I'm thinking of laws as being descriptions of observed regularities... You seem to be talking about the theory side. — Janus
Yes, I suppose so. So how to proceed. I suspect that, as with most of these sorts of problems, it's as much about the choice of wording as the way things are. We agree that there are regularities, and that "what we say about things is not the things themselves, and we should try to match what we say with what happens".
I'm interested in the move from what Apo calls "the specific to the general". And I take this to be the focus of Hume's scepticism. Incidentally, that word, "scepticism", seems to frighten some folk (
@Count Timothy von Icarus), as if Hume were showing that science
can't work - quite the opposite, as
@unenlightened points out. Better, Hume takes science as granted, and looks to see how it might work; finds that it can't be based on a logical deduction, and looks for an alternative.
Since it was questioned, let's go over the logic of induction again. Apo said
To go from the particular to the general isn’t that hard to understand surely? — apokrisis
But yes, that is exactly the problem. The move from any finite sequence of specific statements to a general statement is invalid. More formally, from f(a), f(b), f(c)... we cannot deduce U(x)f(x). This is the "scandal of induction". It is a philosophical problem - scientists and engineers just move on without paying it much attention. But it is part of the plumbing of our understanding of the world, and will niggle at those who worry about such things.
And Hume's response is much the same as that of the scientists and engineers mentioned above - just move on. He talked of moving on as a "habit". Since his time others came up with other suggestions. Most famously, perhaps, is falsification, a very clever response. Instead of proving that U(x)f(x), why not assume it and look for a counter-instance - and x that is not f? We can't prove an universal, but we can disprove it... or so Popper supposed. There are problems there, too, of course.
Now all of this is the standard history of the philosophy of science - regardless of what some here think. The scandal of induction has been the central problem for philosophy of science. Check me on this, if you like. There is a distinct eccentricity in suggesting otherwise, presumably a consequence of a desire to highlight the role or Pierce. Quite specifically, neither Pierce's version of abduction, nor the more recent variations, have satisfactorily answered Hume. And by "satisfactorily" here I mean that it has not gained any general acceptance as a way around the scandal. See the SEP articles for more on this. Point is, I'm right about it. Where the answer sits at present is more in Bayesian Calculus, which accepts Hume's point, and instead of looking to justify our scientific theories as
true, looks to choose which ones are most believable.
That is the topic of this discussion, so far as I can see.
Now I don't think you and I, and even Apo and I, are really very far from agreement on this. It is, after all, what happened. But the narcissism of small differences keeps the posts... interesting.
The acrimony is a shame, but Apo and I have butted heads since before this forum came about. He's convinced by a form of pragmatism that I find wanting, and as is my want, I like to point out the problems with such things.
By the way, since it is a concern of yours, I did prepare this post using AI. I fed paragraphs in, read the response and then edited the text so as to account for issue identified by the AI. Some of the wording was changed as a result, I think for the better, or I wouldn't have made the change. It perhaps also helped in setting a less aggressive tone than i might otherwise have chosen. I believe this is well within the guidelines of the forum. If you don't like that, you do not have to read my posts.