Can someone please clarify the following points for me?
1. How does Hume define 'real' causation, in order to contrast it with mere habitual association? Unless 'cause' is clearly defined, the statement 'we cannot know what can cause what' has no meaning. I suggest it means 'force' or 'compel': when we say that heat causes metal to expand, we mean (albeit without proper justification) that it makes it expand.
Hume defines causation as any two objects* which we consistently observe to be contiguous, and the one to be precedent to the other. Reasoning by causation means that when we receive the impression of a cause or effect, our mind is driven by habit to consider the idea of the related cause or effect with a liveliness approaching an impression. Also, when we observe an object which shares similarities with a cause or effect we are familiar with, we expect it to have been produced by, or to produce a similar cause or effect. However this expectation is attended by some uncertainty untill verified by direct experience.
*(This term has to include objects, and also their particular qualities, which being distinguishable by the mind can be considered seperately, and therefore can be considered as causes or effects on their own. Using the term impressions might be more accurate but probably also more confusing.)
As we discover, through science, ever more intricate qualities of physical objects, by careful experimentation we find which of these subtle qualities are the causes of certain effects. These discoveries are still arrived at through experience, the experiments scientists carry out demonstrate which specific causes are attended by certain effects.
When you say that causation means one object "forces" or "compels" another, you do not imply anything different about the objects than if you were to say that there is a constant conjuction between certain causes and effects. If you insist that there is a necessary connection, this insistence does not change any of the characteristics of the objects, it only changes our feelings towards these objects.
Try it, think of any cause and its effect. First imagine them only as being constantly united in their operation, without forming the idea that they MUST be united so. Repeat several times. Next consider the same cause and effect, but try to imagine the one object as possessing some power or efficacy which necessitates the connection. If this causes a difference in your ideas of the objects themselves, then this difference should be distinguishable and seperable by the mind, to be considered in its own light.
The actual origin of the idea of Force or Necessity which we form comes from the sensation of compulsion we feel in our own thoughts to proceed from the idea of a cause to the idea of its effect. This compulsion we feel is the force of habit. To apply this to our objects is an error in judgement. Just because we feel such a compulsion in our own minds to pass from the idea of a cause to its effect is not evidence that objects themselves labor under some such compulsion. Given that our impressions and the objects they represent really are different, it can only be reasoned that the connections and repulsions we observe between objects must also apply to our impressions, and this is only necessary because we are incapable of considering otherwise. It is not logically necessary that the connections and repulsions we observe between our impressions must apply to the objects they represent as well.
Thus, the only just definition we can give of a cause, is any thing, which we discover by experience to constantly be contiguous and precedent to some other thing.
2. Did Hume believe that it might be possible - perhaps in the distant future - to find a necessary connection between such things as heating and expansion? Or did he think this was impossible in principle?
I rather think Hume considered our idea of necessary connection to be flawed and chimerical, and that he would hope we would one day abandon it as unreasonable. Personally, I consider it a subtle kind of anthropomorphization.
3. Did he believe that there could actually be real causation even if we could never know about it?
I don't think Hume would even consider it, as attempting to answer such a question could only lead us into errors and contradictions. I think that above all he believed that we must rest content with our ignorance once we've taken our reasoning as far as we can, and to accept the limitations we face. The causation that we experience and reason concerning, is *real* causation, and we can hope for nothing more.
4. If two very accurate adjacent clocks have been set so that one always strikes the hour exactly 10 seconds after the other, a person encountering them would not say that one causes the other to strike. So there must be more to the common idea of causation than just habitual association. Did Hume acknowledge this?
Because we already have experience of clocks and how they work. We know that they are governed by their internal machinery, and that they tend to operate in a similar manner wherever we have occasion to encounter them. To form the idea that the striking of one clock causes the striking of the other would contradict reason, and this holds true even if human reasoning is nothing but a customary transition between certain ideas.
If you want examples of strange causal connections that people form based on nothing but the experience of constant, or even inconstant conjuction, superstition will provide you with plenty.