas (opposite inconceivable e.g., 2+2=4; every effect has a cause) and knowledge of Matters of fact (opposite conceivable, e.g. the sun raised today; every event has a cause). The former is obtainable a priori through analysis; the latter a posteriori through experience.
NOTE:
For H. knowledge of matters of fact not directly experienced is based on cause/effect. Ex. Crusoe and the footprint.

The issue is: How do we know matters of fact beyond present sense experience or memory of it (ex. the sun raises now vs. the sun will raise tomorrow)? H. provides a negative analysis (why we don't know matters of fact beyond present sense experience or memory of it), and a positive one (why we think we know them)
Negative analysis:

The alleged knowledge is not from relation of ideas because their opposite is possible.
Hence, from experience (matters of fact).
But experience extends only to what we actually experience now or actually experienced in the past.
Still, we believe that unexperienced causes similar to experienced ones will produce similar effects (Uniformity Principle, UP). For example, we hold that the future will resemble the past.
But our belief in UP cannot be based on unexperienced matters of fact under pain of circularity. However, it is not based on

relation of ideas, since its opposite is logically possible.
experienced matters of fact.

Hence, our belief in UP is not based on rational grounds.

NOTES:
1)Why appeal to probability doesn't work.
2)Why appeal to induction to justify induction is no good (counterinduction)
3) Is accepting PU a part of what is is to be rational? (induction, as deduction, part of rationality)

Positive analysis:
Custom or habit produce in us expectations whose generalizations are embodied in UP thusly.
Suppose that I have experienced that every time I experienced A, immediately afterwards I experienced B (e.g., sight of unsupported object followed by sight of falling object). This, as it were, created a preferred psychological path in the mind, so that now the liveliness of a perception of type A (the sight of an unsupported stone) is transmitted to one of type B (the stone falling).
NOTE: Same for resemblance and contiguity.
But a belief is just a lively idea, although less lively than impressions.
NOTE: Contrast with Descartes
So, upon having an impression of type A, I believe that an event of type B will occur.
NOTE: this genetic account of our inductive beliefs does not constitute a justification of induction because psychological explanations needn't be epistemological ones

Sec. VI : Of Probability (read)

Sec.VII: idea of cause
Idea of cause involves ideas of:

spatio-temporal contiguity
succession (cause antecedes the effect)
necessary connection

Problems

day doesn't cause night; so (1)-(3) not sufficient.

action at a distance; so, (1) not necessary

H. leaves aside (1) and (2), and studies (3).
We never have an impression of necessary connection (power of the cause to produce the effect); we experience only brute connection because the impression of power:

Cannot come from sensation (e.g., billiard balls hitting each other)

Cannot come from introspection of our "power" either to move the body or to produce ideas:

mind movig body

paralized man's experience in volition same as healthy man, since consciousness cannot deceive. But the former is without impression of necessary connection. Hence, same for the latter.
if we felt the original power, we would know it, and since all power is relative to its effect, we would know the effect. But we don't (e.g, what is moved in the brain when we move our arm)

Problem

mind producing ideas

actual production (real productive power) of ideas by will is creation, which seems absurd to attribute to the mind.
we have rather little control on what goes on in our minds.

The source of the idea of necessary connection is not the impression of power, but the expectation (belief) upon perceiving event of type A that event of type B will occur. The belief is the source of the idea of necessary connection, not viceversa. Since the source of this belief is mere habit (nature, not reason or experience) ultimately we are unjustified in holding, e.g., that a cause always produces the same effect (Enquiry) and that every event has a cause (Treatise).

Sec VII: Liberty and necessity.
The idea of necessity arises from experience of constant conjunction which generates belief. Hence, all one should mean in saying that human actions are necessary is that they are found (and expected to be) constantly conjoined to events and states of affairs (e.g., stimuli and character). In this sense, human actions are (and taken to be) as necessary as natural events (the prisoner and the gaoler). True, bizarre behavior at times occurs, but the analogy is to earthquakes: both could be foreseen if we knew more.
H. takes the compatibilist view that liberty is lackof external impediments: as long as one can do what one intends to do, one is free.
NOTE: Compare with Lk.
Problems: Libertarianism? Brainwashing? Confusion of actus imperatus and actus elicitus?

Compatibilism is not only consistent with morality, but necessary for it.
Rationale:
We punish people on the basis of their actions because we consider the actions indications of their character which causes them (e.g manslaughter vs. premeditated murder). Similarly, we tend to pardon people whose character changed.
Problem: here H. seems to confuse responsibility with having grounds to plea for excuses. However, the point remains once the adjustment is made.
H. considers two objections: Determinism

raises problems of theodicy.

Removes moral responsibility

Sec. IX: Reason in Animals
Concerning matters of fact, higher animals "reason" like us (habit). However, we supass them in our capacity to draw inferences.
NOTE: Compare with Descartes

Sec. X: Miracles
Role of miracles in establishing religion (e.g., Lk. and Clarke).
H's definition of miracle: an event which violates a law of nature through the interposition of an invisible agent.
NOTE: Contrast with Lk and Clarke and compare with Leibniz.
H. provides two arguments against the view that we can reasonably believe that a miracle has occurred:

A-priori argument against miracles (from the very notion of miracle):
Even on the assumption (later shown false) that miracles have been related by decent witnesses, they cannot be accepted because:

A weaker evidence cannot overcome a stronger (from Tillotson critique of transubstantiation contrary to sense evidence)
The evidence for a law of nature is by hypothesis stronger than that for a miracle.
Hence, no testimony sufficient to establish miracle.

So, the report of queen Elizabeth dead, interred and reappearing 3 months later would not be reasonable.
NOTE: H's case of the "miraculous" eight days darkness on Jan 1 1600 reported by all everywhere would be believable because of the decay of the universe (Probably a reference to Newton's decay of force). However, in spite of H's misleading terminology, this would not be a miracle in the relevant sense.

A posteriori arguments
These rests on the claim that no reliable testimony for miracles has been in fact provided because:

Few miracles sufficiently attested by reliable witnessess
People are suckers because:

they like surprise and wonder (believe in travelers' accounts)
known fake miracles
miracles more abundant among ignorant and illiterate people (Alexander and the Phlegonians)

Miracles of different religions contradict each other.
Often people relating miracles are personally involved in the religions these miracles support. This makes them unreliable witnesses.

So, miracles can be accepted only by faith, like Scriptures (e.g., Pentateuch unbelievable if analyzed by reason).
However, some "miracles" apparently well attested (e.g., Tacitus's account of Vespasian's curing the lame; miracles on the tomb of Abbé Paris). In this case H. relies on the a priori argument.

Sec. XI: Critique of argument from design
The argument from design (vs. a priori arguments) acquired importance in early 1700's. H.'s point is that the argument is both (a) uncertain and (b) useless:

uncertain because:

reasonable to infer from effect to cause only when many cases observed in the past. But world/God is only one case.
analogy in this case is too vague (is the world like an artifact?)

useless for the ends of religion because

it does not allow to infer the perfection of God because the world does not seem perfect
even if perfection granted, it does not allow to infer that since the world is morally imperfect, there must be an afterlife in which things are put right. Can't go from effect to cause to how effect will be without further assumptions which arise from experience and which in this case are not given (only one world). Half finished house (reasonable to expect it finished because of past experience) vs. half finished world (only one case; no past experience).

Sec. XII: Academic and Sceptical philosophy
H. distinguishes between Academic (insulated) and Phyrronian (uninsulated) scepticism: the former, if taken to imply need for care in thinking and restraining from excessive speculation, is useful and correct; the latter cannot be actually held (the role of nature), .
For H., there are grounds for scepticism both with respect to matters of fact and relations of ideas:
Matters of fact:

Senses unreliable (square towers, bent oars etc.)
From Representationalism to external world

How Lk. fails to establish the existence of ext. world and that ideas correctly represent it (since we can't experience objects directly, we can't compare)
How D. fails (can't prove God exists and is benevolent)

Primary/secondary qualities upheld but unjustified, since both are perceived through senses. How the distinction originates in abstracting primary qualities from the mind. But the theory of abstract ideas is inconsistent (the whole point from Bk.)
Relation of cause/effect is ultimately unjustified
Bk's system as being both unbelievable and unassailable.

Relations of ideas:

Conflict between maths and common sense:

Infinite divisibility (levels of infinitesimals)
Angles of contact.

minimum sensibile

Infinite succession of discrete parts of time.