Talk:New riddle of induction

QUESTION: Why does the article say that "Rachel Turner and Kate keiley (sic)" coined these terms???? Please correct. —Preceding unsigned comment added by 75.3.147.249 (talk) 14:23, 15 August 2010 (UTC)

Note: For the history of this article before 5 April 2004, see http://en.wikipedia.org/w/wiki.phtml?title=Grue&action=history

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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)

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sentence says "Casually, "grue" is used to mean" not "Nelson defined it to be", casual definition should be casual not outdated.--Hq3473 23:28, 5 December 2005 (UTC)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)

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. Lambiam^Talk 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

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...". Lambiam^Talk 22:16, 6 April 2006 (UTC)

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)

Thank you for your example of chicken induction. I am colorblind in the blue-green area of the spectrum and I was having trouble understanding the argument Phil Burnstein (talk) 11:33, 11 November 2008 (UTC)

I think the chicken induction is interesting in its own right, but it is not similar to the "grue" / "green" example. In the latter, there is empirical evidence for emeralds being grue (and green), but in the former, the chickens have evidence only for food supply, not for execution.

I just put an illustration with another example into the article, hoping it is useful, and believing it is similar to "grue"/"green". - Jochen Burghardt (talk) 21:38, 6 January 2014 (UTC)

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)

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. --Lambiam^Talk 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)

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. --Lambiam^Talk 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.

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."

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)

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)

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)

You seem to be implying that grue things are green at first, but change color to blue later. This is not the case. Grue objects don't change color. Let's use a real world example to illustrate this more clearly. Imagine a man who runs safety inspections on toys. He only inspects green and blue toys. He inspects green toys Monday through Wednesday, but then switches and inspects blue toys Thursday and Friday. A bunch of different colored toys are coming down his conveyor belt, but he only labels some of these toys "INSPECTED." His "INSPECTED" toys are all the GRUE toys where T is midweek and he is the observer. (Note: none of these toys change color.) The status as 'INSPECTED' or not depends on two factors: color, and when the toy came to his workstation for initial observation. Now, on Wednesday, if you're a guest at the factory, you'll see this guy inspects all green toys, so you might conclude that he's the green toy inspector. He's actually the 'grue' toy inspector, why don't you conclude that? Bayesian analysis doesn't really help. Each green toy on Tuesday would confirm your 'green inspector' hypothesis as much as it would confirm your 'grue inspector' hypothesis. The probability the inspector will examine green toys on Thursday would appear equal to the probability the inspector will examine blue toys on Thursday to the midweek Bayesian who has only ever seen him inspect green toys! That seems like an odd result, even for a Bayesian. — Preceding unsigned comment added by 204.87.16.4 (talk) 12:14, 9 August 2011 (UTC)

Or maybe you're implying instead that there are these grue things, and the observation time dictates the color of the object? That's very strange to me. I think it's easier to just say, hey, there are green things in the world. If they are observed before T, they become 'grue.' Before they are observed and before time T, their status as 'grue' is undetermined. Think of the toy safety inspector example, things become 'inspected' when he looks at them. Grue is like that. --204.87.16.4 (talk) 19:06, 9 August 2011 (UTC)

Solomonoff induction ciphergoth (talk) 22:58, 6 January 2009 (UTC)

Karl Popper

Karl Popper says about Goodman's paradox: "This is not a paradox, to be formulated and dissolved by linguistic investigations, but it is a demonstrable theorem of the calculus of probability. The theorem can be formulated as follows:

The calculus of probability is incompatible with the conjecture that probability is ampliative (and therefore inductive)." (p. xxxvii)

"ampliative" means:

"It is the idea that evidence e - say, that all swans in Austria are white - will somehow increase the probability of a statement that goes beyond e, such as ... In other words, the idea is that evidence makes things beyond what it actually asserts at least a little more probable."

He concludes:

"Thus there is no spill-over, no ampliative support: there is no ampliative probability, neither for swans nor for emeralds. And this is not absurd, but tautological (and it is unaffected by translation)."

Karl Popper: Realism and the Aim of Science. From the Postcript to the Logic of Scientific Discovery. Edited by W. W. Bartley, III. Rowman and Littlefield Totowa, New Jersey.1983. ISBN: 0-8476-7015-5. (Introduction 1982)

--Meffo (talk) 18:04, 23 February 2011 (UTC)

+1 My knee-jerk reaction is that I really like Popper's view, it resonates. A properly worded version of Popper's statements seem suitable for inclusion in this article, right? linas (talk) 03:42, 7 July 2012 (UTC)

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)

The puzzle presented by Goodman is that we as humans accept that by observing diamonds we can come to the inductive conclusion that "all diamonds are green", yet by the same inductive logic we also must come to the conclusion that "all diamonds are grue" (since empirical data supports both conclusions perfectly). Yet, as humans we do no consider current data sufficient to come to the "grue" conclusion. The puzzle is why is the current data enough for "green" conclusion but not for "grue" conclusion. Hope this helps. --Hq3473 (talk) 16:21, 7 January 2009 (UTC)

• • PS. Also i can easily throw in doubt the proposition that i²=-1, by asking for example this question -- "where does the power to define comes from? How can you just make one thing mean another thing?"--Hq3473 (talk) 16:37, 7 January 2009 (UTC)

    @Hq3473 this is a silly question and a red herring. "i" is a symbol which in a mathematical context is commonly used to denote a certain mathematical object that satisfies a certain property. In other words, it is merely a name. It only "means" something if people agree on what it denotes---which they largely do in this case.

    That such an object exists in a mathematical sense is a logical consequence of (ultimately) general axioms which are commonly adopted, such as those of ZFC set theory; whether or not you accept them is up to you. But in any (non-physical, abstract!) mathematical world which satisfies those axioms and in which classical propositional calculus holds, the existence of the object we call i also holds. Nobody is using any mysterious metaphysical "power" to call this object into physical existence, any more than you used some metaphysical power to give yourself the name Hq3473. And nobody but a strict Platonist would argue that it does physically exist.

    I'm aware that I'm replying to a comment that's over 14 years old, but this sort of lazy, unjustified injection of straw-philosophy into mathematics really irks me. (Straw-philosophy, because it's not really philosophy---just asking meaningless philosophical-sounding questions to try to undercut mathematics, while not understanding that all mathematics is done by convention, that is, the convention of adopting an underlying formal system that we think is reasonable and useful. Everything happens relative to that. "God made the natural numbers; the rest is the work of man" --Kronecker, quoted approximately from memory) 2601:98A:4100:3A:E28B:DD03:334F:19CA (talk) 02:52, 2 March 2023 (UTC)

Analogy to the history of weights and measures

In the proposed resolutions, I see analogies to the evolving definition of the metre:

1. Grue is less fundamental because it is defined in terms of blue and green. Defeated by the fact that green can be defined in terms of grue and bleen.
2. Grue₂₀₁₁ can be defined in terms of blue and green. It is defeated by defining green₂₀₁₁ in terms of grue and bleen.
3. Green₂₀₁₁ can be defined as colors closer to the spectrum of some reference emerald than to that of the Logan sapphire held at the Smithsonian. But then this has the same problem as the Sevres kilogram: the properties of the reference might change.

Conspicuous by its absence is a resolution analogous to one proposed in 1893: "Blue" is any color whose visible component is closer to the spectrum of Rec. 709 blue than to that of Rec. 709 green or Rec. 709 red. How can this be worked into the article? --Damian Yerrick (talk | stalk) 15:43, 10 July 2009 (UTC)

The problem with that idea is that instead of questioning whether "green" or "blue" are primitives, you can question whether "having a particular numeric value" is a primitive. You can define "grue-lookup" and "bleen-lookup" as what we would normally think of as "has the green/blue value on the chart before time t, and has the blue/green value after t". Then you can point out that the actual chart is defined so that its points change from grue-lookup to bleen-lookup as of a certain date. And then raise the question "how can we say that this chart, which changes from grue-lookup to bleen-lookup, is simpler than this other chart which is grue-lookup all along?" Ken Arromdee (talk) 03:28, 26 August 2009 (UTC)

New Response

David Deutsch's book The Fabric of Reality has a chapter (or two) on the problem of induction including an argument similar to this and a response to it that isn't one of the responses listed (which to me all seem like Straw men). It's been awhile since I read it, so I don't remember the neologisms used, but the "problem" concerns a new theory of gravity where everything falls except for this one person (the speaker) who floats, then defining some word so that you can still say "everything flalls (or whatever the new word was)". The argument continues by using "flalls" as a primitive and redefining "floats" and "falls" in terms of it, analogously to the arguments in the first response listed. It then responds to that by taking the use of "flalls" to it's absurd conclusion. If "flalls" were to be used as a primitive than that one special person who needs to be mentioned in the disjunctive definitions of "floats" and "falls" would be so important scientists would be lining up before the child's birth to find out why that child is such an integral part of our scientific theory and language. Even if the discovery isn't made until after the birth, that person would be the most heavily studied being in history. This insane situation shows why "flalls" can never be a primitive.

Analogously, if "grue" were a primitive, it could only be used relative to variable t, in which case the second response holds, or the time t would have to be constant, and would therefore be a special time somehow extremely different from other times. If this special time is one of the seemingly normal moments ticking away right now, then it's specialness is completely bonkers (sorry, I meant "absurd"). If however, the time is special in some way, such as being the beginning (or end) of the universe than the distinction between grue and green (or blue) hardly seems important.

If it seems confusing, I'd consult the book. I believe the chapter I'm referring to is just a big dialogue between two people, one trying to solve the problem of induction and the other poking holes. It'd probably be a better help than me at explaining the original argument and applying it to the Grue/Bleen problem.

--SurrealWarrior (talk) 22:14, 27 July 2009 (UTC)

deleted

I deleted this:

We can solve the New Riddle of Induction by referring to the act of observation itself. Suppose we are on a desert island, somewhere around the time "t", but we have lost our watch and we don't know for sure whether the time is just before "t" or just after "t". We pick up an emerald. We see immediately that it is green. Now we ask ourselves, "Is it grue or is it bleen?" We cannot answer this question because we are unable to observe the time with sufficient accuracy. The emerald may be grue, it may be bleen. Thus we show that the colors green and blue do not require an observation of time, while the colors grue and bleen do require an observation of time. We can proceed with this observational distinction and so develop a definition of scientific method that answers the New Riddle, as presented in A Recipe for Self-Consistent Projection.

First of all, it seems to be from a non-peer-reviewed, self-published paper.

Second, it doesn't make sense anyway. Saying "we see immediately that it is green" assumes that you have a method of observation that can determine a green/blue difference but not a grue/bleen difference. If you make this assumption, you've already begged the question. Of course green is going to be simpler than grue if you assume that observations can detect it while being unable to detect grue. Ken Arromdee (talk) 21:15, 18 January 2010 (UTC)

With respect, you have missed the point. The observer determines which predicate is ill-behaved by the manner in which he is forced to observe the predicate. There is perfect analytical symmetry between grue and green. But there is an absolutely clear and definite observational asymmetry. It is a simple and incontestable fact that we can observe with our own eyes the color green without knowing what time it is. In the example I give, the grue-speaker cannot answer the question, "What color is the emerald" because he does not know what time it is. We cannot observe the color grue unless we know the time. Thus the act of observing green does not require an observation of time, while the act of observing grue does require an observation of time. I can describe any number of empirical means by which I can determine green/blue without observing the time, and you cannot think of any means by which you can observe grue/bleen without observing the time. There is no begging the question. It is a simple matter of allowing the act of observation to dictate which predicates are well-behaved. Once we accept this empirical asymmetry, we exploit the asymmetry to produce a definition of scientific method. Now, I can perfectly understand that you find it absurd that the solution could be so simple. It took me years to see it myself. Nevertheless, I assure you that if you give the idea a chance, you will find it is correct.

As to the paper being self-published, of course it is. But there is nothing in the Wikipedia rules that says that references must be reviewed by a selection of alleged experts to whom the readers do not have access. Therefore, you must judge the merits of my addition on the basis of whether or not readers would be interested. I think it's pretty clear that readers would be interested to see that the symmetry between grue and green can be broken by an examination of the act of observation. Therefore, my addition deserves its place here. I have been succinct and clear. I am not attempting to publish my work. Anyone outside philosophy will understand what I'm saying immediately. It's only those of us who have thought about this problem until we are bleen in the face that can fail to understand it on the first reading.--Kevan Hashemi 03:12, 19 January 2010 (UTC) —Preceding unsigned comment added by Kevanhashemi (talk • contribs)

I deleted it again. Wikipedia policy prohibits self-published sources except under very limited circumstances. Either they are being used as references about themselves, or they are self-published, but written by an expert who has also produced papers that are not self-published.

Your idea about what is in Wikipedia rules doesn't match actual Wikipedia rules.

Wikipedia:RS#Self-published_and_questionable_sources

Ken Arromdee (talk) 22:44, 16 February 2010 (UTC)

So, you accept the fact that the response I have added to the page is correct, and would be of great interest to the reader, but you remove it anyway because you believe that this page should be controlled by self-appointed experts. A "reference" is a basis for backing up a claim that is made without sufficient discussion in the Wikipedia page. In this case, the link to my paper is not a "reference", because there is sufficient argument in the single paragraph I have added to justify its addition. The link I provide is for the interested reader to follow, as a further discussion, but is not used to justify the paragraph. --Kevan Hashemi 14:49, 22 February 2010 (UTC) —Preceding unsigned comment added by Kevanhashemi (talk • contribs)

I do not believe the page should be controlled by self-appointed experts. The page must, however, follow Wikipedia rules, and they don't allow what you're doing. You've got to have a reference. The paper is unacceptable as a reference because it is self-published, and putting it on your department website doesn't change that. Telling me that the paper isn't a reference doesn't help you, because then you just don't have any references at all, and you need them.

WP:NOR "This means that Wikipedia is not the place to publish your own opinions, experiences, arguments, or conclusions."

"Any material that is challenged or likely to be challenged must be supported by a reliable source. Material for which no reliable source can be found is considered original research. The only way you can show that your edit does not come under this category is to cite a reliable published source that contains that same material." Ken Arromdee (talk) 17:45, 25 February 2010 (UTC)

Comment from help desk person..I have posted this to Kevan talk page as well....So i see both of you getting a bit frustrated with this ..

Ok so what to do now?.Well first Kevan can you find the paper you did some time ago cited by some journal etc..Basically what the other editors are saying is that they believe you wrote the paper (you do not deny this in fact say it was you) .. Ken's problem is hes not sure if the greater community has endorsed this view... so what we need to find is a website book journal etc..that has published this view or even recognized its existence. What you need to provide Kevan is proof that someone other then yourself has had a critical look at your paper, be them positive or negative just evidence that people who are experts in this filed except your also a cit-able references. After saying all this we also must keep in mind there is likely a Conflict of interest with Kevan writing in the article about view he published. So we must treed lightly on this matter and make sure there's a Neutral point of view.....So what i suggest is for Kevan to bring his additions here on this talk page first..So we can talk about the changes first with a more reasonable reference. Buzzzsherman (talk) 18:47, 25 February 2010 (UTC)

Okay: I think I understand your point about disputed commentary, and the conflict of interest if I link to my own work to back up my commentary. And let me assure you that I will conform to whatever the majority decides. I have some friends who are willing to step in on my behalf, but I think that would be out of keeping with the spirit you have described to me, so I'll go it alone. So, let me back up a bit and ask what happens if what exists on the page at the moment appears to make no sense. And to pursue such a discussion, I suppose there's no getting around the requirement that the participants in the debate have a basic understanding of the subject: the color grue and its comparison to green. So, let's look at the second of the two existing responses. It claims that we can observe the color grue without knowing what time it is. But that's impossible, as I'm sure we can all agree. An emerald is grue if it is green AND the time is before time "t". If it's green after "t", then it's not grue, it's bleen instead. There is no empirical procedure for observing grue without knowing the time. That's a pretty basic and obvious fact of scientific observation. But we don't have to know what time it is to say that it's green or blue. So how can the second response be logically correct? My response is to point out the simple fact that it is impossible to observe grue without observing time, while it is easy to observe green without observing time, so the symmetry, and therefore this alleged New Riddle of Induction is solved. Now, the fact that philosophers may have been so confused as to have failed to see this point does not mean that the point should be rejected from the page, because the casual reader is going to be perfectly capable of seeing the point, and will be glad to read it. Furthermore, the existing response paragraph doesn't make sense, so why do we have them in at all? Having said that, I see that it's not good policy for me to add a link to my un-published work on the matter. But on the other hand, the fact that philosophers can't see something this obvious also guarantees that they won't publish any such work, so the entry in Wikipedia will be degraded permanently because of a failure among philosophers to see the obvious. If you can dispute my claims about empirical observation, then I will be humbled and grateful at the same time. But if not, then we have a problem, and I await your solution.--Kevan Hashemi 03:26, 1 March 2010 (UTC)

A very similar argument has been made by R. G. Swinburne in 'Grue' Analysis, Vol. 28, No. 4 (Mar., 1968), pp. 123-128. He distinguishes between qualitative and locational predicates. The former, like green, can be assessed without knowing the spatial or temporal relation of the object under observation to a particular time, space or event. The latter, like grue, do require knowing the spatial or temporal relation of the object under observation to a particular time, space or event, in this case time t. Whilst green can be given a definition in terms of the locational predicates grue and bleen, this is irrelevant to the fact that green is a qualitative predicate whereas grue is locational. He argues that when qualitative and locational predicates yield different predictions, we should project the qualitative predicate, in this case green. 92.11.103.10 (talk) 15:36, 30 March 2010 (UTC)

That's great. Thank you for the reference. I think we should insert Mr. Swinburne's analysis as one of the responses. I tried to obtain his paper from home, but couldn't get a copy. I'll try from campus tomorrow. I like your paragraph, what about inserting it as is? Do you know of any application of this response that solves other questions of scientific method, such as when we are entitled to draw a line between observed points, and assume the line works between observations? I believe I did that in my own paper, but it's self-published, and so not permitted as a reference by the Wikipedia rules.--Kevan Hashemi 01:48, 31 March 2010 (UTC) —Preceding unsigned comment added by Kevanhashemi (talk • contribs)

Rainer Gottlob has a go at it in his 'Emeralds Are No Chameleons: Why "Grue" Is Not Projectible for Induction' from the Journal for General Philosophy of Science / Zeitschrift für allgemeine Wissenschaftstheorie. This paper applies to grue a theory he develops in Gottlob, R. (1992): "How Scientists Confirm Universal Propositions (Laws of Nature)" Dialectica 46, 123-139. He suggests that you need i) the evidence to fit your hypothesis, ii) the hypothesis to pass through 'sieves' - whatever these are - and, iii) an explanation as to why your hypothesis should hold. I haven't read the papers fully so can't comment if its any good as a theory.

I've put the Swineburne in. It might be worth adding a sentence saying that although he shows that green and grue are different types of predicate, this doesn't actually give us any reason to suppose that qualitative predicates should be preferred over positional ones when it comes to making predictions. I wonder if this is because he has no reason other than that he wants to call the emerald green not grue. At any rate, he would need to give us reasons on this point for it not to be question-begging.

My own feeling is that Gottlob's approach is more likely to yield fruit, since we have a reliable notion (ultimately dependent on universal laws) of what changes and what doesn't (in the case of the emerald, how it appears to us, or a scientist might say the kind of light which comes of it) and can form our concepts and make conceptual preferences accordingly. Goodman is then useful in showing that our concepts don't have a priori strength but rather are dependent on our trust in universal laws despite not ultimately being able to prove they hold. This is a long winded way of saying that a peer-reviewed version of this argument would improve the article which at the moment has a deficient 'responses' section, given the hoards of philosophers who have responded to the paradox.

Lastly, Goodman's own solution also needs including - that our concepts our entrenched rather than valid. 92.11.103.10 (talk) 16:24, 31 March 2010 (UTC)

Esoteric

This article is ridiculously esoteric. I think somebody needs to explain more clearly exactly what "grue" is (and without resorting to theory or examples). What is "grue"? This article makes no sense to me and I suspect that it doesn't make much sense to anyone who hasn't taken a survey course in philosophy of science. EttaLove (talk) 22:00, 29 October 2010 (UTC)

Apologies - another question about the paradox

I think the article is excellent, but I have a question about the paradox.

I build a decision machine.

I put the object in the input box, where a light shines on the object.

A sensor sits behind a yellow filter. If the light from the object is green, the buzzer rings. If the light is blue, then it is filtered out and no buzzer rings.

My definition of green is: "An object X satisifies the proposition X is green if the buzzer rings when X is inserted in the box."

How does one define grue in this case so it is not disjunctive? Dilaudid (talk) 09:03, 30 April 2012 (UTC)

Based on Ken's comments above it appears that the buzzer sounding can be redefined as not primitive. A buzzer sounding before the year 3000 is a buzzlence ( a word meaning a buzz before the year 3000, or silence afterwards ) but after 3000 is not a buzzlence. Hence the the non-disjunctive definition of grue is "X is grue if the buzzer buzzlences when X is inserted into the box". Any comments on this word-mince? Dilaudid (talk) 13:53, 19 May 2012 (UTC)

argument from complexity?

The article N-universes mentions "Occam's razor" and it got me to think: surely grue is not minimal from the complexity point of view? Complexity, here, would be Kolmogorov complexity or Solomonoff induction. Such an argument is similar to the Bayesian argument discussed above, wherein one assumes that priors must be minimal. To be precise, though, I am obliged to point out that complexity is language dependent, so its possible that there are aliens who would find grue more parsimonious than green, although Kolomogorov complexity puts a limit on the scope of such languages, and such paradoxes... has no philosopher yet attacked this question from this angle? linas (talk) 03:32, 7 July 2012 (UTC)

There's GOT to be some philospher out there that's made a Occam's razor based rebuttal and justified green as more parsimonious using Kolmogorov complexity. After all, green is a subset of the wavelengths in the visible spectrum. Specifying green is just "Wavelength_of_Emerald=540nm", while grue requires something like "if year ≥ 2000AD( Wavelength_of_Emerald=540nm) else (Wavelength_of_Emerald=460nm)" which is over twice as complicated. A good step towards improving this article would be finding the philosopher who has made that (rather obvious) rebuttal and citing them. But googling has not revealed such a source Can anyone more philosophy-paper-literate think of someone? 24.243.183.180 (talk) 06:32, 1 November 2012 (UTC)

Origin of the Words

The List of fictional colors claims (without citation) that the colors grue and bleen were invented by Charles Dodgson in Sylvie and Bruno, but the opening line of this article attributes them to Nelson Goodman. If the words do in fact appear in Dodgson's book, it seems like it would be easy to confirm this, but as of now, the articles link to and contradict each other. 50.195.91.9 (talk) 16:43, 3 May 2013 (UTC)

 Done Fixed by user:the hanged man. Paradoctor (talk)

"Just in case"

On behalf of the general audience, I have replaced the misleading and confusing expression "just in case", with its correct, and easily understood equivalent, "if, and only if" (also, in more technical writing, "if and only if"). The following explains the error:

• Language Log: "Just in Case"
• Southern California Philosophy for philosophy graduate students: "Just in Case".Dr Lindsay B Yeates (talk) 21:47, 9 April 2014 (UTC)

May is not a reliable source. Pullum's post says that "just in case" is how American English speakers "trained in the formal sciences and philosophy" express themselves. Which means that translating "just in case" to "if and only if" would mispresent the source, especially since we are reproducing a definition here. That jargon conflicts with previous usage is hardly new, mathematicians gnash their teeth when physicists talk of the Minkowski "metric". As is par for the course, this problem has already been noted and cited to Pullum's post in another article, so I reinstated the "correct" wording and wikilinked to the article noting this usage.

It might be possible that the use of "just in case" derives from the use of "being the case" in truth theory. This could be coincidence, I'm synthesizing on all cylinders here, but IIRC, in disquotational truth theory, 'p' is true if it is the case that p. Don't quote me on that, though. Paradoctor (talk) 22:59, 9 April 2014 (UTC)

---

I didn't see this talk page before I edited the main page to say "if and only if" instead of "just in case". I am researching the subject now, but I'll start by saying that I was told by a professor (I understand this is hearsay, but it's commonly believed) that the use of "just in case" in place of "if and only if" was originally a misunderstanding. Supposedly, an American philosophy professor used to use "just in the case that" when explaining the biconditional statement "if and only if"... as in "X if and only if Y"="X just in the case that Y". It apparently started to stick in the altered form "just in case". And apparently became a popular replacement for "if and only if" with US philosophers in the mid 20th century, but my understanding is that it's since almost totally died out... as evidenced by the low number of results after a google search of the term: ""just in case" biconditional" (8,850 results compared to 51,500 results for the search term: ""if and only if" biconditional"). I doubt there are any philosophy/mathematics/logic textbooks in use today that exclusively use "just in case" to mean "if and only if".

Admittedly, Nelson Goodman used "just in case" when he wrote about the "new riddle of induction" in his book "Fact, Fiction, and Forecast" (1955), but as I said, I think it can best be described as usage specific to a certain time period and location. "If and only if" is the more correct modern usage now and I really think using "just in case" only serves to confuse the issue for modern readers of Wikipedia.

TL;DR: I think the most important thing is that "just in case" means something different to the vast majority of English speakers. Weigh the pros and cons... using it adds nothing to the article, but it has the potential to confuse a lot of people; whereas by using "if and only if", there is no confusion and no value is lost. Bzzzing (talk) 17:38, 15 November 2015 (UTC)

Induction & deduction

WP DEPENDS ON INDUCTION & DEDUCTION. THEIR MEANING SHOULD BE FIRM. This encyclopedia accepts the premise of enumerative induction that the more editors who agree on the content of an article, the more accurate and useful that content. Induction is practiced on every TALK page. Editors generalize from a few observations, and deduce concrete conclusions from their generalizations.

WP contains 4 repetitive and fragmentary articles on induction: [Inductive reasoning], [The problem of induction]; [New riddle of induction],[Inductivism]. I would like to rectify this chaotic situation by rewriting and merging these 4 articles, retaining only the reasoning title. I ask you—a participant in relevant TALK pages—to judge my rewrite/merge project: SHOULD I PROCEED? Below is the current proposed outline:

Definitions. Induction generalizes conceptually; deduction concludes empirically.

[David Hume], philosopher condemner.

[Pierre Duhem], physicist user.

[John Dewey], philosopher explainer.

[Bertrand Russell], philosopher condemner.

[Karl Popper], philosopher condemner.

Steven Sloman, psychologist explainer.

Lyle E. Bourne, Jr., psychologist user.

[Daniel Kahneman], psychologist user.

[Richard H. Thaler] economist user.

Please respond at Talk:Inductive reasoning. — Preceding unsigned comment added by TBR-qed (talk • contribs) 16:01, 5 January 2020 (UTC)

Yet another real world example: the effectiveness of vaccines

Some vaccines confer lifetime immunity. Polio leaps to mind as an example.

Some vaccines are known to give immunity for a period of time, and then must be renewed or boosted. Tetanus leaps to mind.

Some diseases mutate so rapidly that everybody has to get vaccinated periodically, say, once a year, in order to have continuous protection. Influenza might be a good example, except that the scientists who decide what next year's epidemic is going to be frequently get it wrong and then it doesn't work well (most of the time, they do a pretty good job).

Some diseases have not been present long enough to know. The vaccines for the novel corona viruses fall into this category. We have enough experience with the disease at this time (January 24th, 2022) to know that 2 shots are not enough, the new minimum is 3. The Israelis have done or are doing an experiment to see if a 4th shot would be helpful and the answer so far seems to be "we don't know yet". But it might be the case that in, say, 2023, a fourth shot would be helpful. We honestly do not know. We probably cannot know, but it is possible that an advance in technology will allow for a better prediction.

There is another hypothesis to be considered. It is hypothetically possible that everybody who gets COVID-19 dies within 10 years. 100% COVID-19 infection means death within 10 years. The novel coronavirus hasn't been around for 10 years, yet. There is another disease, shingles, in which the varicella zoster virus can remain dormant for years or decades. 100% death due to coronavirus infection within 10 years is a real world "new riddle of induction" problem.

Don't be as a chicken with regards to the farmer's wife: get vaccinated.

Vaxvms (talk) 07:27, 25 January 2022 (UTC)

References

There is a typo in the first image.

At the bottom row, it says "bleen" instead of green. 103.102.87.140 (talk) 15:07, 28 October 2023 (UTC)

No, the image is right. Following your suggestion, green would be defined in terms of itself. - Jochen Burghardt (talk) 17:43, 28 October 2023 (UTC)