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This argument, including the "will the sun rise tommorow" example, is these days most associated (at least in philosophy) with the 18th-century philosopher David Hume. See here for example: http://www.gutenberg.org/files/9662/9662-h/9662-h.htm#mnum21

... but it is not valid to conclude that the sun will continue to rise in the east forever. (It won't.)

Can you use induction in a valid way to invalidate induction?

Not sure, but I can use deduction: 1) If induction is valid, then it follows that we can use induction to reason about the world. 2) But we can't use it to reason about the world, 3) so it isn't valid. (Modus Tollens) This is valid, but not necessarily sound. Soundness implies that first two statements (premises) are also true. The second premise is clearly not true, because we use induction to reason all the time. So the conclusion #3, while it follows as a valid argument, cannot be said to be a 'sound conclusion.'

> we use induction to reason all the time

Yes, people use all kinds of invalid reasoning techniques and fall victim to a wide variety of logical fallacies and cognitive biases. That doesn't mean that any of them are valid.

I think you are expecting the term 'validity' to mean more than what it technically means to people in philosophy, which is that it 'adheres to the form of either Modus Ponens or Modus Tollens'. Colloquially it has come to mean more like what soundness means, which is valid but also with true premises.

I don't want to quibble over terminology. Inductive reasoning is wrong. Mistaken. Bogus. Intellectually bankrupt. Utterly without redeeming value of any kind. As likely to lead to correct conclusions as reading Tarot cards (which is to say, the probability is higher than 0, but not by a wide enough margin to have any utility).

No. Induction is invalid, full stop. It cannot be validly used to demonstrate anything.

The point sonusario is making is that your assertion about the future behaviour of the Sun is based on our understanding of physics, and physics is itself inherently inductive - it's an abstraction and formalisation of empirical experience. If we'd consistently made very different observations of the world, we'd have come up with different physics, which would make different predictions.

In my view saying things like "induction is invalid" is a bit of dead end, rather like Cartesian doubt. It's not that it's wrong, more that you can't go anywhere interesting from there, unless you abandon your own principles and start wibbling about God and the natural light and pineal glands.

> physics is itself inherently inductive

No, it isn't. It is explanatory. You need to read Deutsch and/or Popper. The argument is too long to reproduce in an HN comment.

> Induction is invalid

Can you rephrase this without using the word "induction"? Since that word seems to be confusing a lot of people in this discussion.

My attempt at rephrasing, based on what it seems like you are using "induction" to mean, would be: it is always invalid to reason that the future will be exactly like the past. Or perhaps: it is always invalid to reason that our future data will show exactly the same patterns as our past data.

If this is what you are using "induction" to mean, then of course you are correct; but I don't think this is what others in this discussion are using "induction" to mean.

Good grief, doesn't anyone on HN understand context any more? The top-level post here is "The new riddle of INDUCTION". When I use the word "induction" I mean what it means in the title, which is explained at great length in the paper. I mean this:

https://en.wikipedia.org/wiki/Inductive_reasoning

Not this:

https://en.wikipedia.org/wiki/Mathematical_induction

> I mean this

How does what the Wikipedia article is describing differ from what you are calling "explanatory"? As far as I can tell, the reasoning used to build scientific models, for example, falls within what is described as "inductive" reasoning in the article (the article's description is very general, leaving room for lots of different kinds of inductive reasoning); but you are saying scientific models aren't built using inductive reasoning but are "explanatory". Is there a one or two sentence description of the difference? Or are we all forced to buy and read Deutsch's book?

Explaining what an explanatory theory is won't fit in an HN comment. I'll have to refer you to David Deutsch [1] (or Karl Popper) for that.

[1] https://www.amazon.com/Fabric-Reality-Parallel-Universes-Imp...

Does explanatory theory make use of observation? Because based on the the wiki page for inductive reasoning, if you use observations for evidence, then you are using inductive reasoning to some capacity.

Well, what I really mean by "induction" is what it means in the paper pointed to by the OP, i.e. the paper entitled "The new riddle of induction." I pointed to the wikipedia article just to contrast that with mathematical induction, which is NOT what I or anyone else is talking about here.

Yes, explanatory theories rely on observations. But they are not just straightforward extrapolations of the form, "Because we have observed something N times (e.g. we have seen N green emeralds) we can reliably conclude that we will continue to observe it (e.g. all emeralds are green)."

> Yes, explanatory theories rely on observations. But they are not just straightforward extrapolations of the form, "Because we have observed something N times (e.g. we have seen N green emeralds) we can reliably conclude that we will continue to observe it (e.g. all emeralds are green)."

Interesting. I will need to look further into explanatory theories, because my current understanding tells me that anything that uses observational evidence is inductive (even without following the "observed something N times" form).

You can choose to lump Popperian epistemology (what I have been calling "explanatory theories") together with other kinds of inductive reasoning, but that misses the point. If you cast your linguistic net wide enough, then there are a lot of different kinds of inductive reasoning. But only one of them actually works, and it's not the one that Goodman uses. At that point calling them both "inductive" robs the word of its utility.

Then how do you know that the sun won't rise forever?

Physics. In about 5 billion years the sun will become a red giant and destroy the earth.

https://www.e-education.psu.edu/astro801/content/l6_p2.html

So induction was not used to determine this?

No.

Then what form of reasoning was used? You stated that we cannot validly claim that the sun will rise forever just because we've observed it rise in the east every day for the last few billion years. Then you cite stellar observations that we use to claim that the sun will become a red giant and destroy the earth. What are the differences in those observations that make one invalid induction and the other not?

> stellar observations that we use to claim that the sun will become a red giant and destroy the earth

No. We have never observed a star become a red giant. That process takes millions of years, and we have only been doing astronomy for a few hundred. The reason we know that the sun will become a red giant is not because we have ever observed this process happen, but because we have an explanatory theory of how stars work. Going into detail on how that process works is a little too long for an HN comment. If you really want to know, read David Deutsch's "The Fabric of Reality", particularly chapter 7. (Or go straight to the source and read Karl Popper.)

> No. We have never observed a star become a red giant.

I never actually claimed that we have seen a star become a red giant, but that we have made observations that allow us to conclude that some stars become red giants.

Perhaps you can enlighten me on what explanatory theory is. Does explanatory theory make use of observation? Because based on the the wiki page for inductive reasoning, if you use observations for evidence, then you are using inductive reasoning to some capacity.

> Going into detail on how that process works is a little too long for an HN comment.

We don't have to get into details on the star life-cycle and I get why there are issues with inductive reasoning regarding certainty. I am just trying to understand what you consider inductive reasoning to be, given that I think you used inductive reasoning to call inductive reasoning invalid.

We have an explanatory theory of how stars have worked in the past.

But we don't have a justification, other than induction, for believing that that theory will remain valid into the future.

> we don't have a justification, other than induction

Yes, we do. Scientific theories are justified by their explanatory power. Read Deutsch.

How much of that explanatory power is derived from explaining things that have happened in the past, vs how much from explaining things that have happened in the future?

You can fire a cannonball and observe a parabolic arc, you can learn to hit a target reliably from any distance, and you can develop a unified theory of gravity, air resistance, and the rotation of the earth that explains why firing at such-and-such angle with such-and-such amount of power will strike a target at a fixed location. That theory will allow you to hit targets reliably even in firing situations that you've never encountered in the past. But induction is your only justification for believing that gravity, air resistance, and the rotation of the earth will affect cannonballs and missiles the same way tomorrow as they did yesterday.

> you can learn to hit a target reliably from any distance

Not without developing an explanatory theory you can't.

Read Deutsch.

> Not without developing an explanatory theory you can't.

This is absolutely false as a matter of historical fact; the theory always follows a period of trial-and-error in which you learn how to hit the target by raw experimentation. There's a pretty simple reason for this, which is that the trial-and-error approach is easy to execute.

> Read Deutsch.

Any reason I should do this? "Read Deutsch" isn't exactly a compelling argument against the idea that theories derive their authority from a track record of success, as opposed to something more non-inductive such as divine ordination.

> This is absolutely false as a matter of historical fact;

No, it isn't.

> the theory always follows a period of trial-and-error

That is true.

> in which you learn how to hit the target by raw experimentation.

No, that is not true. In order to hit the target you have to extrapolate the results of your raw experimentation somehow, because you can never completely reproduce the circumstances of any experiment. If you try to do that extrapolation using induction, you will succeed with odds no greater than chance.

> Any reason I should do this?

Because if you're going to dispute someone's position, you really ought to first inform yourself what that position actually is rather than argue against a straw man.

If the only thing you have to say about your position is "I'm not going to bother to go into it. Read Deutsch", I don't imagine you'll persuade many people that there's anything worthwhile they'd get out of Deutsch.

I'm sorry, but there are some things worth knowing that simply cannot be distilled down to pithy slogans, and if you want to understand them you are going to have to do some work. If you're not willing to do that, well, that is really no concern of mine.

Mathematical induction is a logical method of proof. Don't confuse it with inductive reasoning.

In the context of a discussion of Goodman's "The New Riddle of Induction", the word "induction" means inductive reasoning. Mathematical induction is a completely different thing, notwithstanding that the same word is used to label it.

Wait, what? Do you mean induction in a specific case, or induction overall?

Because your counterexample just isn't provable by induction. There's no inductive step there... There's no reason to believe that if the sun went up east on the n'th day it will do so on the n+1'th as well.

I mean this:

https://en.wikipedia.org/wiki/Inductive_reasoning

which is what the OP is about. Totally different from this:

https://en.wikipedia.org/wiki/Mathematical_induction

which is logically valid.

Thanks you for the clarification! I've seen the OP, didn't understand it really though.