Impressions are one of the two basic kinds of thing that the mind contains (ideas are the other one). When I talk about impressions, I'm talking about all our "more lively perceptions" (source)—that is, everything we are immediately seeing, hearing, feeling, or otherwise experience.
The sight of your fingers perched on top of your keyboard at this very moment, or the smell of that coffee right now deliciously wafting up into your nose? Humean impressions. If it's happening in the here and now, and if it's happening without you having to really think about it, you can bet it's an impression.
Ideas are the other kind of thing that the mind contains. I know what you're thinking: "Hume says that the mind is made up of… ideas? Not concrete blocks or maple syrup? Wow, he truly was a genius! No ordinary mortal could have such an insight."
All right, I know, I know—believe me, I've heard this before. But actually, I'm using the word "idea" in a special sense here. For me, an idea is not just any old thing in the mind; it's a copy or an image of an impression. Therefore, it is "faded," less "forcible and lively," less vivid than an actual impression (source).
Picture it like this: my memory of that great coffee I was smelling yesterday is less intense and vivid than the original perception of that coffee. That memory—or idea—is only a copy of that impression, after all.
So, to take another example, the black marks on this computer screen are your impressions, but your thoughts about what you ate yesterday, or about what you might be eating shortly, or even the thoughts stimulated by the words you're reading—those are all ideas.
Ideas can be combined and augmented in all manner of ways in order to arrive at the full complexity of thought. The point, in short, is that all the contents of the mind are either impressions gained through immediate experience, or they are ideas, which are ultimately traceable back to such impressions.
Matters of Fact
I say there are only two types of assertion (or two types of sentence): matters of fact and relations of ideas. A matter of fact is any claim that is based on experience. If I say, for example, "This book is red," then I'm stating a matter of fact. I can see that this book is red, so I'm making this statement based on my experience of the book.
Now, given that all matters of fact are empirically based, they are never certain, but always contingent—it's possible that they could be different than they are. The book is red, but it wouldn't have to be. After all, it could have been blue, or maybe even covered with pink polka dots."
Relations of Ideas
Relations of ideas are the other main type of assertion. These include the claims of mathematics and logic, as well as assertions that are true by definition, like the assertion: "All bachelors are unmarried." Unlike matters of fact, relations of ideas are necessary statements, statements that cannot be imagined to be otherwise. Can you imagine two plus two not equaling four? You can't.
I insightfully point out that the "necessity" here is simply the result of the way we have combined the ideas in our assertions. That is, all relations of ideas are true or false only by virtue of the meanings of the words involved, and so they do not give us any information about the world. Translation: "2+2=4" tells us something about how the terms '2' and '+' and '=' and '4' are related in our system of arithmetic, but no more than that.
I challenge the notion that there is a "necessary connection" between a cause and its effect. Sure, it seems pretty natural to suppose that if one thing causes something else to happen, then there is some kind of necessity or determination involved in this relationship—a power or force that binds cause to effect.
For example, if one billiard ball strikes another, it seems that as long as the second ball is not glued down to the table, then it must move at this point. It seems like a guaranteed outcome, sort of in the way that two and two must always equal four.
But clever me—I manage to show that no matter how "natural" and unavoidable this assumption seems to be, there is actually no basis to it whatsoever. Why not? Because of a little thing called constant conjunction, of course. Read on.
I believe there's a song in here somewhere. Maybe something like: "Constant conjunction, junction, what's your function?" Somehow, it doesn't quite fit; perhaps one of my successors can work on this idea.
In any case, this is a term that I really want my readers to remember. It describes what we actually observe when we say that two events are causally linked—namely, nothing more than the "constant conjunction" of those events.
When someone says that one billiard ball causes a second billiard ball to move, all this person actually means is that the two events—ball A striking ball B, and ball B beginning to move—have been observed to be "constantly conjoined" or to always have occurred together. We do not ever see any "hidden springs" (source) secretly connecting a cause to its effect.
Basically, cause and effect is all in our minds. We can't ever see the "hidden springs" of cause and effect in action, so we have no empirical basis for thinking that cause and effect is a real thing.
In my critique of causality, I kind of make it sound as if we simply have no reason to accept the notion of causality. The question is, why then do we all believe in causality, then? Why do we all have a strong expectation that upon seeing the occurrence of a particular event (say a wine glass falling on a concrete floor), it will be followed by a familiar outcome (the glass shattering)? Are we just deluded?
I explain that this is all just a matter of custom or habit. In other words, objectively, there is nothing we observe that warrants our belief in a causal connection. Instead, the expectation of a particular outcome is just part of our psychology, part of the way we are built. It's how we tend to operate.
This is a "skeptical solution" not because I'm doubtful that it really is the answer. Au contraire—I am very sure of myself when I make this claim. I call this claim "skeptical" because I know it doesn't seem like a complete answer to most people. Basically, we don't want to hear that our belief in causality is just a matter of habit.
My moral and aesthetic theory is sometimes referred to as "sentimentalism." Now, I will admit to having to wipe away a few tears when I hear the bagpipes playing "Scotland the Brave." Who doesn't? But, actually, my theory is only called sentimentalism because I attribute such importance to the sentiments or feelings.
For me, neither moral nor aesthetic judgment can be based in reason. Like it or not, it is ultimately emotion that is at the core here. That's what I mean in my oft-quoted remark from A Treatise of Human Nature: "Reason is and ought only to be the slave of the passions."