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Just because the sun rises every day, doesn’t mean it will rise tomorrow. Hume points out that the former doesn’t imply the latter.

But he also argues that it doesn’t even imply that it is probable that the sun will rise tomorrow. But given that the very word probably means different things to different people, what exactly is he arguing against?

From a betting perspective, it seems obvious that one should bet literally as much money as they have on the prospect of the sun rising tomorrow. Is this also unjustified? Why isn’t the very idea of someone who would have bet on this literally winning every single time in history not a good rationale for this being justified?

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  • What Hume does argue is that even there is no guarantee that future experiences will be the same as past ones, we will nonetheless continue to expect that associations that we have experienced in the past will continue in the future, not because of reason, but because of habit. After some rather dubious manoeuvres he decides that uniform part experience is an indubitable basis for future expectations and as good as a proof. Philosophers regard this as a poor substitute for a rational argument. They're quite right, of course.
    – Ludwig V
    Commented May 7, 2023 at 21:47
  • But Hume is also quite right. Philosophers who think that induction is no basis for predictions continue to expect that the sun will rise tomorrow morning. To make any money on your bet about tomorrow's sunrise, you have to find someone who will bet that it won't rise. Good luck!
    – Ludwig V
    Commented May 7, 2023 at 21:48

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"But he also argues that it doesn’t even imply that it is probable that the sun will rise tomorrow. But given that the very word probably means different things to different people, what exactly is he arguing against?"

The definition of the word "probable" doesn't really matter... whatever it means, Hume's point is that just because the universe operated a certain way in the past... it doesn't simply logically follow that the universe will behave the same way in the future. Whatever the prediction is that people are making, it will have the same inductive problem.

"From a betting perspective, it seems obvious that one should bet literally as much money as they have on the prospect of the sun rising tomorrow. Is this also unjustified? Why isn’t the very idea of someone who would have bet on this literally winning every single time in history not a good rationale for this being justified?"

It begs the very question. You're making a prediction about the future based on past events, and so the inductive problem presents itself. We have a certain intuition that if the universe operates a certain way in the past, that gives us some information about the future. Hume's point is that we cannot make a logical deduction from past to future.

We need to inject some other principle like the future will resemble the past to make our justification. But we can't get the principle "the future resembles the past" from the mere fact that in the past, "the future resembled the past". So the question is... how do we get such a principle?

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How does Hume get rid of the problem of induction "probabilistically"?

I’m unclear about what you mean by "probabilistically". I would say that Hume nominally solves the problem, but only psychologically.

At the center of the problem lies the Uniformity Principle, the notion that the future will resemble the past. Many philosophers, such as Hume, conclude that there is no justification for the Uniformity Principle. They hold that the principle is a subjective belief supported by common observations and expectations about nature, and nothing more.

Hume himself ascribes belief in the principle to “general habit, by which we always transfer the known to the unknown…”. Hume considers such expectations part of humanity’s “natural instincts”. In other words, says Hume, the source of this belief is wishful thinking.

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  • "In other words, says Hume, the source of this belief is wishful thinking." Hume doesn't say or imply anything like that. As you say, the principle is based on general habit, arising from the way that we continue to associate ideas that have been "contiguous" in the past. It's not, as I understand it, something that we do - i.e. are in control of, and so not wishful. In any case, it applies to things we want to happen AND to things that we don't want to happen.
    – Ludwig V
    Commented Jun 7, 2023 at 11:41
  • Officially, he doesn't even pretend that we are justified in doing so. The process by which he arrives at calling past experience a proof is somewhat convoluted, not to say shifty (IMO). See his footnote on Locke in Enquiry Section 6.
    – Ludwig V
    Commented Jun 7, 2023 at 11:45

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