Hume seeks to show that we have no basis for making inductive inferences. An inductive inference is a conclusion drawn from observations. The sun has risen every day in the past, therefore it will rise tomorrow. That is an example of an inductive inference.
What Hume is saying is that the fact that the sun has risen every day in the past gives us no reason to believe it will rise tomorrow.
There are two parts to this chapter.
In the first part, Hume lays out the problem. As he sees it, you can know everything there is to know about a thing and still not know what effects it can bring about.
The argument works by considering two possible sources of knowledge. Either we know something by comparing ideas with one another or we know it by considering matters of fact. The first kind of knowledge is demonstrative knowledge. A conclusion known this way is certain: 2 + 2 = 4, for example. Knowledge based on matters of fact is only probable: the conclusion is probably true, given the facts that you know, but it might be false. Given that it has risen every day, I think it is probable that the sun will rise tomorrow. But it is logically possible that it will not. I can imagine the sun failing to rise but I cannot imagine 2 + 2 = 5.
Back to the question. Can you know what effects a thing can bring about just by thinking about your idea of that thing? Hume says no. Take any object and you can imagine it producing almost any effects. So your idea of an object does not tell you which effects it can bring about.
That means that our knowledge of cause and effect must depend on matters of fact or probable reasoning.
You probably think this is obvious. I want to spend some time talking about why Hume thought he had to go on so long to establish this point.
Part 2 is about why experience does not allow us to make inductive inferences.
In paragraph 16, Hume says that we need a “medium” between our observations of cause and effect relations in the past and our inferences about what will happen in the future. To use his language, we need a proposition to fit between points 1 and 3 (¶16).
I have found that such an object has always been attended with such an effect
The “medium” proposition goes here.
I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects.
To jump ahead a bit (¶21), this is what Hume thinks fits the bill.
I have found that such an object has always been attended with such an effect.
The future will resemble the past in that similar powers will be conjoined with similar sensible qualities. (For short, “the future will resemble the past.”)
I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects.
How can we establish that the future will resemble the past? Again, there are two possibilities. We could know that the future will resemble the past by demonstration, that is, by comparing the idea of the past with the idea of the future. Or we could know that the future will resemble the past through probable reasoning, by drawing inferences from observed facts.
Hume takes up these two alternatives in paragraphs 18 and 19.
We are going to be especially interested in paragraph 19, where Hume says attempts to show that the future will resemble the past using probabilistic reasoning “must be evidently going in a circle, and taking that for granted, which is the very point in question.”
Here is a homework assignment: draw the circle! Not literally. (You do not have to find a piece of string.) Do it like this.
Start at 12 o’clock and put down “the future will resemble the past.”
Draw an arrow to 6 o’clock. At 3 o’clock write down “why should we believe that?”
Put the answer at 6 o’clock.
Then draw another arrow to 12 o’clock. At 9 o’clock, write “why should we believe that will still be true in the future?”
When you know what to put at 6 o’clock, you will understand Hume’s argument.