Grue and Bleen: New riddle of induction(en.wikipedia.org)
en.wikipedia.org
Grue and Bleen: New riddle of induction
https://en.wikipedia.org/wiki/New_riddle_of_induction
48 comments
Attempts at building in smoothness to logic never seem very useful to me, because true/false based logic already supports real numbers and probabilities as well as you could hope it to. If anything the real discovery of symbolic logic was that you don't need smooth primitives to build arguments about smooth things - it was obvious from the beginning that you could assign something that was one of two things to one of two symbols, but the realization that you could also do math and physics that way came much later.
The apparent paradox is that the choice of blue/green vs grue/bleen appears symmetric: green="grue if before 2028 else bleen" whereas grue="green before 2028 else blue". But then why do we strongly prefer to make predictions using green/blue instead of grue/bleen?
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.
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.
I do not follow the objection to this response (at the top of the section "Responses"):
"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.
"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.
I agree, I think grue and bleen were constructed so that green and blue could be redefined in terms of these new time dependent predicates to confuse the fact that the original colors are not time dependent. In math it is completely normal to write down some complicated formula of time dependent functions and get a result which is independent of time, otherwise there could never be energy conservation for example.
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.
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.
>* Clearly, the predicates grue and bleen are not the kinds of predicates we use in everyday life or in science,*
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.
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.
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Induction is a heuristic, it establishes a pattern but not it's necessity.
Induction [1] is logically invalid, full stop. It was thoroughly debunked by Karl Popper, whose theory was popularized by David Deutsch in his book, "The Fabric of Reality". The easiest way to see that induction is invalid is to observe that the sun has risen in the east every day for the last few billion years, but it is not valid to conclude that the sun will continue to rise in the east forever. (It won't.)
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.
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[1] 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.
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.
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[1] 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.
... 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?
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.
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.
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.
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.
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
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?
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...
[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)."
> 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).
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
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. 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.
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.
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.
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 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.
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.
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.
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.
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.
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
grue is difficult to translate to German because a naive substitution would yield grau (grün/blau), but grau is grey. How would you translate grue to German?
glau
Blün?
...then how would you translate bleen?
Apparently you just avoid naming the other term (if my rudimentary scanning of this German webpage is correct): https://www.sapereaudepls.de/2018/01/20/goodman-paradoxon/
Blün is even in the Wiktionary: https://en.wiktionary.org/wiki/blün
Blün is even in the Wiktionary: https://en.wiktionary.org/wiki/blün
Grüu and blan?
This doesn't work because au is a diphthong (a gliding vowel). In Bernese German you could pronounce üu, but not in Standard German.
[1] https://plato.stanford.edu/entries/goodman/#NewRidInd [2] https://partiallyexaminedlife.com/2010/10/31/episode-28-nels...