There is no doubt that Hume's compatibilism was a great influence on most analytic and logical empiricist philosophers, through John Stuart Mill, G. E. Moore, Bertrand Russell, A. J. Ayer, and Moritz Schlick.

But what distinguishes Hume's compatibilism from earlier compatibilists from Chrysippus to Thomas Hobbes?

On the surface, Hume's compatibilism contains a basic contradiction, one that calls into question the entire theory of causal mechanical determinism that was the basis of Hobbes' compatibilism. Hume showed that causality could not be proved logically from mere induction. For Hume, the necessity of causality was found in the human mind. But if necessity and causality are in the mind and not in nature, how can that explain the work of Isaac Newton, which Hume claimed as his model for the experimental study of human nature?

Hume's academic skepticism about logical proofs has withstood the test of time. There is nothing that can be shown to be logically true of the physical world. Unfortunately for Hume, that includes causality and strict determinism.

In his study of Morals we find another contradiction. Hume famously claims we cannot derive "ought" (logically and rationally) from "is." Yet he affirms the existence of "moral sentiments" which he says we know by direct observation and his experimental study of human nature.

Hume at first appears to state what G. E. Moore will later call the naturalistic fallacy, namely that "good" cannot be defined as corresponding to anything in nature. But then Hume proceeds to find moral sentiments in his human naturalism, studying man as a part of nature.

Hume has put strict limits on what we can know (or derive) from logical analysis. In this he anticipates Immanuel Kant's Critique of Pure Reason, where Kant says he must put limits on Reason to make room for belief in God, Freedom and Immortality.

Unlike Kant, who invented a metaphysical "noumenal" realm to locate our Freedom, Hume could not find God or Freedom in Kant's metaphysical sense. Kant called Hume's compatibilist freedom a "wretched subterfuge."

Most of Hume's followers ignore his skeptical doubts about certain knowledge and causality. Many philosophers of science continue to claim they can put a sound epistemological foundation under physics, probing to find fault with quantum mechanical uncertainty. Many philosophers of mind continue to assert the truth of compatibilism, though under pressure from the success of indeterministic quantum physics, most now claim to be agnostic about the truth of physical determinism.

...there is but one kind of necessity, as there is but one kind of cause, and that the common distinction betwixt moral and physical necessity is without any foundation in nature. This clearly appears from the precedent explication of necessity. 'Tis the constant conjunction of objects, along with the determination of the mind, which constitutes a physical necessity: And the removal of these is the same thing with chance. As objects must either be conjoin'd or not, and as the mind must either be determin'd or not to pass from one object to another, 'tis impossible to admit of any medium betwixt chance and an absolute necessity. In weakening this conjunction and determination you do not change the nature of the necessity; since even in the operation of bodies, these have different degrees of constancy and force, without producing a different species of that relation.
(Treatise, Book I, Part I, Section XIV, p.171)

Of all the immediate effects of pain and pleasure, there is none more remarkable than the WILL. I desire it may be observ'd, that by the will, I mean nothing but the internal impression we feel and are conscious of, when we knowingly give rise to any new motion of our body, or new perception of our mind.

'Tis universally acknowledg'd, that the operations of external bodies are necessary, and that in the communication of their motion, in their attraction, and mutual cohesion, there are not the least traces of indifference or liberty. Every object is determin'd by an absolute fate to a certain degree and direction of its motion, and can no more depart from that precise line, in which it moves, than it can convert itself into an angel, or spirit, or any superior substance. The actions, therefore, of matter are to be regarded as instances of necessary actions; and whatever is in this respect on the same footing with matter, must be acknowledg'd to be necessary. That we may know whether this be the case with the actions of the mind, we shall begin with examining matter, and considering on what the idea of a necessity in its operations are founded, and why we conclude one body or action to be the infallible cause of another. (Treatise, Book II, Part III, Section I, p.399-400)

I dare be positive no one will ever endeavour to refute these reasonings otherwise than by altering my definitions, and assigning a different meaning to the terms of cause, and effect, and necessity, and liberty, and chance. According to my definitions, necessity makes an essential part of causation; and consequently liberty, by removing necessity, removes also causes, and is the very same thing with chance. As chance is commonly thought to imply a contradiction, and is at least directly contrary to experience, there are always the same arguments against liberty or free-will. If any one alters the definitions, I cannot pretend to argue with him, 'till I know the meaning he assigns to these terms.

I believe we may assign the three following reasons for the prevalence of the doctrine of liberty, however absurd it may be in one sense, and unintelligible in any other. First, After we have perform'd any action; tho' we confess we were influenc'd by particular views and motives; 'tis difficult for us to persuade ourselves we were govern'd 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 we are not sensible. Few are capable of distinguishing betwixt the liberty of spontaneity, as it is call'd in the schools, and the liberty of indifference; betwixt that which is oppos'd to violence, and that which means a negation of necessity and causes. (Treatise, Book II, Part III, Sections I-II, p.407)

By liberty, then, we can only mean a power of acting or not 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 every one who is not a prisoner and in chains. Here, then, is no subject of dispute. (Enquiry, p.95)

...liberty when opposed to necessity, not to constraint, is the same thing with chance; which is universally allowed to have no existence. (Enquiry, p.96)

Though there be no such thing as Chance in the world; our ignorance of the real cause of any event has the same influence on the understanding, and begets a like species of belief or opinion.
(Enquiry, Book VI, Of Probability, p. )

Of Liberty and Necessity, Chapter 8, Enquiry Concerning Human Understanding (1750)

Chapter 6.6 - Language	Chapter 6.8 - Progress
Part Five - Problems	Part Seven - Afterword