If and when anyone questions an induction of yours, ask them if they have found an exception. If yes, simply say that's the exception that proves the rule.

But the link itself says that we don't, or rather can't make inductions.

I don't see where it says that. And I'm pretty sure that induction is something we do a lot of the time. "Can I do that?" "Well, they're doing that." "I guess it must be ok if I do that."

I'm lost on why the problem is such a big deal — Darkneos

It's not. Seems like common sense.

The principle of uniformity of nature: The future will resemble the past.

This apparently simple sentence is the foundation for the sciences. It would be great if we could prove it and the proof is: The future resembles the past

In short the argument for the principle of uniformity of nature goes like this:

1. The future resembles the past

Ergo,

2. The future resembles the past

That's a circulus in probando if there ever was one. This is the problem of induction.

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I'm lost on why the problem is such a big deal and whether they mean science doesn't tell us anything about the world? — Darkneos

IMO, it's a fascinating glitch. No one can help trusting induction, so in that sense it's not a big deal. I think I understand Hume, and I was dazzled at first. We apparently have an animal faith in the uniformity of nature, and that's it. It's impressive that Hume could see this and reveal it to others. But it didn't change anything besides making me feel a little more clever than before. If you keep reading about it, it'll suddenly click. The argument people instinctively make against it is circular, as sketched above.

'Of course the future will be like the past, because it always has been!'

Mostly the Proof and Evidence section. I'm lost on why the problem is such a big deal and whether they mean science doesn't tell us anything about the world? — Darkneos

It crashes both empiricism and rationalism. Neither can account for our confidence in natural laws, so it takes aim at foundations.

It might be worth noting that there's another side to the problem of induction viz. the problem of generalization from a set of particulars - the black swan is an embarrassment to science.

Alright, science deals with particular sets of phenomena. Right? So, it deals with particular objects or things I see or perceive. For example, the phone, the bits and pieces of the phone, the weight, mass, charge, spin of the particles of the phone etc. etc.

Okay, there is no "universal" law that is holding these particular bits and pieces together. There are just the bits and pieces. The "whole" phone is just the sum total of the bits and pieces.

That's the problem of induction.

We don't have any experience of the universe in it's sum total, just the bits and pieces. We only assume we have a coherent picture of the universe in it's sum total, because of the regularity of those events. So every day we see that we can walk in a straight direction, so we assume that we can continue to do so. But there is no "thread" connecting the "pearls" of those bits and pieces, those events, all in-and-of-themselves. That's our inference.

Unless, you believe, like I do, that universals, natural laws, etc. exist. But the Modernist tradition is basically unanimously nominalistic. For reasons that are understandable, but nevertheless.

In other words, the problem is that we need to assume a "universal" constancy of a kind to be able to do science or live in the world at all, yet in pure empirical terms, no such universal can be known to exist. Because, by definition, empiricism only deals with particular objects and not universals.

Dunno if that made sense or not, but I tried.

Peace.

In other words, the problem is that we need to assume a "universal" constancy of a kind to be able to do science or live in the world at all, yet in pure empirical terms, no such universal can be known to exist. Because, by definition, empiricism only deals with particular objects and not universals. — Dharmi

Assumptions are good. They don't violate any philosophical or scientific principles. The issue lies in equating assumptions with the universals. Philosophically, we are given a license to talk, heck argue, about universality of things. Scientifically, we earn the right to make assumptions, or inferences, using experimentations and observations. Phenomena in nature works with regularity.

That's fine. But what does it mean to 'assume' a law of nature that isn't actually real?

That's the crux of the problem of induction and the problem of universals as well. We certainly observe that the natural world works uniformly and regularly, but we can't 'prove' that, 'justify' it. It's not like we 'see' the law of nature that indicates that uniformity and regularity.

But what does it mean to 'assume' a law of nature that isn't actually real? — Dharmi

That isn't actually real? In what way the law of gravity isn't real?

Well, I don't say it isn't. I say it is, but pure empiricism cannot justify the claim that laws of nature are truly real. That's the problem of induction.

I'm not a pure empiricist. Pure empiricism is based on nominalist philosophy, which rejects the idea of natural law.

To make it clearer:

You've never seen the law of gravity. You've only seen particular cases and time periods where gravity has operated. That's the crux of the problem. How do you go from particular cases to a universal law?

I say it is, but pure empiricism cannot justify the claim that laws of nature are truly real. That's the problem of induction. — Dharmi

First, I think we need to nail down what we're talking about. Are we talking about scientific empiricism, or metaphysical empiricism, which might be called pure empiricism. We know there is gravity. We also know what happens without gravity.

Right, but the problem is justification. What we know is, gravity functions and operates. What we don't know, and what the problem of induction is, is whether there is a law underlying that function. That's the problem. There's no "string" holding together the "pearls".

If you say there;s a law, then where is it? That's the problem.

[Much] of what contemporary epistemology, logic, and the philosophy of science count as induction infers neither from observation nor from particulars and does not lead to general laws or principles. [Induction] was understood to be what we now know as enumerative induction or universal inference; inference from particular instances:

This is what I am referring to about the link ^