Talk:Grue and bleen

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[edit] Definition of grue

I changed the definition of grue to something truer to Goodman. Never examined emeralds can be grue, but this is not possible given the definition found in the last revision. This is important dialectically, so that green can be defined in terms of grue and bleen. I also added the most common response to the riddle and its basic problem. --Lapidary 23:50, 5 December 2005 (UTC)

[edit] 2000 v 3000

Althoug originally 2000 was used to define grue, i think it is a good idea to change it to 3000 since 2000 has already passed, and therefore the example would be uninteresting. --Hq3473 16:22, 15 November 2005 (UTC)

I think it would be better to use 2000 and explain that the riddle was phrased before 2000. As the article is now, it sounds like Nelson defined grue using t=2000, which is not true. --Gruepig 03:48, 16 November 2005 (UTC)
Ditto. I've so changed it, twice now.
It does not matter how he defined it, saying 2000 now sounds irrelevant and defeats the purpose of the word Grue, just another damage of Y2K bug. The sentence says "Casually, "grue" is used to mean" not "Nelson defined it to be", casual definition should be casual not outdated.--Hq3473 23:28, 5 December 2005 (UTC)
I don’t know why people have such strong aversion to the number 3000. All I am trying to say that using 2000 defeats the purpose of the argument (it already passed therefore we know that no emeralds are grue since they all stayed green). If the number 3000 offends you all so much I will be happy with any number N where N>2006. --Hq3473 18:08, 9 February 2006 (UTC)
There are two reasons I changed it. (1) It is not commonly used to mean 3000, yet, whether or not it should be. There is a well-entrenched convention of setting it at 2000, which is still in use. (2) Your remark here betrays a misunderstanding of the problem which I think your change will encourage. A grue emerald is not one that looks green now but will look blue later. "Grue" is a composite predicate meaning "was first viewed before t and looked green then or was first viewed after t and looked blue then." The result is that if you look at a an emerald before t, and it looks green then, then it is grue. Always and forever. Even if it still looks green after t, it remains grue because grue was defined in terms of the moment of first observation. The original problem was not an epistemological question of whether things are really grue or not: the emerald I mentioned is certainly, by definition, grue. The problem rather is about which predicates are suitable for use in formulating scientific laws. Read Goodman's book if you're in doubt.
The problem is slightly more vivid if t is in the future, but it is still a puzzle even if t is in the past. You are welcome to add remarks elaborating on this, (saying, e.g.: "You might find it helpful to imagine t=3000"). But don't go claiming that conventions for the value of t exist when they don't.
Jod
I know the formal definition has to do with time observed etc. etc. This is not what we are arguing about. Regardless of what the actual definition is, the casual definition should preserve the puzzle. The definition as it is now: “green before January 1, 2000 and blue on or after January 1, 2000" presents no problem with Inductive reasoning. We can conduct a scientific study right now by examimning a lot of emerald and their known histories before and after jan 1, 2000 and determine CONCUSSIVELY that emeralds are NOT “grue” because they DID NOT change color on January 1st. Therefore induction works and induction is not problematic.
Thus moving the date into the future INDUCES the puzzle and not makes it “slightly more vivid.” If you state the grue “casually” as “green before January 1, 3000 and blue on or after January 1, 3000" then scientific study of emeralds NOW will indicate that they ARE grue, while we know that it is false. This puzzle disappears if you change the year back to 2000.
Thus I propose the following 2 options to compromise:
1. Remove “casual” definition altogether and only keep the original Goodman defintion.
2. Change 2000 to any N where N>2006
3. Rewiring the definition to something like “green before time T and blue on or after time T" where T is in the future.
--Hq3473 19:43, 10 February 2006 (UTC)
Also as to your first reason, There is some indication that the use off 2000 is falling out of use. Consider the following example from lecture notes from a class in UCSD Where the grue is "defined as green until the year 2028,” [1]. --Hq3473 19:58, 10 February 2006 (UTC)
A philosopher friend of mine describes Goodman's Paradox in terms of "Thursday" and "the rest of the week", which certainly makes the difference between the two conceptions here, of what the paradox is, clear: she clearly thinks it makes sense in those terms, which suggests to me that "2000" is correct.
Of course, as a scientist, it immediately turns the story from a useful fable about the limits of the value of induction and parsimony, and about why it's wise to temporarily shelve paradigms that cannot presently be distinguished from the dominant paradigm using any available observation, into philosophical babble. But this is a philosopher's story, not a scientist's, and should be respected on those grounds.
That there is an argument at all certainly means the article needs a few lines by a philosopher explaining why "2000" is still the correct date. At present the phrase currently in the article,

"Note. When Goodman originally presented his "riddle", he used a concrete time t in his definitions, namely January 1st, 2000, a date that at the time was far in the future but now in the past. For understanding the problem posed by Goodman, it is best to imagine some time t in the future."

is simply wrong, as philosophers both here and in my acquaintance have insisted that understanding the problem actually posed by Goodman did not depend on the time being in the as-yet-unobserved future. I don't understand how that works, but I must defer to them. Del C 11:43, 11 May 2006 (UTC)
Please provide a VALID and CONCRETE refrence for this statement. While i undertsand that the problem still WORKS if t=2000 it is EASIER for a lay person to imagine t being in the future. If you can find some valid source telling otherwise i might reconsider.--Hq3473 22:39, 25 August 2006 (UTC)

[edit] Other languages

"A large number of the world's languages, including Welsh and Ubykh, do not distinguish colour terms for "green" and "blue", using the same word for both." This is inaccurate, at least for Welsh. Welsh does distinguish between green (gwyrdd) and blue (glas); it is however a fact that English and Welsh do not always agree on what is green or blue. Also, we can see that English may consider grass blue, as does Welsh.

The only English I've ever heard that references blue grass is the music genre.
Bluegrass is also a well-known genus of plants see Bluegrass (grass)--Hq3473 19:34, 28 February 2006 (UTC)
What about Japanese aoi (青い)? Shouldn't be hard to get this verified with a {{user ja}} editor. Verification for Ubykh is a bit more difficult, since the language has been extinct since October 1992. LambiamTalk 22:49, 6 April 2006 (UTC)

There is a very famous anthropology article on the subject of how different cultures define color. Different cultures divide colors according to different types of criteria. In fact, even "a segment of the visible spectrum" (from the article) isn't always the way in which a given culture defines color. Conklin, Harold C. 1955: "Hanunóo Color Categories." Southwestern Journal of Anthropology 11(4):339-44. Randomundergrad

[edit] It has been suggested that this article or section be merged into Grue (color).

Do it: it's one encyclopedia topic, two dictionary entries. Pol098 23:41, 22 February 2006 (UTC)

I agree. Not only are they the same topic, but Bleen should not even be a disambiguation page. That problem will be taken care of if they are merged. -- Natalya 19:55, 3 March 2006 (UTC)
Merge Nelson Goodman's sense if you like, but the term grue also pops up in linguistics, so I think that sense of "grue" should be left here. thefamouseccles 23:24, 28 Mar 2006 (UTC)
Hmm... perhaps merge the two pages, with Grue as the main page and Bleen as a redirect. Then create Grue (disambiguation) for that meaning and also for Grue (monster), which really should be disambiugately linked from this page anyway instead of in the "See also" section. -- Natalya 03:54, 29 March 2006 (UTC)
Agree, make Bleen redirect to Grue. Who's gonna do it? This doesn't require admin action, just boldness. The page should then make "Bleen" more prominent, as in: "Grue and bleen are artificial adjectives...". LambiamTalk 22:16, 6 April 2006 (UTC)

[edit] Chicken induction

"A real-world example of the concept of bleen and grue, is what could be called "chicken induction": a farmyard chicken could use induction to conclude that the farmer's wife is a supplier of food, although of course she will become executioner."

I suppose this bit will be considered irrelevant or unserious and deleted. But it is a concrete, realistic, example of the bleen/grue concept.

Pol098 15:39, 5 March 2006 (UTC)

[edit] Article Not Clear

I do not understand what exactly a grue is, could someone please explain it a little more clearly in the article? --Mohan1986 17:36, 3 April 2006 (UTC)

any PARTICULAR problems with this definition: "x is grue if and only if it is examined before some time T and is green, or is examined after T and is blue."? If so I will be happy to clarify. --Hq3473 18:23, 3 April 2006 (UTC)
Yes. Is it not clear from the defenition that the 'grueness' of an object is a property of both the object, and the time of measuring? Where is the paradox, or logical difficulty? Am I missing something?--203.199.213.36 13:46, 11 April 2006 (UTC)
Techincally every property is at the same time a property of an object, of time and of measurment. So technically "green" means that "the thing is observed right now and is green". For example if you look at the traffic light and see that it is "green" you know that it is a property of time as well as of an object. The puzzle with "grue" against "green" is that when observes say a diamond -- one immediately concludes that it is "green" and does not conlude that it is "grue" -- the puzzle is to explain why(btw it is all in the article).--Hq3473 14:15, 11 April 2006 (UTC)
Ah, the traffic light example is much better. Thanks!--203.199.213.36 14:54, 11 April 2006 (UTC)
You are welcome, for more info you can look at a discussion of the same problem I had with another user User_talk:Ian_Maxwell#Grue
If I may barge in here, I fail to see how this is much of a puzzle at all. Humans aren't logical computers: we predict based on past experience, often irrationally. I conclude future emeralds will be green because they have always been green in the past. If grue were a common experience, then I would predict it. For instance, I know that if I buy milk, it will taste good before time T and will taste sour after time T. Milk thus has a grue-like quality we can call spoilable. I predict that future milk that I buy will also have this quality because all milk I have had before has had it. 128.197.81.181 19:14, 21 April 2006 (UTC)
Re-Read definition of grue:"x is grue if and only if it is examined before some time T and is green, or is examined after T and is blue." Now ALL emeralds you observed in the past WERE in FACT GRUE. So this is the puzzle why do you not assume that all emeralds will be grue in the future?--Hq3473 20:39, 21 April 2006 (UTC)
But I didn't know they were grue at the time, did I? Case 1. Suppose I knew they were grue because every time I'd seen an emerald, someone had told me, "That's grue, you know." Then I would come to expect that future emeralds would also be grue. (I.e., if every time you see a beige box of a consistent size you are told it is a computer, you'll start to assume that all such boxes are computers). Case 2. I'd heard about grue-ness but had never been told that emeralds have that property. In that case, having never experienced an emerald as grue, I would never predict that an emerald I see is grue. I suppose that my objection seems to relate to the disjunction addressed in the article. I don't accept the disjunctive definition of green because green is a sensory primitive, in a sense (no pun intended). It is time-invariant and defined, for instance, by the spectrum of visible light it reflects (as long as the green object isn't destroyed/rusted/painted/etc). To argue that green depends on time as in the traffic light case is to confuse two uses of green. To say that a traffic light is green doesn't mean it is literally green, but rather that the green light is turned on. Whether on or off, it is still physically green. I guess my claim is simply: 1. green does not depend on time because it is grounded in sensation (or can be defined as a spectral feature when an object is illuminated by white light). 2. Expectations are based on experience, thus we would only predict grue-ness if past experiences made us think the earlier emeralds were in fact grue. (I'm interested in this, so I hope my asking doesn't bore you).128.197.81.181 21:27, 21 April 2006 (UTC)
Quote: "I'd heard about grue-ness but had never been told that emeralds have that property. In that case, having never experienced an emerald as grue, I would never predict that an emerald I see is grue". EXACTLY! But note the same is not true for green, suppose you have never seen green, but we explain to you all properties of “green” including what should spectrometer read when you point it at a green object, now you start observing emeralds, after a while you will (correctly) predict that "All Emeralds are GREEN", but as you have just stated the same is not true for Grue, no amount of observation will lead you to a conclusion that "All emeralds of Grue". The puzzle is Why does induction work for green and not for grue? Rejecting disjunctive definition of green is really just begging the question, if induction DID work for grue and bleen then such definition would nt be problematic, thus explaining the invalidity of a disjunctive definition of green is the same as explaining The problem of grue. --Hq3473 14:57, 25 April 2006 (UTC)
In any case this discussion should stop because it does not help clarify the article and if we want to continue our (now purely philosophical debate) we should find some other forum(e-mail maybe?). As an alternative you can read "Fact, Fiction, and Forecast" by Goodman where he deals with these issues at length.--Hq3473 14:57, 25 April 2006 (UTC)

[edit] Latest changes to definition

I would like to keep the definition as it is now referring to "blue if observed before T and green if not observed before T" because this definition does not REQUIRE the object to change color. While the other definition offered REQUIRES the object to change color to be grue. Not having to change the color makes the "riddle" much stronger. While “Simplifying” the definition also makes the riddle weaker.--Hq3473 04:30, 15 May 2006 (UTC)

No definition has the power to require objects to change color. Perhaps you mean colour-steady objects are not grue under the other definition? In any case, I think the present definition is plain wrong. For example, assume some pea going by the name Pete was only examined before t. Then, according to the present definition, the following propositions should all be equivalent:
Pete is grue
Pete is green and was examined before time t, or Pete is blue and was not examined after t
Pete is green and true, or Pete is blue and true
Pete is green, or Pete is blue
So steadily blue peas are grue, even when they have been examined before t. That can't be right. It is also wrong grammatically to use the past tense for an event in the future. Perhaps your intention was the following:

An object X satisfies the proposition "X is grue" if X is green and observed before time t, or blue and not observed before t.

If you insist on Goodman's original version, then please stick as much as possible to his actual wording. What we have now is wrong. --LambiamTalk 07:56, 15 May 2006 (UTC)
I would be happy with: X satisfies the proposition "X is grue" if X is green and observed before time t, or blue and not observed before t, but NOT with "X is green before t and blue after t".--Hq3473 22:50, 15 May 2006 (UTC)

[edit] Goodman's proposed solution

Goodman proposed a solution to the new riddle of induction in the same book, "Fact, Fiction and Forecast". As I recall, he said that a predicate should only be used inductively if it is projectible. As for what that means, I no longer clearly recall, though it is fairly clear to me that the idea didn't pan out in the long run. Anyway, this leads to an exchange of many articles with Goodman and Joseph Ullian on one side and Andrzej Zabludowski on the other. If others are interested and know more about projectibility, that might be worth adding to the page. On the other hand, ideas that don't pan out may not be of interest, at least in this case. Any thoughts? 68.162.143.29 04:35, 19 May 2006 (UTC)

If it can be made understandable and be kept concise, and a refutation meeting WP:V and WP:NOR can be included, why not. Apart from the intrinsic interest of seeing how great minds may dig their own pitfalls, it can help the philosophically inclined reader to avoid the same. --LambiamTalk 05:57, 19 May 2006 (UTC)
Few philosophical ideas really "pan out." A lot of the interest in philosophy, I think, comes from failed attempts at ideas that fail in an interesting or instructive way.

[edit] Real World Examples

Neither of the "Real World Examples" makes any sense as examples of Grue in the real world. The first example is bad because its not even clear what situation the example is describing. The second is more clear, but its connection to Grue is not at all clear.

I'm deleting the following text:

"Real-world examples:

A claim that the real world does not contain objects that are grue can be refuted by examples:

A real-world example of the concept of bleen and grue might be a traffic light that is red now, and might be assumed to always remain red by a hypothetical group of visiting aliens who live at a much faster pace. Likewise, a turkey may be led to conclude by induction that the farmer's wife is a supplier of food, rather than a "supplier of food before time t, but executioner at t", where t = Thanksgiving."

[edit] Proposed solution

I am moving to talk this paragraph: "The explanation of the above is that the "problem" is not a legitimate problem. It's a matter of choice, or put differently, a matter of freedom. Hence, the "problem" cannot legitimately be situated within the realm of inductive logic. Therefore, inductive logic finds itself compelled to classify the phenomenon as a problem, while in truth it is not. So within the realm of inductive logic no conclusive answer will ever be found." This "solution" needs to be sourced before it can be included.--Hq3473 20:17, 13 March 2007 (UTC)

[edit] Categorization

Can this article perhaps be categorized "Paradoxes"? --Popperipopp 15:56, 15 August 2007 (UTC)

The philosophical discussion should be categorized Grue (Philosophy), not Grue (Color), and have its own article. Bill Jefferys 02:20, 16 August 2007 (UTC)

[edit] Bayesian Explanation

As a Bayesian, I find the whole "Grue" business rather silly. In my opinion there is a ready explanation that comports both with mathematical necessity and cognitive consistency.

It's quite true that when you pick a particular, arbitrary date (which was originally placed in the year 2000, but now that it is 2007, the original argument has lost its force), then observing that the emerald is still green before that arbitrary date should not logically change our opinion about whether an emerald is green or grue. Yet we intuitively feel that it ought to diminish our confidence that the emerald is grue, if only by a little bit. The cognitive dissonance comes about because of a conflict between the mathematics and our intuition.

The classical result is obvious from a Bayesian point of view. The likelihood function for observing that the emerald is green before the "special date" is 1. That is, P(observe G | Green, t<t_0) = 1 and P(observe G | Grue, t<t_0) = 1. Thus, the likelihood ratio is 1 and ones opinion doesn't change.

So where does the cognitive dissonance come from?

I believe that it comes from the fact that the setting of a particular arbitrary (measure zero) date for the emerald to turn blue is on its face unbelievable and in fact untenable. If one is entertaining the notion that physical laws may change (as they might very well, thus turning green-appearing emeralds into blue-appearing ones), then it's rather silly to imagine that this would occur on a particular date in the future (e.g., January 1, 2000, or 3000, pick your date). Mentally, we would really imagine that it might happen at any time, unknown to us.

Thus, from a Bayesian point of view, one would put a (proper, normalized) prior on the possible date t_0 at which this event would happen. It would be zero before the date on which you thought of this idea, nonzero for a possibly long time (and possibly varying in time, but that does not affect my argument), and then zero when the Sun becomes a red giant and sentient life ceases to exist, so that the concept of "grue" has no meaning since there are no sentient observers to have concepts.

From this point of view, the integrated likelihood of the data "the emerald is still green at time t<t_0) is no longer constant in time, but decreases secularly. This is because it is now the integral, from t to infinity, of the prior on t_0 times the likelihood (equal to 1), and since the prior is now "spreading its bets" over many dates at which the green to blue transition may take place, this integral decreases secularly as more and more dates are tested and found not to be the transition date. "It hasn't happened yet, so we are still in business," but the longer the date is postponed, the less we believe in the hypothesis. That is, the grue hypothesis "spends" its credibility more and more, the longer that it fails to be confirmed.

Therefore, the likelihood ratio more and more favors the "green" hypothesis as time marches on and emeralds don't turn blue.

Note that the prior on the classical "grue" hypothesis puts all of the mass on t_0 (a Dirac delta function, so that the integral is 1 for t<t_0 and zero afterwards (so long as the color of the emerald doesn't change). This makes the likelihood ratio 1 so long as t<t_0, and 0 afterwards (assuming the transition doesn't take place).

Thus, I conclude that the sense of "paradox" in the grue example comes essentially from a conflict between the formal statement of the paradox ("date certain"), which on a Bayesian analysis gives the result that nothing changes until after the "date certain" t_0, and the fact that we don't really believe the "date certain" notion, so observing "green, green, green,..." indefinitely before t_0 ought to make us believe more and more in green and not in grue. Bill Jefferys 00:32, 16 August 2007 (UTC)

I would like to point out that you begged the question by saying that "The likelihood function for observing that the emerald is green before the "special date" is 1"! We do not know that! The whole point of induction is to prove that "emeralds are green" by observing numerous cases, if you just plainly assume that they are all green the point is moot. The riddle lies in the fact that one seemingly can use induction to prove that all emeralds are green but cannot use it to prove that emeralds are grue.--Hq3473 19:39, 16 August 2007 (UTC)

Anyhow this discussion constitutes a violation of WP:OR as wikipedia is not a place to publish original research.--Hq3473 19:39, 16 August 2007 (UTC)

I was merely making an observation. I do not propose including this point in the article. I agree that it is OR and not appropriate for the article (though I may write an article on it sometime, since it is an interesting observation). I supposed that it is possible that someone has published on this...I am not familiar with the literature on the grue problem, so I don't know. So I put the comment on the talk page, in the hopes that someone might know about this. I do not think that such discussions on the talk page violate WP:OR. If they were to do so, then a large fraction of WikiPedia's talk pages violate that principle, and a large fraction of WikiPedia's work could not be accomplished. But I could be wrong, and if so, I apologize.
But, to respond to Hq3473, I am not begging the question. The likelihood is the probability that we would observe that the emerald appears green prior to the critical date, given that the grue hypothesis is true. That is by definition 1. It doesn't depend on "plainly assuming" that they are all green.
You do understand the definition of the likelihood, I hope! Bill Jefferys 22:42, 16 August 2007 (UTC)
Postscript. I think that Hq3473 may have misunderstood me. I did not intent to say that the emeralds were green before the critical date, but that they would appear or be observed to be green. The problem is that we are using the term 'green' in two senses, one to refer to the hypothesis that emeralds aren't grue, and the other to describe our sensory observation. If 'grue' is true, then emeralds appear green prior to the critical date with probability 1, and appear blue after that critical date with probability 1. If 'green' is true, then emeralds always appear green with probability 1, both before and after the critical date. Does this clarify things? Bill Jefferys 22:50, 16 August 2007 (UTC)
I think you misunderstand the definition of grue. A grue object is NOT required to change color at magical time T. A grue object is green if observed before T or blue and NOT observed before T. Thus if X is grue it is green with probability 1 before T ONLY IF OBSERVED. Assuming that X is green ALWAYS before T is begging the question.--Hq3473 17:14, 17 August 2007 (UTC)
I thought that was what I said. If an object is grue, and it is observed before T, then it will be seen to be green when it is observed. If an object is grue, and it is observed after T, it will be seen to be blue when it is observed. If an object is green (not grue), and it is observed at any time whatsoever, it will be seen to be green when it is observed. All of my comments referred to what is observed, and said nothing about the nature of any observation that was not made but might have been. This is in keeping with standard Bayesian reasoning. I do not say that X is green ALWAYS before T, only that if X is observed before T, and it is grue, then it will be observed to be green. My comments only apply to what is observed. Bill Jefferys 17:50, 17 August 2007 (UTC)

[edit] Request for clarification

Two questions. These are honest questions; I am much puzzled by the article:

1. On what grounds does Goodman's hypothetical opponent object to the definition of grue? There is no reason why a color could not be so defined, but what objection to the definition would constitute begging the question?

2. Is Goodman's thesis simply that induction cannot provide certain conclusions? We already know that deductive logic provides certain conclusions from certain premises and inductive logic produces merely probable conclusions without the need for absolutely certain premises. We need induction because the only certain premises concern abstractions(e.g. the properties of the imaginary unit, i*); while observations of concrete things (e.g. the color of an emerald at the moment at which one is observing it), let alone conclusions induced from those observations (e.g. the color of an emerald on January 2nd, 3000), can always be mistaken. Does the grue concept address this and, if so, how?

  • Even the most complete solipsism cannot throw doubt on the proposition that i2=-1, because that is the definition of i.

Randomundergrad —Preceding comment was added at 23:24, 18 October 2007 (UTC)