8 ms·

Grue and Bleen: New riddle of induction

49 points by shry4ns 8y ago

deleted 8y ago
[deleted]
mannykannot 8y ago
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.
- BlackFly 8y ago
  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.
_nalply 8y ago
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?
- theoh 8y ago
  Blün?
  - thaumasiotes 8y ago
    ...then how would you translate bleen?
    - theoh 8y ago
      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/ https://www.sapereaudepls.de/2018/01/20/goodman-paradoxon/ Blün is even in the Wiktionary: https://en.wiktionary.org/wiki/blün https://en.wiktionary.org/wiki/blün
- bonoboTP 8y ago
  glau
- occamrazor 8y ago
  Grüu and blan?
  - _nalply 8y ago
    This doesn't work because au is a diphthong (a gliding vowel). In Bernese German you could pronounce üu, but not in Standard German.
lisper 8y ago
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. --- [1] Note that in the context of Goodman, this means logical induction (https://en.wikipedia.org/wiki/Inductive_reasoning https://en.wikipedia.org/wiki/Inductive_reasoning), not mathematical induction (https://en.wikipedia.org/wiki/Mathematical_induction https://en.wikipedia.org/wiki/Mathematical_induction). The former is invalid, the latter is not.
- sonusario 8y ago
  ... 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?
  - lisper 8y ago
    No. Induction is invalid, full stop. It cannot be validly used to demonstrate anything.
    - sonusario 8y ago
nathias 8y ago
Induction is a heuristic, it establishes a pattern but not it's necessity.
aggerdom 8y ago
I found the SEP article to be a much better explanation of the issues posed [1]. Wish Goodman was known more widely for his other work though. Had some fascinating work trying to establish mereology as an alternative to set theory. And he takes an interesting approach elsewhere by grounding epistemology within aesthetics to some degree. Essentially making true and false subsets of "rightness" and "wrongness". One example iirc we could call a painting "jazzy" and it applying more or less right about it's subject but not necessarily capital T true. Would recommend the Partially Examined Life episode on his epistemology. [1] https://plato.stanford.edu/entries/goodman/#NewRidInd https://plato.stanford.edu/entries/goodman/#NewRidInd [2] https://partiallyexaminedlife.com/2010/10/31/episode-28-nelson-goodman-on-art-as-epistemology/ https://partiallyexaminedlife.com/2010/10/31/episode-28-nels...
- whatshisface 8y ago
  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.
Strilanc 8y ago
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.
whatshisface 8y ago
>* 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.

49 points by shry4ns 8y ago

deleted 8y ago

[deleted]

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.

BlackFly 8y ago
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.

_nalply 8y ago

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?

theoh 8y ago
Blün?
- thaumasiotes 8y ago
  ...then how would you translate bleen?
  - theoh 8y ago
    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/ https://www.sapereaudepls.de/2018/01/20/goodman-paradoxon/ Blün is even in the Wiktionary: https://en.wiktionary.org/wiki/blün https://en.wiktionary.org/wiki/blün
bonoboTP 8y ago
glau
occamrazor 8y ago
Grüu and blan?
- _nalply 8y ago
  This doesn't work because au is a diphthong (a gliding vowel). In Bernese German you could pronounce üu, but not in Standard German.

lisper 8y ago

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. --- [1] Note that in the context of Goodman, this means logical induction (https://en.wikipedia.org/wiki/Inductive_reasoning https://en.wikipedia.org/wiki/Inductive_reasoning), not mathematical induction (https://en.wikipedia.org/wiki/Mathematical_induction https://en.wikipedia.org/wiki/Mathematical_induction). The former is invalid, the latter is not.

sonusario 8y ago
... 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?
- lisper 8y ago
  No. Induction is invalid, full stop. It cannot be validly used to demonstrate anything.
  - sonusario 8y ago

nathias 8y ago

Induction is a heuristic, it establishes a pattern but not it's necessity.

aggerdom 8y ago

I found the SEP article to be a much better explanation of the issues posed [1]. Wish Goodman was known more widely for his other work though. Had some fascinating work trying to establish mereology as an alternative to set theory. And he takes an interesting approach elsewhere by grounding epistemology within aesthetics to some degree. Essentially making true and false subsets of "rightness" and "wrongness". One example iirc we could call a painting "jazzy" and it applying more or less right about it's subject but not necessarily capital T true. Would recommend the Partially Examined Life episode on his epistemology. [1] https://plato.stanford.edu/entries/goodman/#NewRidInd https://plato.stanford.edu/entries/goodman/#NewRidInd [2] https://partiallyexaminedlife.com/2010/10/31/episode-28-nelson-goodman-on-art-as-epistemology/ https://partiallyexaminedlife.com/2010/10/31/episode-28-nels...

whatshisface 8y ago
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.

Strilanc 8y ago

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.

whatshisface 8y ago

>* 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.