You can reason effectively, but proving is another thing entirely. You can never prove beyond the shadow of a doubt we are not about to be razed by gamma rays--there could be some arbitrary rules to the universe that only kick in right now.
Sorry, but it's stuff like this that causes me to avoid most philosophy.
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.
This one's at the foundation of our science though. Karl Popper's ideas on falsification have been very influential in how scientists frame their work. And errors of induction have caused some notable financial blowups because models missed tail risks.
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.
Please notice how far afield you went to find a failure of inductive reasoning: Financial markets. Not a bad math proof. Not an incorrect physics theorem. Not even a civil engineering disaster. Markets!
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.
Ok, Newtonian physics. That was accepted for a long time because it was utterly, utterly consistent with all our evidence.
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.
No, the universe Newton described was falsified. In the Newtonian universe, information (including gravitation and electrical attraction) travelled instantly.
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.
> Please notice how far afield you went to find a failure of inductive reasoning
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.
You can show that the likelihood (read: P(data|~X) of ~X is low, given a particular underlying model and a set of observations. To bootstrap that to a probability of ~X (read: P(~X | data) ), you need philosophy to help choose a prior on the underlying set of models.
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."
> That doesn't make tools like induction any less useful
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.
> 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.
