One way to resolve this paradox is to translate the terms into the raw language of physics, at which point it's obvious which one is simpler. More concretely, imagine trying to make a camera that recognizes "bleen" vs making a camera that recognizes "blue". Which camera only works if you include a clock? More abstractly, I would say that the Solomonoff complexity (aka algorithmic complexity) of bleen is higher than blue (for basically any programming language or hardware you will run into). Therefore you prefer blue/green.
Yes, one can generalize the paradox by reformulating all of physics or all of computer architecture to be based on the before/after 2028 distinction. And yet, it does seem that that would make the physics harder and the hardware more expensive, right? There seems to be an objective sense in which nature is built around blue/green rather than grue/bleen.
"x is grue" is not solely a predicate of x, but of x and a time t — we can know that an object is green without knowing the time t, but we cannot know that it is grue. If this is the case, we should not expect "x is grue" to remain true when the time changes. However, one might ask why "x is green" is not considered a predicate of a particular time t - the more common definition of green does not require any mention of a time t, but the definition grue does.
Surely "x is green" is not considered a predicate of a particular time t simply because it isn't, by definition, and the fact that grue and bleen are defined as such is simply being used in a faulty analogy that is beside the point?
It continues this response also begs the question because blue can be defined in terms of grue and bleen, which explicitly refer to time - but blue, so defined, loses any dependence on time even if it is nominally a parameter, and so can be used in inductive arguments with respect to time in ways that would be invalid for grue and bleen.
There are conventional time dependent predicates like a person's name that nobody has a problem intuiting that induction fails for (many people take their spouse's name after marriage or return to their original name after divorce). It seems like these predicates were invented just to try to confuse what it means for a predicate to be time dependent.
I would argue that this situation actually does show up in every-day life and science. Any situation where your coordinate system changes from one arbitrary thing to another will result in a situation where the name, place or other quality you assign to something "changes" without any real change being involved. I think that a lot of philosophical problems can be reduced to the verbal equivalent of switching between arbitrary coordinate systems.
The grue/bleen riddle was also debunked by Deutsch with the pithy slogan, "Languages are theories." The words you use to describe your theory are not arbitrary. The concepts they stand for can themselves be judged in the same terms that the theory overall is judged by, namely, do they have explanatory power? "Green" and "blue" have explanatory power. They sum up complex physical processes in a very compact form. "Grue" and "bleen" do not. There are in fact blue and green things in the world, and physics can explain why there are blue and green things. But there are no grue or bleen things, and Goodman cannot justify why he wants to insert an arbitrary time parameter into his terminology. The grue/bleen theory can be rejected on those grounds alone.
There are some legitimately time-dependent terms in use, for example, "President of the United States", or "main-sequence star". But the time-dependence of both of those can be justified in terms of phenomena that actually occur in the world.
 Note that in the context of Goodman, this means logical induction (https://en.wikipedia.org/wiki/Inductive_reasoning), not mathematical induction (https://en.wikipedia.org/wiki/Mathematical_induction). The former is invalid, the latter is not.
Can you use induction in a valid way to invalidate induction?
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.
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.
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.
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.
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?
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).
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.)
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.
But we don't have a justification, other than induction, for believing that that theory will remain valid into the future.
Yes, we do. Scientific theories are justified by their explanatory power. Read Deutsch.
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.
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.
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.
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.
which is what the OP is about. Totally different from this:
which is logically valid.
Blün is even in the Wiktionary: https://en.wiktionary.org/wiki/blün