Hume on Induction

I. Hume on Induction
Causal inferences are essentially inductive inferences. They go from “constant conjunction” in the past to constant conjunction in the future. Hence, for example, we infer that the sun will rise tomorrow because we have seen it rising in the past.
Hence they will work only on the assumption that a resemblance principle, “The future will resemble the past,” is a good one.
II. The sun will come up tomorrow. Bet your bottom dollar that tomorrow, we’ll have sun.
The argument has to go something like this:
1) In the past, the sun has risen every day.
2) The laws of nature will continue to operate in the future just as they have in the past.
3) Therefore, the sun will rise tomorrow.
III. Justifying the resemblance principle
By what reasoning can we justify the resemblance principle? By relations of ideas? Is it a contradiction to say that although the sun has risen every day in the past, it won’t rise tomorrow? The past is, after all, the past, and we are talking about the future here. So it has to be based on experience.

IV. Why is this argument circular?
In the past, I have observed numerous cases where two events have been consistently conjoined together.
It has always been the case at a future time that these same pairs of events continued to be conjoined.
Therefore, the laws of nature will continue to operate in the future just as they have in the past.
V. Begging the question
Attempting to support the resemblance principle seems to be a doomed enterprise, once we grant Hume’s fork. Since it’s not contradictory to deny it, it can only be defended by an argument based on experience. But past experience is only relevant to the future if there is a resemblance between the future and the past.
VI. So do we stop making inductive inferences?
Hume says, of course not. First we can’t help making them. It comes naturally to us. Second, it is practical for us to continue to make them—we couldn’t guide our lives without making past-to-future inferences. So if a hot stove has burned us in the past, we are perfectly justified in supposing that it will burn us in the future, even though we have no argument in defense of the claim that the future will resemble the past.
VII. What is the great guide of life?
According to Hume, it’s custom. This reverses the idea many people have that we have to examine our customary beliefs to see if they can stand up to philosophical analysis.