David Hume's Theory of Free Action
1. The texts
Hume wrote two main works on philosophy. They are similarly structured but very different concerning style and length.
1) "A Treatise of Human Nature" (1740), in what follows: T, 700 pages, written between the age of 21 and 25, hard to read, hardly sold after publication, today a classic.
2) "Enquiries Concerning Human Understanding and Concerning the Principles of Morals" (last edition during Hume's life: 1772), in what follows: E1 und E2, 340 p., more elegant but not always as interstingly argued as T, more successful.
Humes theory of free action is contained in:
T, Book II "Of the passions", part III "Of the will and direct passions", section 1-2 "Of liberty and necessity", section 3 "Of the influencing motives of the will", Penguin paperback edition (London 1969) S. 447 - 465; Selby-Bigges edition (Oxford 1978), pp. 399-427.
E1, Section VIII, Part I §§ 62-74, part II §§ 75-81, Selby-Bigges edition (Oxford 1975) pp. 80-103.
2. The aim: the reconciliation of "necessity" and "liberty"
Hume aim is a "reconciling project with regard to the question of liberty and necessity" (E1 §73, S.95). This conforms, Hume says, to common sense:
"All men have ever agreed in the doctrine both of necessity and liberty, according to any reasonable sense which can be put to these terms." (E1 §63, p.81).
3. The "doctrine of necessity"
3.1. The content of the "doctrine of necessity"...
...is, in Hume's words: "The conjunction between motives and voluntary actions is as regular and uniform as that between the cause and effect in any part of nature" (E1 §69, p.88)
3.2. The pragmatic argument for the "doctrine of necessity"
We just rely every day on the maxim that:
"There is a great uniformity among the actions of men" (E1 §65, S.83)
This may be illustrated as Hume does in T:
"A prince, who imposes a tax upon his subjects, expects their compliance. A general, who conducts an army, makes account of a certain degree of courage. A merchant looks for fidelity and skill in his factor... A man, who gives orders for his dinner, doubts not of the obedience of his servants... whoever reasons after this manner, does ipso facto believe the actions of the will to arise from necessity." (T p.454/405, The first reference refers to the Penguin, the second one to the Selby-Bigges edition.)
In E1 he analyses some basic motives as constants of human action:
"The same motives always produce the same actions: The same events follow from the same causes. Ambition, avarice [Geiz], self-love, vanity, friendship, generosity, public spirit ... have been from the beginning of the world, and still are, the sources of all the actions and enterprises, which have ever been observed among mankind. Would you know the sentiments [...] and inclinations [...] of the Greeks and Romans? Study well the temper and actions of the French and English..." (E1 §65, p.83)
History, politics, ethics and literature would be impossible without the belief that human actions are caused by motives (E1 §70):
"It seems almost impossible [...] to engage either in science or action of any kind without acknowledging the doctrine of necessity, and this inference from motives to voluntary actions, from character to conduct." (E1 §70, p.90)
3.3. The paradox of the "doctrine of necessity"
"All mankind, though they have ever, without hesitation, acknowledged the doctrine of necessity in their whole practice and reasoning, have yet discovered ... a reluctance to aknowledge it in words..." (E §71, p.92)
3.4. Objections against the "doctrine of necessity"
Hume discusses several objections against the "doctrine of necessity":
3.4.1. General objections
A) The uniformity thesis is wrong. For:
a) Different people behave very differently.
b) "Necessity is regular and certain. Human conduct is irregular and uncertain"(T p.451/403)
B) "Can't I raise my arm just like that if I wish...?"
C) You can't justify punishment if the "doctrine of necessity" is true: "necessity utterly destroys all merit and demerit either towards mankind or superior powers" (T p.459/411)
D) If the "doctrine of necessity" is true then all action, also all evil deeds, have been predetermined by God and it's all God's fault, not ours (E1 §78, p.99, not in T)
E) If the "doctrine of necessity" is true, we are the slaves of our passions. But shouldn't reason rule the passions?(T. 460-465/413-418, not in E1)
3.4.2. Objections from the concept of causation
F) The doctrine of universal causation is applicable only to the material realm but not to the mental realm.
G) If the "doctrine of necessity" were true we would be forced by natural necessity to do the things we do.
"After we have perform'd any action; tho' we confess we were influenc'd by particular views and motives; 'tis difficult to persuade ourselves we were governed by necessity, and that 'twas utterly impossible for us to have acted otherwise; the idea of necessity seeming to imply something of force, and violence, and constraint, of which [, however,] we are not sensible." (T S.455/407, indirectly also E1 §75, p.97, T 454, 457f/406, 408f)
So...: "When [we] turn [our] reflections towards the operations of [our] own minds, and feel no [...] connexion of the motive and the action, [we...] thence [...] suppose, that there is a difference between the effects which result from material force, and those which arise from thought and intelligence" (E1 §71, p.92)
Therefore the "doctrine of necessity" must be wrong.
3.5. Hume's answers to the general objection
Ad A) a) Different people - sure! But they've got different characters...
b) (i) This depends on the perpective you have. Take clouds (E1 p.88). They seem chaotic, but aren't we convinced that the follow the laws of physics, only that much about them depends on "conceal'd causes" (T 451/404) or a "secret operation of causes" (E §67, p.87)? It's just the same with human beings (T 456/408f, E1 p.87f.).
(ii) "the characters of men are, to a certain degree, inconstant and irregular. This is, in a manner, the constant character of human nature." (E1 §68, p.88)
Ad B) "We feel that our actions are subject to our will on most occasions, and imagine we feel that the will is subject to nothing. [But] whatever capricious and irregular actions we may perform, as the desire of showing our liberty is the sole motive of our actions; we can never free ourselves from the bonds of necessity. We may imagine we feel a liberty within ourselves; but a spectator can commonly infer our actions from our motives and character; and even where he cannot, he concludes in general that he might..." (T 456/408)
Ad C) Just the contrary is true: We can't justify punishment if the "doctrine of necessity" is wrong (T 459/411)!
(i) If the aim of punishment is prevention: "as all human laws are founded on rewards and punishments, 'tis supposed as a fundamental principle, that these motives have an influence on the mind, and produce the good and prevent the evil action." (T 458/410)
(ii) If the aim of punishment is retaliation: If an action were not the effect of character we should have to say that: "The action itself may be blameable...But the person is not responsible... nor is his character any way concerned in his actions; since they are not derived from it... (T459/411).
Ad D) Hume's answer is unusually unclear (E1 §78, p.99-103, not in T): It's all a mystery. It may be assumed that this is irony and that his real answer is that theists' problems are not his problems.
Ad E) The picture behind E) is traditionally held to be true, but nevertheless completely false: "Reason alone can never be a motive to any action of the will. [Reason] can never oppose passion in the direction of the will. [...] Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them." (T 462/415)
The conflict described in E) is really between "calm passions" and "violent passions" (ibid.).
3.6. Hume's answer to the objections from the concept of causation
3.6.1. Hume's theory of causation...
"'Tis constant union alone with which we are acquainted; and 'tis from from the constant union the necessity arises... the necessity, which enters into that idea, is nothing but a determination of the mind to pass from one object to its usual attendant, and infer the existence of one from that of the other." (T 448/400)
"The necessity of any action, whether of matter or of the mind, is not properly a quality in the agent, but in any thinking and intelligent being, who may consider the action, and consists in the determination of his thought to infer its existence from some preceding objects... (T 455f/408, E1 94))
3.6.2. ... and what follows from it as an answer to the objections
Ad F) If causation is somehow "in the observer" then psychophysical causation is no problem: "The same experienced union has the same effect on the mind, whether the united objects be motives, volitions or actions." (T p.454/406f)
Zu G) If (in lucky cases) the motive is not force this does not mean that there is no relation of cause and effect between motive and action. For someone who has grasped that causation is somehow "in the observer" will not assume any longer that causal relations between physical objects is "something of force, and violence, and constraint, of which we are not sensible" in the first place. Instead, he will say that the succession of motive and action and the succession of the billiard ball's being pushed and its rolling away do not differ in the presence of any force in the second case and the absence of it in the first case. There is only regular succession in both cases, and this is all we can expect from a causal relation:
"Let no one [object] that I assert the necessity of human actions, and place them on the same footing with the operations of senseless matter. I do not ascribe to the will that unintelligible necessity, which is suppos'd to lie in matter. But I ascribe to matter that intelligible quality, call it necessity or not, which the most rigorous orthodoxy ... must allow to belong to the will [predictability]. I change, therefore, nothing in the receiv'd systems with regard to the will, but only with regard to material objects." (T p.457f/410)
4. The "doctrine of liberty"
Hume makes a difference between two kinds of liberty:
" that [liberty] which is oppos'd to violence [liberty of spontaneity]
 and that which means a negation of necessity and causes [liberty of indifference]."(T455/407)
" liberty, ... when opposed to constraint"
" liberty, when opposed to necessity..."(E1 §74, p.96)
Hume believes that there is liberty according to  but not according to :
"The first is even the most common sense of the word; and as 'tis only that species of liberty, which it concerns us to preserve, our thoughts have been principally turn'd towards it, and have almost universally confounded it with the other." (T 455/407f)
"liberty, when opposed to necessity... is the same thing with chance; which is universally allowed to have no existence." (E1 §74, p.96)
"What is meant by liberty, when applied to voluntary actions? We cannot surely mean that actions have so little connexion with motives [...] that one affords no inference [to] to the existence of the other. [...] By liberty [when applied to voluntary actions], then, we can only mean a power of acting or not acting according to the determinations of the will; that is, if we choose to remain at rest, we may; if we choose to move, we also may. Now this hypothetical liberty is universally allowed to belong to everyone who is not a prisoner and in chains." (E1 §73, p.95)
5. The compatibility of the "doctrine of necessity" and the "doctrine of liberty"
Hume's opinion is: liberty according to  is compatible with the "doctrine of necessity", liberty according to  isn't. But liberty according to  doesn't exist anyway, since there is no chance in nature. Liberty according to  suffices in order to justify punishment. So the kind of liberty there is is also just the kind of liberty we want.
6. Big Questions (to my knowledge unsolved)
1) Is a regularity theory of causation compatible with the doctrine of necessity?
2) Is liberty according to  not counter-intuitively weak?
3) "It follows from this definition of a cause, that night is the cause of day, and day the cause of night. For no things have more constantly followed each other since the beginning of the world." Thomas Reid (1710-1796), Of Arguments for Necessity, Collected Works p.627. How is this objection to the regularity theory to be evaluated?
4) Does compatibilism depend on the regularity theory of causation?
5) Does Hume have a regularity theory of causation?