Let's return to the issue of causality. If Hume is right that most of our beliefs about matters of fact are grounded by claims about causality, then maybe we can find a way around the problem of induction by defending a robust conception of causality.
Section VII: Of the Idea of Necessary Connexion
p. 514 "There are no ideas, which occur in metaphysics more obscure and uncertain, than those of power, force, energy or necessary connexion, of which it is every moment necessary for us to treat in all our disquisitions. We shall, therefore, endeavour in this section, to fix, if possible, the precise meaning of these terms, and thereby remove some part of that obscurity, which is so much complained of in this species of philosophy."
Given Hume's concept empiricism, what must be the source of the "precise meaning"?
p. 515 "When we look about us towards external objects, and consider the operation of causes, we are never able in a single instance, to discover any power or necessary connexion; any quality, which binds the effect to the cause, and renders the one an infallible consequence of the other. We only find, that the one does actually, in fact, follow the other. The impulse of one billiard-ball is attended with the motion in the second. This is the whole that appears to the outward senses. The mind feels no sentiment or inward impression from this succession of objects: Consequently, there is not, in any single, particular instance of cause and effect, anything which can suggest the idea of power or necessary connexion."
But maybe the idea comes from reflection.
p. 516 "It may be said, that we are every moment conscious of internal power; while we feel, that, by the simple command of our will, we can move the organs of our body, or direct the faculties of our mind. An act of volition produces motion in our limbs, or raises a new idea in our imagination. This influence of the will we know by consciousness. Hence we acquire the idea of power or energy; and are certain, that we ourselves and all other intelligient beings are possessed of power."
What are Hume's objections to this idea? He defends three objections on pages 345-6 to the claim that we acquire the idea of power from our experience of moving our limbs, and three more objections to the claim that we acquire the idea of power from our experience of directing our own mind. Evaluate those objections.
(pp. 519-20) Part II: . . ."We have sought in vain for an idea of power or necessary connexion in all the sources from which we could suppose it to be derived. It appears that, in single instances of the operation of bodies, we never can, by our utmost scrutiny, discover any thing but one event following another; without being able to comprehend any force or power by which the cause operates, or any connexion between it and its supposed effect.. . . All events seem entirely loose and separate. One event follows another; but we never can observe any tie between them. They seem conjoined, but never connected. And as we can have no idea of any thing which never appeared to our outward sense or inward sentiments, the necessary conclusion seems to be that we have no idea of connexion or power at all, and that these words are absolutely without any meaning, when employed either in philosophical reasonings or common life. . . . The first time a many saw the communication of motion by impulse, as by the shock of two billiard balls, he could not pronounce that the one event was connected: but only that it was conjoined with the other. After he has observed several instances of this nature, he then pronounces them to be connected."
So--what is Hume's view of causality? He defines "cause" on page 521. What is that definition? What is the relation between that definition and his concept empiricism?