Given that inductive reasoning is possible and that that it is (in the case of Solomonoff induction) on very solid philosophical and mathematical footing, I'm skeptical of any book which claims it's impossible.
The question is not whether or not it is possible (in the sense that it is useful) but whether it leads to knowledge. This, of course, depends on your definition of knowledge, which is the question of epistemology. In some circles these days there is a move back to a utilitarian definition of knowledge, namely, if you can interact with a system and predict its behavior then you can say you know how it works, because your model is useful. This is not, however, the commonly accepted view of what constitutes knowledge.
Funny thing: the consequence of the Gettier problem (sort of like the "incompleteness conjecture" of epistemology) is that either we must accept a very unsatisfying definition to what constitutes knowledge, or use a good, rigorous and satisfying definition and then find out that nothing we think we know actually qualifies.
It isn't logically possible to prove anything affirmatively. That's what Hume was referring to.
Yes, there are extremely small likelihoods for all kinds of extremely unlikely things. That doesn't make tools like induction any less useful. Sure you can't prove X, but you can show that the likelihood of ~X is far, far lower than the likelihood that you will hallucinate ~X.
The example you replied to was farfetched, but not an abstract ivory tower notion – it's something deeply built into how we view the world.
This doesn't mean there's no use of inductive reasoning, or that we shouldn't suspect that some things are far more likely true than others. But remembering the ultimate impossibility of inductive proof can help avoid real world errors.
Markets aren't exactly known for regular behavior. If anything, they are anti-inductive.[1] If you find and exploit any regularity in them, the regularity eventually disappears.
It's for these reasons that I remain unswayed by your claim.
Until it wasn't, in some edge cases. And we adopted a new theory that explained things better.
My point was that the impossibility of induction is at the core of science. Science generally does things well because it accounts for this. I cited financial crashes as an example of what can happen if you don't account for induction.
What, exactly, are you disagreeing with?
It hasn't been falsified, it's been expanded. There's a difference.
Kuhn talks about this concept quite a bit in "The Structure of Scientific Revolutions". Relativity was not merely an expansion of the Newtonian explanation of the universe. It was a complete change of our understanding of how the universe worked, even though relativity reduces to the same equations as Newtonian mechanics at low velocities and low masses.
That was rather bad news for Alfred North Whitehead and Bertrand Russell ;)
Philosophy doesn't "find a failure" of inductive reasoning because it doesn't care (in this context) about how well things work. It questions whether induction creates knowledge[1] (vs. "mere" utility). You're arguing about plumbing with a banker. If all you care about is plumbing, the bank is indeed a bad place to discuss it. It sounds as if you simply have no interest in looking at the world from a perspective other than utility, and the that you take the value of utility as an axiom. Philosophy is simply an exploration of views of reality with axioms different from yours. It is like the study of logics, while you like sticking to a particular logic system, building on top of that one. What you consider to be the end of the chain of questions that interest you, philosophy considers the beginning. That's perfectly fine and maybe philosophy isn't for you, but you've got no quarrel with it, and so far stated no disagreement with it.
Also Gödel's stuff. I still like Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter.
But philosophy isn't concerned with the question of utility. It is also not at all just playing language games (although philosophers have pondered both language and games). But if you're limiting your field of view only to that which is practically useful, you may be excluding other ways of looking at the world which you may find satisfying.
Of course it is. It's just that you have defined the word "utility" to exclude some of the things it means to certain philosophers.
On the contrary. I pointed out the previous commenter's hidden assumption that "it works" equals "it is valuable". If you believe they are equal, you need to justify your belief. I also pointed out that "it works" most certainly is not equal to "we know", unless you have a good justification to believe that this is the case. The goal of philosophy is to uncover hidden assumptions and question them.
Or of course you can just ignore these details and fallaciously conflate likelihood and probability like most pop-frequentists, but that leads to crazy results even in the "real world."
Also, the problem of induction is only one part of this marvelous tome. Protip: get the new Fate-Norton Oxford edition and not the Selby-Bigge-Nidditch.
The motivation for the "Humean problem of induction" along with a description of how it has evolved needs to be set up somewhat carefully. Marc Lange provides a nice intro if anyone is interested. http://www.stephanhartmann.org/HHL10_Lange.pdf
But once you've got the basics from a "mere" phil of science perspective, you can go a lot further. For example, you can look at how "knowledge" is linked with human values and what it is to live a good life. Or at how the experience of art is connected to learning or human development. How does the "Humean problem of induction" bear on these themes? These far reaching connections---which typically involve an empirical or "scientific" component---are where philosophy really gets fun!