I have seen other people try to explain this argument both on youtube and other places. And everyone seem to think that something is "grue" if it changes colour from green to blue at time t. This is wrong and it annoys me that so many misunderstands the argument. So I want to thank you for getting this right.
It's not really wrong though. I think the video makes it more confusing by not talking about this. If something changes from green to blue at time t, it will be grue before t and grue after t. Whether it changes colour or not, it still will have been grue before t, so you're quite correct that the definition of grue needs to allow for that. But at the same time, the point of the riddle is that it's very unlikely for emeralds to change from green to blue, yet it's very likely for them to change from grue to bleen, despite there being equal amounts of observed evidence for both possibilities. So it's vital to the argument that we talk about how something grue *could* change from green to blue.
As it is said @3:35, the definition of "grue" _is_ disjunctive, and that _does_ change the structure of the argument. Nothing that was said in answer to that objection makes the remotest sense to me.
mothman84 Green can be defined in terms of grue and bleen in exactly the same way grue can be defined in terms of blue and green. Thus, if you accept that that definition of grue is distinctive, you also have to accept that at least one definition of green is disjunctive.
@@plasmaballin But green can be reduced to existing outside time, whereas grue introduces temporal elements. That is what makes grue a more complex term.
@@cameronmarnoch5236 Green definitely cannot be reduced to existing outside of time. When I refer to a green object, I am referring to an object that is green at the moment I refer to it, not one that is eternally green (the same goes for a grue object), and the physical meaning of the color green is a certain frequency of light (frequency is very much a temporal property). That being said, I do still think that grue can be considered more complex - green can be defined in a simple way like "the color of an electromagnetic wave with a frequency between 540 and 580 THz", while grue cannot be defined in this simple way. However, that doesn't change the *form* of the argument. In deductive arguments, the complexity of the terms doesn't matter. "All emeralds are green. The gem in my hand is an emerald. Therefore, the gem in my hand is green," is valid, and so is "All emeralds are grue. The gem in my hand is an emerald. Therefore, the gem in my hand is grue." That's what makes the new problem of induction interesting - it shows that we need to know more than just the form of the argument to determine whether an inductive argument is strong.
Right. I struggle with the disjunction, the weirdness of past tense in a world where "yet" is always a moving goalpost, and the difficulty of defining "observed", and especially combining "not yet observed" with a claim about a quality that must be observed to be confirmed, which involves the unfulfilled motion of "yet".
I think that there is a fundamental difference between green/blue and grue/bleen. The key here is that inductive logic is based on observation and observing things does not change their green/blue properties, but it changes their grue/bleen properties. Therefore I think we can use inductive logic to make statements about the greenness and blueness of objects, but not grueness and bleenness because the fact of observation influencing grue/bleen state makes our sample fundamentally biased and unrepresentative of the whole population.
+Adam Kucz (Acalc79) Now, on second thoughts, I see that my previous explanation is incomplete. While it probably is true, we have no way of checking which of the properties (greenness or grueness) changes with observation. We conventionally assume it is grueness because we are not used to it, but it may as well be greenness. If that were to be the case then the conclusion from the second argument is correct: all emeralds are grue, the observed ones are green and unobserved are blue, but the very fact of observation changes the green/blue property and any emerald we observe remains grue because it changes color to green. With that said, I don't think there is any point in caring too much which properties are "real" and which are "observation dependent" as the only things we will ever experience are the observed ones. Therefore I suggest changing both arguments into "all observed emeralds are green" and "all observed emeralds are grue". Both of them are correct no matter which property is "observation dependent", moreover, they reflect the true state of our knowledge of the world: we can say anything only about things that has been or will be observed, the "true" reality is inaccessible to us.
@@AdamAcalc79Kucz so what 'is' induction? The idea is that we'll always resort to fallible and inexact kinds of definitions. I think Goodman is right in highlighting this problem. My intuition is that there is fundamental asymmetry between ampliative systems and the exactness of deductive logic. The strange thing though is how the reverse seems so easily applicable (math is physics for example). Perhaps deduction truly is more fundamental to our reality, but that just further tempts us to define the foundation of science on similar terms.
That's not really the point here, we're not worried about whether unobserved emeralds are turning from blue to green as soon as we observe them. The original meaning of grue is that at some specific time, such as 2025, every emerald, if it is to remain grue, will actually turn blue. So it is a fact that all emeralds are definitely grue right now, as well as being green. So given the weight of evidence that all emeralds are grue, should we conclude that all emeralds will be turning blue in 2025? That is the point of the riddle.
I'm having difficulty buying that the definition of green can be more complicated than the definition for grue/bleen because both grue and bleen use green in their definition, meaning that they are recursively defined. In fact, the references in the second definition of green all seem circular to me. What am I missing?
You're missing the fact that "green" is not more fundamental than "grue". Suppose mankind had no concept of green, and instead understood things in terms of grue. This should not change the logical structure of the argument, right? It's just a different perspective of looking at things. Well, if this is the case, then because we defined grue as our "fundamental" color, green would then become more complex.
I agree with you. It does not matter if green or grue is more fundamental as Axe Menace said, because the second definition of green is self referential and is a non-statement. The second definition of green when it is further examined simply means Green is green when it is unobserved and it is green when it is observed.
I believe the puzzle is birthed out of the partial improvable nature of 'grue'. In order for something to have a good definition it must be based on experienced criteria. So the puzzle is less to do with the nature of logic and more to do with the nature of definition. Which I understand was explained to be true in the video.
I am quite confused on a matter and was wondering if somebody could provide some clarification. So an emerald is grue if it is green upon observation and blue if yet to be observed, correct? If this statement is true then how can we conclude that the all emeralds are grue if no emerald has been observed to portray the color blue? What I am trying to say is that if we have never seen a blue emerald how can we make the claim that all emeralds are grue? Do we simply assume that emeralds not yet observed must be blue (or better yet not green) ? I need to write an essay on the Grue paradox so any feedback would be appreciated
I think the point Nelson Goodman is trying to make is NOT that at the moment of the observation the emerald is blue, but if the the moment of the observation is after time (t) then the emerald is blue, but if the emerald is observed before time (t) then is it perfectly consistent with being grue because grue is only blue after time (t). So, here Goodman is trying to make the point the observation can support any proposition about emeralds as long as it is observed before time (t) So, the problem is not that observation can not justify inductive reasoning as argued by David Hume, but instead it can justify an infinite number of propositions about emeralds properties as long as they are observed before time (t).
I finally understand this argument. Goodman's a great logician. From what I can tell, this seems to be a fatal blow to the project of creating a formal account of induction. Yet this is clearly a case of a paradox, not an issue with induction itself. It's too bad that we can't incorporate induction into a logical framework (unless someone figures out a solution). Justifying induction on more superficial levels is quite depressing.
I don't get it. The moment we observe a new green emerald, then grue has been falsified. So obviously green and grue are very different inductive claims. The only way around this is to create a definition of grue that constantly updates with our observations. However, that violates simple concepts of identity. An emerald that was not "grue' yesterday might suddenly become "grue" today simply because I looked at it. Unless there is a good, pragmatic reason to want to define emeralds in such a way that updates with us looking at them, then that's obviously a stupidly nonparsemonious definition.
+AntiCitizenX 'The moment we observe a new green emerald, then grue has been falsified.' You miss the point. It's not about falsifying anything, it's an attempt to demonstrate what makes inductive arguments good or bad cannot be just their form (as is the case for deductive arguments). The practicality of the definition of grue is irrelevant.
+AntiCitizenX Parsimony is not part of inductive logic and thus there is no issue with having "grue" update with new observations. Of course, you don't need to have "grue" update with new observations as part of the observation, you can just make up a new "grue". So you'll have "grue 1" at first and then have "grue 2" and so on ad infinitum without a problem.
***** *It's not about falsifying anything, it's an attempt to demonstrate what makes inductive arguments good or bad cannot be just their form* That's a fair point, but I don't really know of a single philosopher in existence who honestly disputes this. Everyone knows that induction is a little more nuanced than some rote, mechanical operation on propositions.
+James Glover Also, why can't we argue the form of grue? The definition contains propositional elements that are obviously unfounded and unjustified. Green does not.
Grue is more complex depending on the understanding of what it is to be grue. If grue refers to two separate classes of object: green observed objects and blue unobserved objects, and cannot be reduced to one class of objects, then it is more complex. Green is less complex because it implies only one class of object regardless of whether it is being observed, unobserved, or even non-existent. Green is not conditional in that we when told that something is green we do not have to ask whether or not it has been observed in order to know what color it should appear if it were currently observed. There is another possible case of grue, however, which could refer to an object which changes colors once it has been observed. If we are referring to this class of grue, objects which change from blue to green once observed, then there is no paradox, because it seems perfectly plausible to say that if all previously discovered gems were grue that upon observing the next object it should also be grue because the very act of observation makes it become grue. It is grue before we observe it and it becomes grue after we observe it while still being a green grue gem once observed. In the first case it isn't really a fair comparison, however, because in the first case grue actually refers to two separate classes of object while green only refers to one, and the meaning of grue is exchanged in the act of observation creating a paradox which would not have taken place if grue referred only to a single class of object. You could create a similar paradox by categorizing two disparate classes under the same term by the use of a disjunction, so for instance a buman refers to birds when not being punched in the face and humans when being punched in the face. If we cycle through an array of items punching them in the face and all previous items have been bumans it is unreasonable to assert that the next as of yet unpunched item will be a buman because by its nature as an unpunched item we're actually referring to an entirely different class of buman, that being the unpunched bird class which is entirely distinct from the punched human class. We can avoid such paradoxes by simply not referring to things under the same name which in context cannot be exchanged. For instance organism is a good umbrella term when referring to things which carry out homeostatic functions, but not as useful when talking about things that fly since not all organisms are things which can fly, so when discussing things which can fly unless we are given additional context, we would simply avoid the use of the word organism so as to avoid confusion. Likewise we would simply avoid the use of grue where it would cause a contradiction in cases where observed and unobserved grue objects cannot be exchanged for one another while retaining the same essential meaning and semantic function.
What you are saying is false. Consider one class of objects - called and emerhire. And object is an emerhire if and only if it has been observed, and is an emerald, or has not been observed, and is a sapphire. It is the case that each time we had observed an emerhire to be grue, it gives some credence to the notion that all emerhires that will be found in the future will be grue. Also, it is not the case that, each time we had observed an emerhire to be green, it had given any credence to the notion that all emerhires that will be found in the future will be green. We can also imagine things such as Sappheralds which are saphires if they were originally observed previously, or emerald if they will only be discovered in the future. Just like all emerhires are grue, all Sappheralds are Bleen. It happens that we have a natural language where words like green and emeralds are more ordinary than words like Grue and emerhire. But it does not have to be so. More importantly, having a language where words like Grue and emerhire and common seems to be metaphysically innocent compared to a language that uses words such as emerald and green. In other words, that our language mostly has words such as green and emerald is only an accident of history, and is philosophically irrelevant for that reason.
+Annaelle Jacques-Morel I never claimed the commonality of the words mattered, merely that in have more characteristics, more qualities, and various disparate natures in fact makes a thing more complex because like in the example the first type of grue is not the same as the second type of grue.
+Annaelle Jacques-Morel Even when green is defined in terms of grue and bleen it is still simpler because it retains its same nature and characteristics whether observed or unobserved and only has the one characteristic regardless of how it may be defined. Even if bleen and grue were more common they would still have dual characteristics to greens single characteristic. It's like with humans. Humans are so large that they can lift boulders and so small they can be lifted and held with one arm. How can this be? We are really talking about different kinds of humans: grown adults and babies. Why two names for one thing? The characteristics have changed and that observation must be acknowledged to avoid confusion. Grue likewise must be given thesame consideration since green grue isn't the same as blue grue. Even if the grue logic would work on emerhire it is only because emerhire is also two different kinds of object loosely regarded under one name though it has disparate properties under different conditions of discovery.
You ARE aware that «green» is actually a word that describes a specific wave length of electromagnetic radiation in the specific context of interacting with the retina of a live human eye, and that green can be a different wave lenght of electromagnetic radiation whenever it interacts with the retina of a live animal of another specie such as a dog? Right? It is arbitrary and disingenuous to say that green is a metaphysically simple term. It is nothing of that sort.
+Annaelle Jacques-Morel Even by that understanding it is a specific set of wavelengths while grue denotes two sets of wavelengths at different times. Even then there is sometimes a need to distinguish for instance lime green and forest green.
Can someone help me? Isn't the structure of the induction flawed in the first place? If "all emerald observed by now are green", you cannot induce that "all emeralds are green". Since "All emeralds observed by now are green" only infers that if you have an emerald observed by now, it is green. It says nothing about the remaining emeralds in existence.
My thought too but isn't this the difference between deductive and inductive logic? In this argument it simply gives and indication that they probably will be green and hense is a good inductive argument..
What I understood was that the word grue was made to demonstrate a situation where an inductive reasoning is "definitely" wrong, rather than being "possibly" wrong or not definitely right. We know that quantitative data cannot be converted into qualitative data, which means no matter how many times one observes emeralds as being green, it cannot necessarily lead to the conclusion "therefore, all emeralds are green," since the thesis can be proven wrong whenever a non-green emerald is found, which means there is always a possibility that it is false. But in the second example with grue, the inductive argument is always wrong, without a possibility of ever being right by its definition. But I don't understand what is so paradoxical about this problem honestly, because it just seems like another more complicated way of proving that induction cannot guarantee truth.
That is the original "problem of induction". This "new riddle of induction" is a further exploration of the problem of induction, but you're right that it's really the same thing. It's a mistake to say it's about "good induction" vs. "bad induction", because we really can't predict the future. If we're tempted to believe that all emeralds are green and will stay green forever, it's still conceivable that we are unaware of some law of the universe that turns all green things blue in 2025, or that we're living in a simulation and somebody starts messing with the RGB parameters.
GRUE's meaning depends on the context so it is not a very well defined term, right? It's more like GRUE(x) function and you cover up the (x) part with language semantics so it looks like a constant.
it's just that the strange definition of grue creates a contradiction. It's not really a paradox. You could invent many other words with wacky definitions that will create this contradiction. The important thing is that the definition of the word changes based on observation which is key to the deductive logic. It's like me defining a new number 2, but the difference is that when you add this 2 to another number it becomes 3. So then 2+1=4. Not a paradox but rather a manipulated outcome.
Is 'grue' isn't even a consistent definition? If the next emerald I observe is grue, what colour will it be? Will it be blue, since it has not been observed yet and hence is blue, or will it be green, since it will have been observed and hence green? It seems that to say an object is grue we are actually saying it had to have changed colour: it was blue whilst in the ground, but as soon as it was observed it became green. Thus it is not true at all to say that all emeralds observed thus far are grue, since they did not change colour (or if they did we wouldn't know, hence we wouldn't know they were grue). So it does not follow that the next emerald to be discovered will be grue. And even if it is, what we will find is that it is only blue NOW, before being observed: as soon as it IS observed it will change to green, hence it will be like all the others we've seen and hence green.
Sometimes in literature, Gruefullness is given a specific deadline (such as being originally observed by human eyes before the 15 of december 2020 at 11h59 PM) to avoid the confusion you seem to be having.
Because you asked : "Is 'grue' isn't even a consistent definition?" The consistency of the word grue is beside the point. The point is that there cannot be a purely formal account of inductive reasoning the way it exists for deductive reasoning.
+Annaelle Jacques-Morel Thank you for the caveat you added, which makes this more interesting. However, without it i stand by my statement that none of the emeralds were grue before they were discovered and the chances that the next undiscovered emerald will also not be grue are very high as a result. As for the caveat, that seems to be making the definition even more contrived and complex, but I'll think on that one
"The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction. The process of subsuming new instances under a known concept is, in essence, a process of deduction." -Ayn Rand. "In reasoning, the conclusion follows from the premise necessarily...in deduction, the conclusion is necessary, otherwise you negate one specific product of the conceptual faculty, one specific generalization. In induction, the conclusion is necessary, otherwise you negate the whole system of human concepts." -Leonard Peikoff.
1:50 this is not induction as to negate the conclusion would not negate the whole system of human concepts. If it is the case that by the chemical structure of an emerald that the only possible frequency of light that can reflect is green then we can induce from one emerald that all emeralds must be green because the alternative would negate the whole system of human concepts about light and matter and microscopes and science and identity and existence.
2:10 This is a meaningless concept with no ties to reality and cannot be used to negate the whole system of human concepts as it is not a real concept of a real thing. It is a concept about our knowledge given silly constraints. Grue is not a color, it is an idea about our knowledge and color. There is nothing you can do with this word which will affect induction one way or the other. To negate grue is perfectly valid, to accept grue is perfectly meaningless. It has no effect on knowledge as such.
5:11 "What does this mean?" It means philosophers will say whatever they want in order to continue receiving funding, and will intentionally make it difficult for their employers to question them and fire them.
I belief the semantic proposition is time dependent. If lets say the stones were light dependent it will be similar, the observer wont know until what amount of light is present at the time of observation. And the invented terms grue and bleen are disjunctive make all the different and drags with the terms green and blue. Nice film, now I understand the argument against formal induction
So something that is grue is observed green and unobserved blue. How can we tell that emeralds aren't grue? Once we observe them they are green. we have No way of checking what color something is before it is observed?
+Turt1eXing It is not strictly about observation but about the theory that infects the observation. In a crude sense, you can make up any hypothesis that will confirm all your observations, yet due to its content make the next observation highly improbable. In this way, a valid formal structure for inductive logic is harder than deductive logic (where, as this video showed, the particular predicates can not override the logical structure).
Don't know if it's posted, I don't have time to read through the comments right now... Question: is this puzzle not just an example of how arbitrarily changing the premise invalidates the conclusion? GRUE cannot exist, and therefore GRUE cannot be real. Therefore GRUE cannot invalidate a "real" deductive argument. Let me explain: In the observable and measurable world we exist in GRUE would have to have the magic ability of changing it's nature based purely on whether or not it is observed, i.e. green when observed and blue when not observed. This means anything that is GRUE is blue until you look at it and then GRUE becomes green, which is the same thing as saying it was never blue in the 1st place because by definition you cannot observe it in it's blue state. Because it cannot be quantified OR qualified, it doesn't exist and in the end green is effectively always green. The only alternative theory for GRUE is that an unobserved object is GRUE/blue until it observed at which point it remains blue, in which case blue = blue. Even if we had the ability to observe an unobserved thing in it's GRUE/blue state (which is also impossible because then we have observed it, but let's set that aside for the moment) and then observe it and see it transform into green, syllogistic logic still works. All unobserved GRUE is blue. All observed GRUE is green. The grass is green. Therefore, grass is observed GRUE. All unobserved BLEEN is green. All observed BLEEN is blue. The sky is blue. Therefore, the sky is observed BLEEN . What it all boils down to is: green is green unless you prefer to BELIEVE in GRUE, in which case it merely becomes "observed GRUE" instead of "green" so at its simplest GRUE is more complicated in naming convention alone (AND now we open the can of worms on belief systems and faith as quantifiable constructs vs. emotional states), and the same is true of blue. This implies that GRUE and BLEEN are then just more complicated ways of describing the quantifiable qualities of color. OR I could be wrong.
I believe this is objection is wrong. Remember, this whole discussion is related the concept of logic, which is independent of how physical reality manifests. Grue is a totally logically consistent color, and metaphysically, poses no problems. Because logic is independent on physics, the fact that grue may not exist in our physical reality does not invalidate the fact that there appears to be a logical inconsistency.
If you guys are interested, we actually discussed this topic on our latest podcast. You can check out the video on our channel. It's titled "THE SUN COULD EXPLODE!"
it seems to me that you are defining green with the word green. that is because both grue and bleen use green in their definitions and you are using them in the definition of green
You can't define green in terms of grue and bleen because that's circular defining. You used green to define grue and bleen, so you can't use grue and bleen to define a term used in their own definitions. Since there's no way to define grue or bleen without using green, green is the simpler term.
It seems like an issue is that the definition of grue cannot be simplified, whereas the definition of green can be. The given definition is sufficient and true, but it can be simplified to be true no matter the context: Green is the color observed of an object that emits or reflects specific wavelengths of light. One could also argue. Grue cannot be defined without a temporal context. Another argument might also be that Grue is more complex because (if green=grue before, and bleen after discovery), then Grue= (grue before or bleen after) before, or blue after, creating an infinite regress.
I think this video is incomplete without including some thoughts on words such as Emerhire - as in, and emerhire is an object that is an emerald if it was observed in the past, and a sapphire if it will be discovered in the future. And the observation of a grue emerhire increases the probability that all emerhire are grue.
Nothing could be that object, at least not invariantly in time, for the future in which such an object will be discovered will eventually become the past in which it was observed. The same reasoning can be applied in reverse. So unless sapphires and emeralds are the same thing, and blue and green are also the same, such an object is impossible
You cannot possibly be all at once smart, believe what you said, and have understood the video properly. In the context of this video, the assumption is that there is a point of reference in time that is fixed, and we are interested in whether or not object have yet to be discovered by that specific point in time. Objects that will be discovered later are grue if and only if they are blue. Objects that have already been discovered earlier are grue if and only if they are green.
Annaelle Jacques-Morel I'm ignoring it because it wasn't presented on the video and you are not the video maker. You can't add stuff to an argument some other person did and put words in their mouth. But even if you did, "grueness" is not a real property, it's not intrinsic of the object as it depends on an arbitrary point in time and whether some dude looked at it or not. If you want me to believe you when you say the two arguments (P then Q, R then S) then you have to use good premises. You cannot go around making stupid shit up (grue, bleen) and then cranking up the stupid gauge all the way to graham's number (defining green from bleen and grue, whose definitions necesarily use green) and being all like "look, this stupid thing I pulled out of my ass is just as stupid as this other thing that doesn't make any sense! Therefore I'm right!"
Or does Green rely on the definition of Bleen? All definitions will eventually become circular? How do you define "define"? or what is the meaning of "meaning"? What is "is"?
The issue with the GRUE paradox that I see of the top of my head is that it relies on asserting the characteristic of something that is unobserved. All observed emeralds are both Green (P->Q) and Grue (R->S). All unobserved emeralds are unknown since they have not been observed. They could be Green, or Grue, or red, or yellow as long as at the moment you observe them they are observed as Green. You can't observe a Grue emerald to be blue like you did in your example, so, I would say that example is bad. The two statements on there own P->Q and R->S are equally likely and the more likely one can not be distinguished based solely on those two statements. So, this is another error in your video where you assert the P->Q is correct and R->S is incorrect. How one decides which is correct is based on how this statement fits into a broader theory. You have the belief that in your world things don't generally change color when no one is observing them, which is why you believe P->Q is correct. Also, the simple theory that things don't change color simplifies things. As, that means you can simply call things green instead of having many many indistinguishable states. Such as Grue, Grack, Gred, Grellow, Grown, etc. None of these many states can be distinguished since you can only distinguish something by observing them and by definition they are exactly the same when observed. This means that Grue is simply a bad concept since it is indistinguishable from Green, hence, all things that are Green are Grue (P->Q = R->S). Your assertion that one is correct and the other is wrong is based only on your beliefs and nothing else. We also have an example where something like this actually happens. In the quantum physics world observing something can actually change the state of it. Where something can behave like Blue (whatever that means) when it is unobserved and be Green when it is observed. However, in the Quantum Physics world we can use math to kinda figure out what is going on when we are not observing something, and predict what will happen when we make an observation. So, concepts LIKE Grue make more sense in the quantum realm because it is distinguishable. Since, everything ultimate derives from the quantum realm it very well could be that R->S is true. I mean how do you know you couch isn't blue when nothing is observing it. The point is that trying to distinguish P->Q from R->S is pointless and a waist of time unless you can devise an experiment to make such a distinction. Otherwise they are equivalent.
The first argument is false. If all observed emeralds are green, that does not mean all emeralds are green, as there could be an unobserved one that's blue. It might be a reasonable conclusion, but it is not inductively true. Both statements are built on the same false logic: everything seen so far has a property ergo all objects have that property. There is no paradox; it's just that one statement looks right and one looks wrong.
I would agree. The problem is the conclusion is correct in the real world, but is not correct by the argument. I first encountered this in the winter rose argument. P1: Some flowers do not bloom in the winter. P2: Roses are flowers. C: Roses do not bloom in the winter. In this argument, there is no reason to assign P2 to the "some" in P1, other than the fact that roses really do not bloom in the winter. And because we know that the conclusion is correct, we overlook the flaw in the argument. The form; All observed X are Y, therefore all yet to be observed X are Y, is completely flawed and is actually called prejudice. Assume that the first time I meet any Scots (X) is at a party, and they are all drinking, all the time (Y). Therefore all Scots (X) drink all the time (Y).
You are being to skeptical for the context. The 'if A then B' is ok. The grue is just a dumbass modification that makes it into a different statement. It doesn't invalidate the simple version. It's just stupid as hell. I'm SO tired of 'these kinds' of philosophical statements.
Common mistake, whether the proposition will always lead to a true conclusion is somewhat irrelevant. There's a difference between being logically valid and being wrong. If you had only seen green emeralds it would be logical to suggest the next emerald will probably be green. Even if you err you have at least been logical. However if you applied the same logic to something grue you wouldn't just be wrong, you would have created a contradiction. Your argument not only wouldn't be true but also wouldn't be logically valid.
For something to be logically valid but not true it has to deduced using correct logic from a false assumption. If you started with the assumption that all emeralds were green that might or might not be a false assumption. But the assumption that all observed emeralds are green is a correct one. Applying the logical method 'all observed P => all P' is false logic, so you can't say that the proposition is logically valid.
+Jim Smith It's inductive, not deductive logic. It's a perfectly logical inductive argument. If you disagree with that then it's possible that you simply don't understand inductive logic. I don't mean that as an insult, merely that in treating inductive logic as if it ought to adhere to the standard of deductive logic suggests that you might be confused on the subject. Inductive logic reveals only what is likely to be true and not what must absolutely be true.
So basically the form of the argument isn't all important to the validity of the argument. The variable inputted into the argument form matters a lot as well. But isn't this basically the same as the false analogy fallacy? The argument/logic applied to one thing cannot be transferred to another thing.
Induction depends on observation, so it's not really fair to say that the two arguments have the same 'form' insofar as the nature of their subjects is different.
The idea is to show that induction makes good common sense, but no formal/logical account of it is possible. Goodman's own example was in the case of emeralds. The problem with observation is that it is fallible in more advanced and varied ways than some rule of logic. Creating an abstract account of a fundamental system like induction using observation seems unusually weak. I think I agree with Goodman's diagnosis that induction is rational but illogical.
Wait a second, why is the argument in this video put in a deductive way? All emeralds so far observed have been green. Therefore, the next emerald to be observed will be green is not a deductive argument. It can not be put in the form of: 1) P implies Q. 2) P 3) Therefore, Q. Am I wrong?
I believe he is showing exactly why it can't be put into deductive form because the subject matter, for induction, changes the quality of the statement. i.e. Grue.
If an object is green, then it is bleen before observation and grue after observation. So, observation changes this property of an object, while it doesn't change its property of being green. Isn't that the difference? Like, imagine you're driving a car along a line of flags, and you observe each flag fluttering, and conclude that all flags are fluttering, but if you look back from your car, you'll see calm flags - because they were fluttering only due to wind caused by your car. But ok, we can construct another definition of grue and bleen, like, grue is {[a green object observed before 01.01.2001] or a [blue object that wasn't observed before 01.01.2001]}. (The green/blue and grue/bleen terms still stay symmetric here, possible to express in the same way as in the video.) Then, on the day 01.01.2001, we can make this conclusion that since all observed emeralds are grue, then all other are also grue, so they will be blue when observed (and still grue, because the fixed date has already passed). Well, that's a trickier question.
Hold on, I don't get it. Modus ponens is: ((P) and (P -> Q)) -> (Q) The implication (P -> Q) - in this case (all observed are green -> all are green) may be incorrect if not all are green. If there exists an emerald that is not green the implication fails, the outer implication becomes false -> false and is still correct. Your example does not break the rules of logic in any way.
You're missing something. The whole point of this paradox is to build a concept of inductive logic. We want to be able to say "observing that a P is a Q supports that all P is Q". This is the central assumption that we make in our day-to-day lives. You think that the fact that bread nourished you in the past supports that all bread nourishes you, for example. However, this paradox shows that such a construction of inductive logic is not a good one.
Isn't the Grue Paradox supposed to show how, two mutually incompatible hypotheses, can be supported by the same observations? On this video/comments, the 'Grue Puzzle' appears to be getting too caught up in a deductive/inductive debate. The puzzle does, however, give an attack against the instantial model of Confirmation Theory. H1 All Emeralds are Green H2 All Emeralds are Grue ( Grue = x that is green before 3000, blue after 3000) The hypotheses are rivals because, H1 claims that emeralds not observed before 3000 are green, whereas H2 predicts them to be blue. Both hypotheses, despite being rivals, are supported by observations where an observed emerald is green. So then, observations of Emeralds that support H1 because they are green. However, they also support H2 because they are both green and observed before 3000. (The key is to remember that grue is not a definition tied to an emerald, grue can be anything that is green observed before 3000 and blue when observed after.)
Hi Wahey, Here, you said, "The hypotheses are rivals because, H1 claims that emeralds not observed before 3000 are green, whereas H2 predicts them to be blue." I don't think H2 or Godman's argument claim that if an emerald is not observed before 3000 it is blue. They are blue if they are observed after time(t), which in your example is 3000, but before time(t) an emerald observed or not observed is always green. So, as long as time(t) does not happen the observations can be used to support both propositions because before time(t) the emeralds, observed or not, are green.
Sorry, what I mean by unobserved is that they will be observed after (t). So, where H1 would predict all emeralds to be green regardless of (t) H2 predicts after (t) observed emeralds will be blue (if grue). The colour they are after (t) is irrelevant, the point is that the same evidence supports both statements despite different conclusions.
Exactly, it is irrelevant coz time(t) is always indexed to a point in future, and as long as this point in future never actualise the observation does indeed support both arguments.
That is pretty much the ultimate point, but the wording is tricky. Grue is defined such that we know definitively that all emeralds are grue now, regardless of what happens after 3000. But the point is the same, you just need to replace H1 and H2 with H1 All emeralds will remain green after 3000; at that time they will change from grue to bleen H1 All emeralds will remain grue after 3000; they will change from green to blue
You say you can't distinguish those two arguments merely by form. I say: Yes you can. It's really not that hard. Your properties "green", and "blue" are axiomatic. Your set of atoms looks something like {isObserved(Emerald1), isObserved(Emerald2), isObserved(Emerald3), isObserved(Emerald4), ...} ∪ {isGreen(Emerald1), isGreen(Emerald2), isGreen(Emerald3), isGreen(Emerald4), ...}. Your property "grue" on the other hand is not. It's a rule that can be expressed as isGrue(entity) := ( isObserved(entity) ∧ isGreen(entity) ) ∨ isBlue(entity). In your second argument using the rule grue, before you can evaluate it, you have to eliminate the rules: P: All observed emeralds are grue. C: All emeralds are grue. P: All observed emeralds are either observed and green or blue. C: All emeralds are either observed and green or blue. P: All observed emeralds are green. C: All observed emeralds are green and all not observed emeralds are blue. P: All observed emeralds are green. C: All not observed emeralds are blue. It's obvious that this argument is quite different from your first one. The same goes for this silly attempt of showing that "green" is more "complex" than "grue". I can use this argument to show that something is more complex than itself by using it in an arbitrarily long disjunction of unrelated properties. If you eliminate all the rules and simplify the formular you'll end up with the simple atom "isGreen".
I love idiots on youtube who waste their time trying to refute sophisticated arguments, because they just think that highly of themselves (I bet you spent at least 30 minutes on this, ahem, gem). Bruh, none of what you said made sense. One must first understand what is being discussed before one can critique it, eh?
FruitGod - I love idiots who believe stupid arguments are sophisticated. 'Grue' involves a change, 'green' doesn't. Change is more complicated than not change. The only people confused by this are philosophers. This is not unique to inductive logic. Compare "all chairs are furniture, X is a chair, therefore X is furniture" and "all chairs are airplanes, X is a chair, therefore X is an airplane". You can't tell from the form which is a good argument, you need more information. The same for the grue argument. So the whole argument is based on an obvious falsehood.
'Good' here doesn't mean 'good' in the normal sense: it means 'valid' in the formal logic (which, by the way, is a branch of maths, not "philosophy" in a pejorative sense) technical sense of 'has a conclusion that must be true if the premises are'. Both 'all chairs are furniture, X is a chair, therefore X is furniture' and 'all chairs are airplanes, X is a chair, therefore X is an airplane' are *valid* arguments in this sense. It's just one has a false premise. But the claim the video is making is just that validity in the technical sense depends on form alone; no one thinks that being a 'good' argument in the sense of being valid and having true or plausibly true premises depends on form alone; obviously whether the premises are true/plausible depends on what you are talking about.
There's nothing funny about 'grue' that isn't equally funny about 'green'. Consider a community of language users that use the terms 'grue' and 'bleen'. Since you are part of a community that uses 'blue ' and 'green', we have to define 'grue' and 'bleen' using the terms you know, and so to you, they will end up looking funny. But this is only skin deep. Consider explaining to this community your own color terms of 'blue' and 'green'. you'll have to use the terms they know to explain it. You'll end up having to tell them that 'blue' means: bleen before time t and grue afterward. Then they will look at you like you're an idiot and demand an explanation for why you sue such stupid color terms as 'blue' which seem to build in that stuff just changes color. He will in fact say, "'Blue' involves a change, 'Bleen' doesn't. When something's bleen, it's always bleen. Only philosophers would be confused about that." And he would be just as right as you.
So the definition of this exercise is to prove that if you make things more complicated than they need to be, that you sound more intelligent that you appear to be...or appear to be more intelligent that you actually are. Therefore if you make up words to prove your unprovable point you can prove your unprovable point.
If you buy an old computer, you can salvage copper wire out of it using power tools, but that doesn't mean copper wire is more complex than computers and power tools. Green is simpler than grue and bleen, even if you can recover the concept of green you used to define them. These inductive arguments rely on the implied premise that an [x] object will remain [x] even after it is observed. Just explicitly say that and grue will stop breaking them.
+The Next Freud that's the point. Philosophy of science during this time was dominated by individuals who wanted to show how inductive reasoning can be expressed in terms of deductive logic. Popper for example saw science as progressing via modus tollens and not via standard induction.
grue is definitely more complex than green because for grue to exist, an object has to exist in two colours. Green if observed, blue if not. meanwhile it is commonly believed that a green object will still be green if you're not looking at it. Therefore, if you argue that all emeralds have been green and will continue to be Green, you are arguing that colour remains constant. If you argue that emeralds are blue unless they are observed, you argue that colour is not constant.
It green is defined by grue and bleen, both of which contain the word green, then you've just got a tautology. That seems to me a pretty good case for green being a simpler concept.
I did NOT understand this at all.. why not show a few examples of how the argument is used? It's really hard to understand when you only speak in the abstract terms without any concrete examples of how those terms apply or don't apply.
+PIneapple29 This is impossible. Grue is a word whose only purpose is to behave differently at different positions in the argument. There are no real words that behave this way.
Actually, all real words behave this way. Green looks like what we have SO FAR observed it to look like. Chicken tastes like what we have SO FAR observed it to taste like. The word 'crocodile' seems to us, based on experience so far, to pick out a natural kind. The point of the argument is that the sum total of our experience is always insufficient to tell us whether our concepts and language actually cut reality at the seams. natural laws that seem to govern crocodiles may really be a distortion of a more general natural law that really governs brocosaxodiles. Something is a brocosaxodile if it is either broccoli, a saxophone, or a crocodile.
emerald: - a bright green precious stone consisting of a chromium-rich variety of beryl. - If the hue is too yellowish or too bluish, the stone is not emerald, but a different variety of beryl, and its value drops accordingly. P: All of the numerous emeralds observed in the past have been green. C: All emeralds, those observed and yet to be observed, are green. - - - - - bachelor: - a man who is not, and has never been, married. P: All of the numerous bachelors observed in the past have not been married. C: All bachelors, those observed and yet to be observed, are not married. = = = = = Probabilistic: - Based on or adapted to a theory of probability; subject to or involving chance variation. Q. What is the probability of finding a non-green emerald or married bachelor? = = = = = GRUE: A thing is GRUE if, A: either it has been observed by now and it is green; or, B: it has not been observed yet and it is blue. Q. Can a emerald that has not been observed yet be GRUE?
The term "inductive logic" here and attempts to draw any parallels between it and actually formalized deductive logic don't sit well with me: inductive "logic" seems like it should simply be called probability based inductive reasoning. I mean, I have never eaten a baby. Therefore, all babies I have eaten were trivially blue. Therefore, by inductive logic, the next baby I eat will be blue.
Maybe this video is oversimplifying things, but the problems seems to be arising when an object property definition that is contingent on observation. Since induction is about going from the observed to the unobserved, it seems likely that this can create the same kind of self-referential paradoxes that are in Godel's completeness theorem. I have my own problems with induction in that it assumes homogeneity between the set space of where you have taken your measurements and what you are extrapolating to. You simply have no system independent way of knowing the nothing essential has changed or that your sample is representative of the whole. Part of the reason why deduction works in a logically tight manner is that it is restricting the set space with each step so that there is nothing new that might have different properties or follow different rules.
Green = Observed and Grue OR Not Observed and Bleen When we replace Grue and Bleen with their definitions we get Green = Observed and Green OR Not Observed and Green. So Green = Green. This has not made the definition any more complicated, it just tried to obscure it.
The same thing can be done with Grue: Grue = Observed and Green OR Not Observed and Blue. When we replace Green and Blue with their definitions we get Grue = Observed and Grue OR Not Observed and Grue. So Grue = Grue.
Alternate definition : Green : Discovered, and the color of and emerhire OR unobserved and the colour of a Sappherald. "The fact that we usually rely on words like green, blue, emerald and sapphire rather than words like Grue, Bleen, emerhire and Sappherald is nothing more than an accident of history." Also, we should assume that the words in our natural languages have stranger semantic properties than properties such as grue-like words. Most of our natural words have more than one meaning. Get rekt. My philosophy-fu is stronger than your philosophy-fu :P
Annaelle Jacques-Morel I do believe you missed the point. Definitions are just a way to give meaning to a word... it has nothing to do with "discovery". There are many metaphysical words (like grue) that have come about in order to discuss complex ideas.
Oh, no - I got the point completely right - the ultimate goal is to discuss why inductive reasoning cannot be given a purely formal account the way deductive reasoning can. And the immediate goal was to shut down people who claim that Goodman's argument about grue was invalid because of some inherent semantic property of grueness that made it an illogical word or concept. In this case, an allegation of circularity.
How can the concept of Grue even be true? Doesn't positing the truth of Grue beg the question? (Owing to the fact that it has an antecedent dependent on an unobserved [and unobservable] variable)
Maybe there is no perfect definition of _complexity_, but only an idiot would say that a description of a colour which contains the concept *green*, the concept *blue* and then a *condition* is interchangeable with the concept *green*, and only a moron would suggest that { a colour that is *grue* (*green* while *observed* and *blue* if yet *unobserved*) if *already observed* OR *bleen* (*blue* while *observed* and *green* if yet *unobserved*) if *yet unobserved* } can be substituted to *green* because it's just a different perspective on the same thing. I didn't get it from the video, but I hope that Goodman was being ironic.
Argument 1: All Observed A are Green => All A are Green => All Non-observed A are Green. Definition of set B: All Observed B are Green AND All Non-observed B are Blue. Argument 2: All Observed A are B => All A are B. Author states that antecedent of argument 2 (All Observed A are B) is true. But it's not since if set A belongs to set Green and set B belongs to set Green than it just means Green is a super-set of A and B. But in no way it implies A is equivalent to B or they even intersect. So it's another Fakeadox.
The answer is actually quite simple. Neither of the arguments is valid. A valid form needs additional premise about invariance of colour, which needs justification/evidence on its own. The first argument seems valid, because there is assumed pre-existing precedent about colour green being independent of date of first observation. Such precedent does not exist for grue. Note that the puzzle is not "why the first argument IS valid and the second is not?" - the puzzle is "why the first argument SEEMS valid while the second does not?"
I have a horrible feeling that sone day, could be tomorrow, could be years from now, I will be faced with a situation where I am tasked with looking at green or blue objects and will use Grue but no one will understand.
@@lightningandodinify deduction cannot be used like that. If the premise is "all observed astronauts are human" then you can't conclude "therefore all unobserved astronauts are also human." that is induction. To assume characteristics from one set onto another. Deduction works more like: "P1:every astronaut on the Apollo missions was human. P2:Buzz Aldrin was on the Apollo missions. P3:buzz aldrin was an astronaut C: buzz aldrin was human" If you agree that all the premises are true, then it is impossible to disagree with the conclusion. In the first example you could get an incorrect answer despite the premise being true. In this case some astronauts (which you were not aware of) were mice or chimpanzees.
@@lloydnicholls1439 none of that is relevant. The idea here to create a definition for induction that can be defended through formal logic. Deduction is only relevant as a means to explain induction. Grue shows that even with exact form (remember that the content of variables don't matter for deduction) induction cannot be explained through logic. The statement "all unobserved emeralds will be green" suddenly stops making sense when we substitute green for grue or even the disjunctive definition of green (grue + bleen). This is not possible for any true formal account. We all "know" that ampliative inferences work, but it seems that we still have no way of creatibg a valid and functional explanation what we're even doing.
@@lightningandodinify I understood the point of the video. I just felt the use of the term "deductive" logic was incorrect as I have come to understand the word. Deductive logic is simple. It's either valid or invalid and if it's valid, then conclusion follows necessarily. Inductive reasoning becomes complicated because we're are dealing with strong evidence and weak evidence, good arguments and poor ones. You should look up the "raven paradox" for another interesting problem with inductive reasoning.
@@lloydnicholls1439 i know about the raven case. I think Bayes' theorem can solve it. As for deduction, the project was to make induction seem reasonable because it always looks like a strangely poor argument unless we substitute the variables with common sense cases (like emeralds being green or copper being conductive). The "natural kinds" argument seems okay as a response to grue. It would argue that examples like copper's conductivity is "law-like" and thus projectible through induction, but the counter examples are "accidental" and their frequency is not projectible. The problem is in defining what is law-like in this way.
Ok, so, a grue object is green if observed, and blue if not. If emeralds are grue, then any unobserved emerald is blue. BUT, the moment we observe it it becomes green. After all, we've observed it so it must be green. If not, then our definition of grue is wrong for we would have observed a contradiction to the definition of grue. Similar with bleen. Blue if observed, and green if not. The paradox arises because our definition includes an observer. Emeralds don't, as far as we know, magically change color once observed. And if they do magically change, it still doesn't change our observations about them. They're green when we observe them. They're also grue if they magically change from blue to green when we observe them. I find that most paradoxes appear when we don't take one step further back and look at our definitions. If the definitions are poorly defined, then induction doesn't work properly. That was Goodman's point. The concrete definition "all emeralds are green" is not the same as "observed emeralds are green, but unobserved ones are blue and therefore all emeralds are grue." Again, we can never observe an unobserved grue object and not break the definition of grue unless the object magically changes color. The Schroedinger's Cat thought experiment has a similar flaw. That cat is clearly either dead or alive because the cat itself is an observer in the experiment.
Most of those arguments seem to fail simply because they make absolute statements about what is true. You need to be very very careful about what you say in absolute terms, as chances are at some point you're going to be found incorrect. At this point in my life, I think gravity might be only thing I'd be willing call an absolute, and having said that, I now expect someone to one day prove my statement wrong.
not only is the first argument wrong as Jim Smith points out, but it is also an untenable position to assume you can classify as of yet unobserved things into categories a priori.
how is it that "grue" is considered a simple predicate in the same way that "blue" or "green is. if "grue" represents two different states isn't it by nature less simple than either "blue" or "green" and a poor substitution for this example?
Not when you introduce bleen to define green through grue and bleen. Green becomes the more conplex and disjunctive term then. I dont think this puzzle can be solved. I think Goodman was right in thinking that a formal account of induction is impossible. I believe induction requires an abandoning of formal support. Im in the camp that this isn't a vulnerability for induction but rather a special challenge for applying logic to induction. Our intuitive support for induction definitely makes sense, a formal account might just be incomprehensible if we found one.
This is all based on humans conceptualize of linear time. But if time is not linear and the past, present and future happens all at once that would ultimately challenge the paradox.
We only know that emeralds are grue after they have been observed, and can only make a prediction about whether emeralds will be grue once they are observed. Example: All emeralds that have been observed are grue. Therefore, all emeralds that will be observed will be grue. Any assertions about the state of emeralds before they are observed are baseless. Just because all emeralds have been grue once they were observed does not mean that they were grue before they were observed, and therefore, it does not necessarily follow that all emeralds are grue. We can not say what the state of reality is for things outside of our observed experience. Unobserved emeralds are outside of our observed experience. Therefore, we can not say what the state of reality is for unobserved emeralds. What we really mean when we say things like "All emeralds are green" is that all emeralds that will be observed, will be green when they are observed. How do we know that emeralds aren't purple when they aren't being observed, or that we aren't in the matrix and they just disappear when nobody is looking? We don't, and can't know that. What the puzzle of grue does is bring attention to the fact that we don't experience reality directly, but only through our perception. When we typically make definitions about the nature of what we consider reality, it's taken for granted that it applies to our observed experience. This puzzle breaks that.
Also, defining Green in terms of Grue and Bleen doesn't make sense. Grue: Items that are unobserved and blue, and items that are observed and green. Bleen: Items that are observed and blue, and items that are unobserved and green. Green: grue and observed, and unobserved and bleen. Green:(grue and observed) + (unobserved and bleen) Green:(If something is grue and observed, then it is green by the definition of grue) + (If something is bleen and observed, then it is green by the definition of bleen) Green:(green) + (green) Green: green and green Green: green With the new definition of green, there is nothing being observed to determine if an object is green. Instead, the definition depends on the word itself. Here is an actual definition, for comparison. Green: The color between blue and yellow on the spectrum of visible light. It is evoked by light with a predominant wavelength of roughly 495-570 nm. With the new definition, green is somehow supposed to be determined by observing the emeralds, but not seeing the color green. It completely removes the word "green" from the color "green", changing the meaning of the word.
Green is observed, grue is deduced. Observed emeralds are observed to be green. Observed emeralds are deduced to be grue. Emeralds have never been observed to change color after time t, so it is likely that they were the same color before time t. If emeralds were green before time t, then we can deduce that they were not grue before time t. If all observed emeralds were not grue before time t, we can assume that all emeralds are not grue before time t.
This is a faulty argument in as much as it requires creating no existent words to make its case. Is this really the state of philosophical study in 2019? As a person considering studying philosophy I really am dissuaded from doing so if faulty arguments are being heralded as “gotcha” statements to disprove something.
Your gross misunderstandings about what constitutes "faulty" reasoning means that you should probably stay away from philosophy and all STEM fields. You won't be missed 😃
OK, so I haven't studied logic in anyway, so I'm probably about to crap out of my mouth, but I'm going to do it anyway. I think the problem isn't that grue is more complex than green, but that grue specifically refers to whether or not a thing has been observed, while green does not. Because of that, they are not equivalent when used in a sentence that specifically refers to whether or not a thing has been observed.
«Grue» is a logical tool to help Goodman show that there cannot be such a thing as a purely formal account of inductive logic. You can reject that grue is «as simple» as green, but then, you still have to show that there can be a formal account of inductive logic. It doesn't help that, when you say that grue «is more complex» than green, you are appealing to the content semantic content of a problematic word to help an account of logic that says you shouldn't have to appeal to the content of words to build a logical system, thereby fatally undermining yourself.
I immediately see the solution to Mr. Goodman’s problem. Where you state the premise “All emeralds observed in the past have been grue.” you making an implied mistake that is easy to spot. Since being already observed is a prerequisite of an emerald being grue, it would be more accurate to state “all emeralds so far observed became grue as soon as they were observed, so we assumed that they must have been not grue until the observation was made. The assumption was reasonable, because we saw nothing about the observation that would change the color, and observations of the same kind have never changed the color of things before.” There was an implicit falsehood in the premise, as you stated it, because you failed to state that it became grue as soon as you observed it. That is different than color, or green, because we ordinarily assume that color doesn’t change just because you looked at it. But grue is exactly the opposite. If you merely correct that one premise, you see it easily resolved the problem. Certainly, if you had observed many emeralds in the past, you would have certainly noticed if observing them changed their color. So if you merely include the thoroughly implied premise that things don’t change color just because you observe them, you are back to sound inductive reasoning. For example, you could made the alternative premise, “all emeralds in the past became grue as soon as they were observed.” And you would be good again. (Most inductive arguments can be made into deductive arguments, if you just include qualifiers about your certainty of every premise. But the problem does touch upon one of the big problems of 20th century physics. We take it for granted in observing nature that it is possible to make observations of it without changing it, and draw conclusions, because in an everyday experience, we can do that. But in many fields of 20th century physics, people realized you can’t do that. It didn’t destroy inductive reasoning, but it made it necessary to make many implicit premises explicitly known.
The premise : All Emeralds have been GRUE is false. The Emeralds were NOT observed and were green : thus NOT GRUE. The premise should be : All Emeralds ARE GRUE once observed. OR : All Emeralds are NOT GRUE until they are observed.
Grue is more complex than green because it describes different properties of an object in different points in the time continuum. Like 'mountain' is more complex than 'slope'. 'Mountain' has different properties in different points in the space continuum (positive slope vs negative slope), while 'slope' does not. You can define 'slope' in 'mountain' terms, but the difference still holds.
I have a new term. Pave it is a particle if it has been observed and a wave if it has not been observed yet. All electrons are Pave. This is more likely than all electrons are particles..
What are you trying to say? Likelihood has nothing to do with the grue puzzle. It's that fact that we have no formal concept with which we can define induction (or any ampliative inference for that matter).
Goodman defines GRUE as "all emeralds are observed to be green OR have not yet been observed and are blue". And then states that premise (1) "all emeralds Observed are grue" is True. And then says the conclusion (2) that "all emeralds are grue" is not true (thereby demonstrating that syllogistic form alone is not sufficient for proof). With the first statement (1) we only have to evaluate the first part of the definition of GRUE: "A or B", since A is true B can be ignored, it does not apply. In (2) since we are supposedly dealing with unobserved emeralds (the condition of A are not met), we have to evaluate B and we find that is a statement that depends on the future - we have something unobserved and then we observe it - there is an event happens in time, and that event takes us from the unknown to the known. By the definition of Grue we are led into believing that the next emerald (unobserved) has to be blue - then we observe it and find it is not blue. This is an absurd. Making a claim about the unobserved is absurd. The absurdity does not play out in the premise (1) so we ignore it, and say yes, the premise is true. In (2) it does play out and we see we are not dealing with a valid statement. Deductive logic cannot include statements about the unknown and the changeable. Goodman is basically executing a slight-of-hand, a trick. The CAT is right - GRUE is a different order of complexity than Green. Grue makes a statement about the known and unknown. Whereas in a deductive syllogism, the premises are always about the known. That Goodman thinks he proves that Green is the more complex term by introducing another to-be-determined definition, BLEEN, is bordering on ridiculous. It's fairly intuitive that induction cannot be reduced to syllogism. But Goodman's attempt to prove this, Fails. What I get out of this video is that it might be interesting to look at if there are any kinds of logic that work with future states.
Our entire language is based on the assumption that we know who is talking. It is not so strange to think that we could have a natural language based on the assumption that we know whether or not we can see the things we are talking about. In such a language, predicates such as green-ness and chair-ness would seem weird. We would instead have predicates such as grue and chable (a chair if it is discovered, and a table otherwise) The fact that we have words such as green and emerald and chair in our natural language is a mere accident of history, with no philosophical relevance.
Interesting idea. Not sure I agree with the assumption we always know who is talking - - look at any random written material with no author... Language tends to include articles for what is assumed, and they are optional but they are there. For example in Spanish the "I" is often dropped. But you can include it.
The fact that we don't always actually know who is talking in fact is not incompatible with the notion that our language assume that we do. I think our language assumes you know who I am. Is a valid proposition in English. But to formalize such a proposition is complex. Such as : There is a Bry Boss There is a Annaelle Bry Boss and Annaelle speak a common language. Suppose a P such as : When Annaelle is talking to Bry Boss, it is known to Bry Boss that it is Annaelle who is talking. There is a built-in assumption in Bry Boss' and Annaelle's language such that it assumes P to be true. Also, remember that I don't have to be that convincing - I have to be just convincing enough that you would accept to surrender all hope that inductive reasoning cannot be given a completely formal account the way deductive reasoning can. If you are very certain that there can be such a thing as a completely formal account of inductive reasoning, then I have to be more convincing than your certitude. If your certitude is weak, you ought not make that particularly hard.
If emeralds really are grue, then I think the next one we find will appear green, because grue things are green when observed. Maybe we can leave behind a blue light sensor next to the grue emerald and then look away, and then see what the sensor detected, but maybe grue objects are sensor savvy and will only be blue when the property of blueness cannot have any effect on anything else in reality at all what so ever. This is basically a tree falling in the forest problem. So functionally, a grue emerald is the same as an always-green emerald. So I'll just use Occam's Razor and live as if the emeralds are always green.
this is silly. if green = that silly definition, it incorporates 'grue' which itself used 'green' in its definition; its circular. I would most certainly side with the cat. further, how can we declare something to be anything (for example, blue), if we have not yet observed it? the definition of grue itself is a fallacy- it claims to know something it cannot possibly know, which is later accepted as a truth condition in one's rejection of the 'bad' argument. i swear, ever since kant people have been obsessed with turning things on their heads. maybe green is more complex - lol?
The analysis you have done is faulty in that the premises you declare are in fact not premises. "All emeralds observed thus far are green" is not a premise in the context of the argument you present. A premise would rather be: "All emeralds are green". Furthermore, "grue" is not a property but merely a shorthand way of building the disjunction you mention, into the argument. The whole thing is a mess of category errors and is thus without merit as either a phenomenon or a tool of instruction. I am surprised it has become part of the curriculum.
Well, the definition of green as "grue or bleen" is recursive because the definitions of gure and bleen both contain green. So the more complicated definition clearly doesn't make sense. It can be either simplified to the original green, or it's recursive and therefore useless. If you define green as reflecting certain wavelengths or something like that, than that's clearly the simplest possible definition by far and therefore the best.
This is not a good argument because an emerald is a beryl that is green. If the beryl was blue it would be an aquamarine. Therefor this argument fails on the definition of emerald.
Maybe it is, but it hasn't been proven yet, not on this video. It's like saying a given mathematical theorem is true even before it's been proven (e.g. Fermat's last theorem), it may be so but unless you proove it I'm not gonna take your word as true.
The "definition of emerald" is established via induction. The argument dejustifies induction. The point is that whatever physical processes we assume produce greenness in beryls may in fact produce grueness in them instead, and we simply have insufficient experience to judge between the hyphothesis that process x creates greenness in beryls and the hypothesis that process x creates grueness, (or grinkness or grackness, etc.) in beryls.
Can this idea be communicated without making up a bullshit term just to do it? Grue/Bleen my butt, explain this with real words that have a known meaning. My brain trying to decide weigh this thing by fighting with itself over whether the unknown traits of an imaginary color might have relevance to comparing them with the known properties of a known color and it's just pissing me off. This is inductive nonsense, it seems. I wish Wittgenstein had bothered to make up a better language instead of just criticizing the ones we already use. >
NothingIsSacred "...make something up to explain something real." the literal definition of abstract thinking.. it is very clear you cannot grasp it at all
The argument is actually well served by using a "bullshit" term. If the argument had pointed out that induction can't tell us the difference between two subtly different terms that both seemed reasonable, it wouldn't be clear that there was any bad problem with induction. It's the fact that induction can't tell us the difference between an ordinary predicate and a more clearly fanciful one that illustrates that there's a problem with induction.
![CRITICAL THINKING - Cognitive Biases: The GI Joe Fallacy [HD]](http://i.ytimg.com/vi/sO9xwAyeWX0/mqdefault.jpg)
![CRITICAL THINKING - Cognitive Biases: The GI Joe Fallacy [HD]](/img/tr.png)
![PHILOSOPHY - Metaphysics: Ship of Theseus [HD]](/img/n.gif)
I have seen other people try to explain this argument both on youtube and other places. And everyone seem to think that something is "grue" if it changes colour from green to blue at time t. This is wrong and it annoys me that so many misunderstands the argument. So I want to thank you for getting this right.
It's not really wrong though. I think the video makes it more confusing by not talking about this. If something changes from green to blue at time t, it will be grue before t and grue after t. Whether it changes colour or not, it still will have been grue before t, so you're quite correct that the definition of grue needs to allow for that. But at the same time, the point of the riddle is that it's very unlikely for emeralds to change from green to blue, yet it's very likely for them to change from grue to bleen, despite there being equal amounts of observed evidence for both possibilities. So it's vital to the argument that we talk about how something grue *could* change from green to blue.
As it is said @3:35, the definition of "grue" _is_ disjunctive, and that _does_ change the structure of the argument. Nothing that was said in answer to that objection makes the remotest sense to me.
mothman84 Green can be defined in terms of grue and bleen in exactly the same way grue can be defined in terms of blue and green. Thus, if you accept that that definition of grue is distinctive, you also have to accept that at least one definition of green is disjunctive.
@@plasmaballin But green can be reduced to existing outside time, whereas grue introduces temporal elements. That is what makes grue a more complex term.
@@cameronmarnoch5236 Green definitely cannot be reduced to existing outside of time. When I refer to a green object, I am referring to an object that is green at the moment I refer to it, not one that is eternally green (the same goes for a grue object), and the physical meaning of the color green is a certain frequency of light (frequency is very much a temporal property). That being said, I do still think that grue can be considered more complex - green can be defined in a simple way like "the color of an electromagnetic wave with a frequency between 540 and 580 THz", while grue cannot be defined in this simple way. However, that doesn't change the *form* of the argument. In deductive arguments, the complexity of the terms doesn't matter. "All emeralds are green. The gem in my hand is an emerald. Therefore, the gem in my hand is green," is valid, and so is "All emeralds are grue. The gem in my hand is an emerald. Therefore, the gem in my hand is grue." That's what makes the new problem of induction interesting - it shows that we need to know more than just the form of the argument to determine whether an inductive argument is strong.
Right. I struggle with the disjunction, the weirdness of past tense in a world where "yet" is always a moving goalpost, and the difficulty of defining "observed", and especially combining "not yet observed" with a claim about a quality that must be observed to be confirmed, which involves the unfulfilled motion of "yet".
I think that there is a fundamental difference between green/blue and grue/bleen. The key here is that inductive logic is based on observation and observing things does not change their green/blue properties, but it changes their grue/bleen properties. Therefore I think we can use inductive logic to make statements about the greenness and blueness of objects, but not grueness and bleenness because the fact of observation influencing grue/bleen state makes our sample fundamentally biased and unrepresentative of the whole population.
+Adam Kucz (Acalc79) Now, on second thoughts, I see that my previous explanation is incomplete. While it probably is true, we have no way of checking which of the properties (greenness or grueness) changes with observation. We conventionally assume it is grueness because we are not used to it, but it may as well be greenness. If that were to be the case then the conclusion from the second argument is correct: all emeralds are grue, the observed ones are green and unobserved are blue, but the very fact of observation changes the green/blue property and any emerald we observe remains grue because it changes color to green. With that said, I don't think there is any point in caring too much which properties are "real" and which are "observation dependent" as the only things we will ever experience are the observed ones. Therefore I suggest changing both arguments into "all observed emeralds are green" and "all observed emeralds are grue". Both of them are correct no matter which property is "observation dependent", moreover, they reflect the true state of our knowledge of the world: we can say anything only about things that has been or will be observed, the "true" reality is inaccessible to us.
@@AdamAcalc79Kucz so what 'is' induction? The idea is that we'll always resort to fallible and inexact kinds of definitions. I think Goodman is right in highlighting this problem. My intuition is that there is fundamental asymmetry between ampliative systems and the exactness of deductive logic. The strange thing though is how the reverse seems so easily applicable (math is physics for example). Perhaps deduction truly is more fundamental to our reality, but that just further tempts us to define the foundation of science on similar terms.
That's not really the point here, we're not worried about whether unobserved emeralds are turning from blue to green as soon as we observe them. The original meaning of grue is that at some specific time, such as 2025, every emerald, if it is to remain grue, will actually turn blue. So it is a fact that all emeralds are definitely grue right now, as well as being green. So given the weight of evidence that all emeralds are grue, should we conclude that all emeralds will be turning blue in 2025? That is the point of the riddle.
I'm having difficulty buying that the definition of green can be more complicated than the definition for grue/bleen because both grue and bleen use green in their definition, meaning that they are recursively defined. In fact, the references in the second definition of green all seem circular to me. What am I missing?
You're missing the fact that "green" is not more fundamental than "grue". Suppose mankind had no concept of green, and instead understood things in terms of grue. This should not change the logical structure of the argument, right? It's just a different perspective of looking at things. Well, if this is the case, then because we defined grue as our "fundamental" color, green would then become more complex.
I agree with you. It does not matter if green or grue is more fundamental as Axe Menace said, because the second definition of green is self referential and is a non-statement. The second definition of green when it is further examined simply means Green is green when it is unobserved and it is green when it is observed.
I believe the puzzle is birthed out of the partial improvable nature of 'grue'. In order for something to have a good definition it must be based on experienced criteria. So the puzzle is less to do with the nature of logic and more to do with the nature of definition. Which I understand was explained to be true in the video.
I am quite confused on a matter and was wondering if somebody could provide some clarification. So an emerald is grue if it is green upon observation and blue if yet to be observed, correct? If this statement is true then how can we conclude that the all emeralds are grue if no emerald has been observed to portray the color blue?
What I am trying to say is that if we have never seen a blue emerald how can we make the claim that all emeralds are grue?
Do we simply assume that emeralds not yet observed must be blue (or better yet not green) ?
I need to write an essay on the Grue paradox so any feedback would be appreciated
In complete darkness, you don't see colours....... but instead, you are most likely to be eaten by a Grue.
I think the point Nelson Goodman is trying to make is NOT that at the moment of the observation the emerald is blue, but if the the moment of the observation is after time (t) then the emerald is blue, but if the emerald is observed before time (t) then is it perfectly consistent with being grue because grue is only blue after time (t). So, here Goodman is trying to make the point the observation can support any proposition about emeralds as long as it is observed before time (t) So, the problem is not that observation can not justify inductive reasoning as argued by David Hume, but instead it can justify an infinite number of propositions about emeralds properties as long as they are observed before time (t).
I finally understand this argument. Goodman's a great logician. From what I can tell, this seems to be a fatal blow to the project of creating a formal account of induction. Yet this is clearly a case of a paradox, not an issue with induction itself. It's too bad that we can't incorporate induction into a logical framework (unless someone figures out a solution). Justifying induction on more superficial levels is quite depressing.
Thanks, honestly struggling to understand this.
Wow so my brain hurts trying to keep up with this one lol why am I doing this to myself on spring break?😂
I don't get it. The moment we observe a new green emerald, then grue has been falsified. So obviously green and grue are very different inductive claims.
The only way around this is to create a definition of grue that constantly updates with our observations. However, that violates simple concepts of identity. An emerald that was not "grue' yesterday might suddenly become "grue" today simply because I looked at it. Unless there is a good, pragmatic reason to want to define emeralds in such a way that updates with us looking at them, then that's obviously a stupidly nonparsemonious definition.
+AntiCitizenX 'The moment we observe a new green emerald, then grue has been falsified.'
You miss the point. It's not about falsifying anything, it's an attempt to demonstrate what makes inductive arguments good or bad cannot be just their form (as is the case for deductive arguments).
The practicality of the definition of grue is irrelevant.
+AntiCitizenX Parsimony is not part of inductive logic and thus there is no issue with having "grue" update with new observations. Of course, you don't need to have "grue" update with new observations as part of the observation, you can just make up a new "grue". So you'll have "grue 1" at first and then have "grue 2" and so on ad infinitum without a problem.
*****
*It's not about falsifying anything, it's an attempt to demonstrate what makes inductive arguments good or bad cannot be just their form*
That's a fair point, but I don't really know of a single philosopher in existence who honestly disputes this. Everyone knows that induction is a little more nuanced than some rote, mechanical operation on propositions.
+James Glover
Also, why can't we argue the form of grue? The definition contains propositional elements that are obviously unfounded and unjustified. Green does not.
*****
That background would actually be very helpful in these videos so that we understand more of the context. Thanks.
Grue is more complex depending on the understanding of what it is to be grue. If grue refers to two separate classes of object: green observed objects and blue unobserved objects, and cannot be reduced to one class of objects, then it is more complex. Green is less complex because it implies only one class of object regardless of whether it is being observed, unobserved, or even non-existent. Green is not conditional in that we when told that something is green we do not have to ask whether or not it has been observed in order to know what color it should appear if it were currently observed.
There is another possible case of grue, however, which could refer to an object which changes colors once it has been observed. If we are referring to this class of grue, objects which change from blue to green once observed, then there is no paradox, because it seems perfectly plausible to say that if all previously discovered gems were grue that upon observing the next object it should also be grue because the very act of observation makes it become grue. It is grue before we observe it and it becomes grue after we observe it while still being a green grue gem once observed.
In the first case it isn't really a fair comparison, however, because in the first case grue actually refers to two separate classes of object while green only refers to one, and the meaning of grue is exchanged in the act of observation creating a paradox which would not have taken place if grue referred only to a single class of object. You could create a similar paradox by categorizing two disparate classes under the same term by the use of a disjunction, so for instance a buman refers to birds when not being punched in the face and humans when being punched in the face. If we cycle through an array of items punching them in the face and all previous items have been bumans it is unreasonable to assert that the next as of yet unpunched item will be a buman because by its nature as an unpunched item we're actually referring to an entirely different class of buman, that being the unpunched bird class which is entirely distinct from the punched human class. We can avoid such paradoxes by simply not referring to things under the same name which in context cannot be exchanged. For instance organism is a good umbrella term when referring to things which carry out homeostatic functions, but not as useful when talking about things that fly since not all organisms are things which can fly, so when discussing things which can fly unless we are given additional context, we would simply avoid the use of the word organism so as to avoid confusion.
Likewise we would simply avoid the use of grue where it would cause a contradiction in cases where observed and unobserved grue objects cannot be exchanged for one another while retaining the same essential meaning and semantic function.
What you are saying is false.
Consider one class of objects - called and emerhire. And object is an emerhire if and only if it has been observed, and is an emerald, or has not been observed, and is a sapphire.
It is the case that each time we had observed an emerhire to be grue, it gives some credence to the notion that all emerhires that will be found in the future will be grue.
Also, it is not the case that, each time we had observed an emerhire to be green, it had given any credence to the notion that all emerhires that will be found in the future will be green.
We can also imagine things such as Sappheralds which are saphires if they were originally observed previously, or emerald if they will only be discovered in the future.
Just like all emerhires are grue, all Sappheralds are Bleen.
It happens that we have a natural language where words like green and emeralds are more ordinary than words like Grue and emerhire.
But it does not have to be so. More importantly, having a language where words like Grue and emerhire and common seems to be metaphysically innocent compared to a language that uses words such as emerald and green.
In other words, that our language mostly has words such as green and emerald is only an accident of history, and is philosophically irrelevant for that reason.
+Annaelle Jacques-Morel I never claimed the commonality of the words mattered, merely that in have more characteristics, more qualities, and various disparate natures in fact makes a thing more complex because like in the example the first type of grue is not the same as the second type of grue.
+Annaelle Jacques-Morel Even when green is defined in terms of grue and bleen it is still simpler because it retains its same nature and characteristics whether observed or unobserved and only has the one characteristic regardless of how it may be defined.
Even if bleen and grue were more common they would still have dual characteristics to greens single characteristic.
It's like with humans. Humans are so large that they can lift boulders and so small they can be lifted and held with one arm. How can this be? We are really talking about different kinds of humans: grown adults and babies. Why two names for one thing? The characteristics have changed and that observation must be acknowledged to avoid confusion. Grue likewise must be given thesame consideration since green grue isn't the same as blue grue. Even if the grue logic would work on emerhire it is only because emerhire is also two different kinds of object loosely regarded under one name though it has disparate properties under different conditions of discovery.
You ARE aware that «green» is actually a word that describes a specific wave length of electromagnetic radiation in the specific context of interacting with the retina of a live human eye, and that green can be a different wave lenght of electromagnetic radiation whenever it interacts with the retina of a live animal of another specie such as a dog? Right?
It is arbitrary and disingenuous to say that green is a metaphysically simple term.
It is nothing of that sort.
+Annaelle Jacques-Morel Even by that understanding it is a specific set of wavelengths while grue denotes two sets of wavelengths at different times. Even then there is sometimes a need to distinguish for instance lime green and forest green.
Can't any already observed, and while observed, green emerald still be grue, and when it is observed in the future to be blue?
Can someone help me? Isn't the structure of the induction flawed in the first place? If "all emerald observed by now are green", you cannot induce that "all emeralds are green". Since "All emeralds observed by now are green" only infers that if you have an emerald observed by now, it is green. It says nothing about the remaining emeralds in existence.
My thought too but isn't this the difference between deductive and inductive logic? In this argument it simply gives and indication that they probably will be green and hense is a good inductive argument..
What I understood was that the word grue was made to demonstrate a situation where an inductive reasoning is "definitely" wrong, rather than being "possibly" wrong or not definitely right. We know that quantitative data cannot be converted into qualitative data, which means no matter how many times one observes emeralds as being green, it cannot necessarily lead to the conclusion "therefore, all emeralds are green," since the thesis can be proven wrong whenever a non-green emerald is found, which means there is always a possibility that it is false. But in the second example with grue, the inductive argument is always wrong, without a possibility of ever being right by its definition. But I don't understand what is so paradoxical about this problem honestly, because it just seems like another more complicated way of proving that induction cannot guarantee truth.
That is the original "problem of induction". This "new riddle of induction" is a further exploration of the problem of induction, but you're right that it's really the same thing. It's a mistake to say it's about "good induction" vs. "bad induction", because we really can't predict the future. If we're tempted to believe that all emeralds are green and will stay green forever, it's still conceivable that we are unaware of some law of the universe that turns all green things blue in 2025, or that we're living in a simulation and somebody starts messing with the RGB parameters.
Can we have a similar example in reality? Like which pair of concepts might be same as "green/blue" VS "glue"?
That would make this video even better
How do you know wich colour something has when it's not observed? So how can you say something is 'unobserved and blue'?
Being color blind is probably the only way to solve this puzzle without even trying
But specifically blue/green colorblind.
Can somebody tell me the application of this besides writing a paper at school?
Absolutely none
Well I'm certainly glad we're pawning this off as philosophy and logic
It highlights a weakness in logical structure when we apply language to it.
All emeralds that have been observed in the past have been observed in the past. Therefore, all emeralds have been observed in the past.
This is a deductive argument. You can have premise A and conclude that A.
your conclusion just doesn't follow. I can accept your premiss and find an emerald in the ground which was not observed in the past
Is Bleen more complex than Green also? Of equal complexity of Grue too? Or Less/More than Grue?
GRUE's meaning depends on the context so it is not a very well defined term, right? It's more like GRUE(x) function and you cover up the (x) part with language semantics so it looks like a constant.
it's just that the strange definition of grue creates a contradiction. It's not really a paradox. You could invent many other words with wacky definitions that will create this contradiction. The important thing is that the definition of the word changes based on observation which is key to the deductive logic. It's like me defining a new number 2, but the difference is that when you add this 2 to another number it becomes 3. So then 2+1=4. Not a paradox but rather a manipulated outcome.
Is 'grue' isn't even a consistent definition? If the next emerald I observe is grue, what colour will it be? Will it be blue, since it has not been observed yet and hence is blue, or will it be green, since it will have been observed and hence green? It seems that to say an object is grue we are actually saying it had to have changed colour: it was blue whilst in the ground, but as soon as it was observed it became green. Thus it is not true at all to say that all emeralds observed thus far are grue, since they did not change colour (or if they did we wouldn't know, hence we wouldn't know they were grue). So it does not follow that the next emerald to be discovered will be grue. And even if it is, what we will find is that it is only blue NOW, before being observed: as soon as it IS observed it will change to green, hence it will be like all the others we've seen and hence green.
yeah. Thats what i thought as well.
Sometimes in literature, Gruefullness is given a specific deadline (such as being originally observed by human eyes before the 15 of december 2020 at 11h59 PM) to avoid the confusion you seem to be having.
Why do you call what i said a 'confusion'?
Because you asked :
"Is 'grue' isn't even a consistent definition?"
The consistency of the word grue is beside the point. The point is that there cannot be a purely formal account of inductive reasoning the way it exists for deductive reasoning.
+Annaelle Jacques-Morel
Thank you for the caveat you added, which makes this more interesting. However, without it i stand by my statement that none of the emeralds were grue before they were discovered and the chances that the next undiscovered emerald will also not be grue are very high as a result. As for the caveat, that seems to be making the definition even more contrived and complex, but I'll think on that one
"The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction. The process of subsuming new instances under a known concept is, in essence, a process of deduction."
-Ayn Rand.
"In reasoning, the conclusion follows from the premise necessarily...in deduction, the conclusion is necessary, otherwise you negate one specific product of the conceptual faculty, one specific generalization. In induction, the conclusion is necessary, otherwise you negate the whole system of human concepts."
-Leonard Peikoff.
1:50 this is not induction as to negate the conclusion would not negate the whole system of human concepts. If it is the case that by the chemical structure of an emerald that the only possible frequency of light that can reflect is green then we can induce from one emerald that all emeralds must be green because the alternative would negate the whole system of human concepts about light and matter and microscopes and science and identity and existence.
2:10 This is a meaningless concept with no ties to reality and cannot be used to negate the whole system of human concepts as it is not a real concept of a real thing. It is a concept about our knowledge given silly constraints. Grue is not a color, it is an idea about our knowledge and color. There is nothing you can do with this word which will affect induction one way or the other. To negate grue is perfectly valid, to accept grue is perfectly meaningless. It has no effect on knowledge as such.
4:15 That is just childish word play with no concern for reality and consciousness and concept-formation. Green is perceived, Grue is conceived.
4:40 Giving a percept a concept based on a concept that requires the percept is insanity. Just quit.
5:11 "What does this mean?"
It means philosophers will say whatever they want in order to continue receiving funding, and will intentionally make it difficult for their employers to question them and fire them.
I belief the semantic proposition is time dependent. If lets say the stones were light dependent it will be similar, the observer wont know until what amount of light is present at the time of observation. And the invented terms grue and bleen are disjunctive make all the different and drags with the terms green and blue. Nice film, now I understand the argument against formal induction
Sinan Dogramaci wrote a paper on boltzmann brains and i dont understand the 4th part
Speaker: That's a pretty good definition of Green.
Me: NO IT'S NOT!
So something that is grue is observed green and unobserved blue. How can we tell that emeralds aren't grue? Once we observe them they are green. we have No way of checking what color something is before it is observed?
+Turt1eXing It is not strictly about observation but about the theory that infects the observation. In a crude sense, you can make up any hypothesis that will confirm all your observations, yet due to its content make the next observation highly improbable. In this way, a valid formal structure for inductive logic is harder than deductive logic (where, as this video showed, the particular predicates can not override the logical structure).
Thanks, Sinan
Why you can define Green using Grue and Bleen if their definitions use Green? Why this is not circular?
Don't know if it's posted, I don't have time to read through the comments right now...
Question: is this puzzle not just an example of how arbitrarily changing the premise invalidates the conclusion?
GRUE cannot exist, and therefore GRUE cannot be real. Therefore GRUE cannot invalidate a "real" deductive argument.
Let me explain:
In the observable and measurable world we exist in GRUE would have to have the magic ability of changing it's nature based purely on whether or not it is observed, i.e. green when observed and blue when not observed. This means anything that is GRUE is blue until you look at it and then GRUE becomes green, which is the same thing as saying it was never blue in the 1st place because by definition you cannot observe it in it's blue state. Because it cannot be quantified OR qualified, it doesn't exist and in the end green is effectively always green.
The only alternative theory for GRUE is that an unobserved object is GRUE/blue until it observed at which point it remains blue, in which case blue = blue.
Even if we had the ability to observe an unobserved thing in it's GRUE/blue state (which is also impossible because then we have observed it, but let's set that aside for the moment) and then observe it and see it transform into green, syllogistic logic still works.
All unobserved GRUE is blue.
All observed GRUE is green.
The grass is green.
Therefore, grass is observed GRUE.
All unobserved BLEEN is green.
All observed BLEEN is blue.
The sky is blue.
Therefore, the sky is observed BLEEN .
What it all boils down to is: green is green unless you prefer to BELIEVE in GRUE, in which case it merely becomes "observed GRUE" instead of "green" so at its simplest GRUE is more complicated in naming convention alone (AND now we open the can of worms on belief systems and faith as quantifiable constructs vs. emotional states), and the same is true of blue. This implies that GRUE and BLEEN are then just more complicated ways of describing the quantifiable qualities of color.
OR
I could be wrong.
I believe this is objection is wrong. Remember, this whole discussion is related the concept of logic, which is independent of how physical reality manifests. Grue is a totally logically consistent color, and metaphysically, poses no problems. Because logic is independent on physics, the fact that grue may not exist in our physical reality does not invalidate the fact that there appears to be a logical inconsistency.
@@axemenace6637 If Grue is a totally logically consistent color, can you tell me its wavelength?
@@ssll3393 Before you observe it it's wavelength is that of blue, and after observation it is that of green.
If you guys are interested, we actually discussed this topic on our latest podcast. You can check out the video on our channel. It's titled "THE SUN COULD EXPLODE!"
I would really like to see a video about amygdala hijack! could you make one??
it seems to me that you are defining green with the word green. that is because both grue and bleen use green in their definitions and you are using them in the definition of green
It's also possible to define green in terms of grue and bleen. Green is grue up until now, and bleen any time later.
You can't define green in terms of grue and bleen because that's circular defining. You used green to define grue and bleen, so you can't use grue and bleen to define a term used in their own definitions. Since there's no way to define grue or bleen without using green, green is the simpler term.
It seems like an issue is that the definition of grue cannot be simplified, whereas the definition of green can be. The given definition is sufficient and true, but it can be simplified to be true no matter the context: Green is the color observed of an object that emits or reflects specific wavelengths of light. One could also argue. Grue cannot be defined without a temporal context. Another argument might also be that Grue is more complex because (if green=grue before, and bleen after discovery), then Grue= (grue before or bleen after) before, or blue after, creating an infinite regress.
I think this video is incomplete without including some thoughts on words such as Emerhire - as in, and emerhire is an object that is an emerald if it was observed in the past, and a sapphire if it will be discovered in the future.
And the observation of a grue emerhire increases the probability that all emerhire are grue.
Nothing could be that object, at least not invariantly in time, for the future in which such an object will be discovered will eventually become the past in which it was observed. The same reasoning can be applied in reverse. So unless sapphires and emeralds are the same thing, and blue and green are also the same, such an object is impossible
You cannot possibly be all at once smart, believe what you said, and have understood the video properly.
In the context of this video, the assumption is that there is a point of reference in time that is fixed, and we are interested in whether or not object have yet to be discovered by that specific point in time. Objects that will be discovered later are grue if and only if they are blue. Objects that have already been discovered earlier are grue if and only if they are green.
Annaelle Jacques-Morel It's a bad definition. And that's not said in the video, so it's not the premise.
It is said so extensively in philosophical literature about grue. The fact that you are ignorant of this does not make you right.
Annaelle Jacques-Morel I'm ignoring it because it wasn't presented on the video and you are not the video maker. You can't add stuff to an argument some other person did and put words in their mouth.
But even if you did, "grueness" is not a real property, it's not intrinsic of the object as it depends on an arbitrary point in time and whether some dude looked at it or not. If you want me to believe you when you say the two arguments (P then Q, R then S) then you have to use good premises. You cannot go around making stupid shit up (grue, bleen) and then cranking up the stupid gauge all the way to graham's number (defining green from bleen and grue, whose definitions necesarily use green) and being all like "look, this stupid thing I pulled out of my ass is just as stupid as this other thing that doesn't make any sense! Therefore I'm right!"
But the definition of Bleen relies on the definition of Green. Circular logic, anyone?
Or does Green rely on the definition of Bleen? All definitions will eventually become circular? How do you define "define"? or what is the meaning of "meaning"? What is "is"?
The issue with the GRUE paradox that I see of the top of my head is that it relies on asserting the characteristic of something that is unobserved.
All observed emeralds are both Green (P->Q) and Grue (R->S). All unobserved emeralds are unknown since they have not been observed. They could be Green, or Grue, or red, or yellow as long as at the moment you observe them they are observed as Green. You can't observe a Grue emerald to be blue like you did in your example, so, I would say that example is bad.
The two statements on there own P->Q and R->S are equally likely and the more likely one can not be distinguished based solely on those two statements. So, this is another error in your video where you assert the P->Q is correct and R->S is incorrect.
How one decides which is correct is based on how this statement fits into a broader theory. You have the belief that in your world things don't generally change color when no one is observing them, which is why you believe P->Q is correct. Also, the simple theory that things don't change color simplifies things. As, that means you can simply call things green instead of having many many indistinguishable states. Such as Grue, Grack, Gred, Grellow, Grown, etc. None of these many states can be distinguished since you can only distinguish something by observing them and by definition they are exactly the same when observed.
This means that Grue is simply a bad concept since it is indistinguishable from Green, hence, all things that are Green are Grue (P->Q = R->S). Your assertion that one is correct and the other is wrong is based only on your beliefs and nothing else. We also have an example where something like this actually happens.
In the quantum physics world observing something can actually change the state of it. Where something can behave like Blue (whatever that means) when it is unobserved and be Green when it is observed. However, in the Quantum Physics world we can use math to kinda figure out what is going on when we are not observing something, and predict what will happen when we make an observation. So, concepts LIKE Grue make more sense in the quantum realm because it is distinguishable.
Since, everything ultimate derives from the quantum realm it very well could be that R->S is true. I mean how do you know you couch isn't blue when nothing is observing it. The point is that trying to distinguish P->Q from R->S is pointless and a waist of time unless you can devise an experiment to make such a distinction. Otherwise they are equivalent.
amcnea Yeah after watching this video, I thought that there was a connection between the paradox and quantum physics.
The first argument is false. If all observed emeralds are green, that does not mean all emeralds are green, as there could be an unobserved one that's blue. It might be a reasonable conclusion, but it is not inductively true. Both statements are built on the same false logic: everything seen so far has a property ergo all objects have that property. There is no paradox; it's just that one statement looks right and one looks wrong.
I would agree. The problem is the conclusion is correct in the real world, but is not correct by the argument. I first encountered this in the winter rose argument. P1: Some flowers do not bloom in the winter. P2: Roses are flowers. C: Roses do not bloom in the winter. In this argument, there is no reason to assign P2 to the "some" in P1, other than the fact that roses really do not bloom in the winter. And because we know that the conclusion is correct, we overlook the flaw in the argument.
The form; All observed X are Y, therefore all yet to be observed X are Y, is completely flawed and is actually called prejudice. Assume that the first time I meet any Scots (X) is at a party, and they are all drinking, all the time (Y). Therefore all Scots (X) drink all the time (Y).
You are being to skeptical for the context. The 'if A then B' is ok. The grue is just a dumbass modification that makes it into a different statement. It doesn't invalidate the simple version. It's just stupid as hell. I'm SO tired of 'these kinds' of philosophical statements.
Common mistake, whether the proposition will always lead to a true conclusion is somewhat irrelevant. There's a difference between being logically valid and being wrong. If you had only seen green emeralds it would be logical to suggest the next emerald will probably be green. Even if you err you have at least been logical.
However if you applied the same logic to something grue you wouldn't just be wrong, you would have created a contradiction. Your argument not only wouldn't be true but also wouldn't be logically valid.
For something to be logically valid but not true it has to deduced using correct logic from a false assumption. If you started with the assumption that all emeralds were green that might or might not be a false assumption. But the assumption that all observed emeralds are green is a correct one. Applying the logical method 'all observed P => all P' is false logic, so you can't say that the proposition is logically valid.
+Jim Smith It's inductive, not deductive logic. It's a perfectly logical inductive argument. If you disagree with that then it's possible that you simply don't understand inductive logic.
I don't mean that as an insult, merely that in treating inductive logic as if it ought to adhere to the standard of deductive logic suggests that you might be confused on the subject. Inductive logic reveals only what is likely to be true and not what must absolutely be true.
So basically the form of the argument isn't all important to the validity of the argument. The variable inputted into the argument form matters a lot as well.
But isn't this basically the same as the false analogy fallacy? The argument/logic applied to one thing cannot be transferred to another thing.
Induction depends on observation, so it's not really fair to say that the two arguments have the same 'form' insofar as the nature of their subjects is different.
The idea is to show that induction makes good common sense, but no formal/logical account of it is possible. Goodman's own example was in the case of emeralds. The problem with observation is that it is fallible in more advanced and varied ways than some rule of logic. Creating an abstract account of a fundamental system like induction using observation seems unusually weak. I think I agree with Goodman's diagnosis that induction is rational but illogical.
Wait a second, why is the argument in this video put in a deductive way? All emeralds so far observed have been green. Therefore, the next emerald to be observed will be green is not a deductive argument. It can not be put in the form of:
1) P implies Q.
2) P
3) Therefore, Q.
Am I wrong?
I believe he is showing exactly why it can't be put into deductive form because the subject matter, for induction, changes the quality of the statement. i.e. Grue.
If an object is green, then it is bleen before observation and grue after observation. So, observation changes this property of an object, while it doesn't change its property of being green. Isn't that the difference? Like, imagine you're driving a car along a line of flags, and you observe each flag fluttering, and conclude that all flags are fluttering, but if you look back from your car, you'll see calm flags - because they were fluttering only due to wind caused by your car.
But ok, we can construct another definition of grue and bleen, like, grue is {[a green object observed before 01.01.2001] or a [blue object that wasn't observed before 01.01.2001]}. (The green/blue and grue/bleen terms still stay symmetric here, possible to express in the same way as in the video.) Then, on the day 01.01.2001, we can make this conclusion that since all observed emeralds are grue, then all other are also grue, so they will be blue when observed (and still grue, because the fixed date has already passed).
Well, that's a trickier question.
Oh! I know this one!
"I fly to the moon. I shrink the moon. I grab the moon. I sit on the toilet."
G. Rost lol
Hold on, I don't get it.
Modus ponens is: ((P) and (P -> Q)) -> (Q)
The implication (P -> Q) - in this case (all observed are green -> all are green) may be incorrect if not all are green. If there exists an emerald that is not green the implication fails, the outer implication becomes false -> false and is still correct. Your example does not break the rules of logic in any way.
You're missing something. The whole point of this paradox is to build a concept of inductive logic. We want to be able to say "observing that a P is a Q supports that all P is Q". This is the central assumption that we make in our day-to-day lives. You think that the fact that bread nourished you in the past supports that all bread nourishes you, for example. However, this paradox shows that such a construction of inductive logic is not a good one.
Grue and Bleen are more complex in that they have a parameter: the time at which the transition occurs.
But green can also be defined with t
Isn't the Grue Paradox supposed to show how, two mutually incompatible hypotheses, can be supported by the same observations?
On this video/comments, the 'Grue Puzzle' appears to be getting too caught up in a deductive/inductive debate. The puzzle does, however, give an attack against the instantial model of Confirmation Theory.
H1 All Emeralds are Green
H2 All Emeralds are Grue ( Grue = x that is green before 3000, blue after 3000)
The hypotheses are rivals because, H1 claims that emeralds not observed before 3000 are green, whereas H2 predicts them to be blue.
Both hypotheses, despite being rivals, are supported by observations where an observed emerald is green.
So then, observations of Emeralds that support H1 because they are green.
However, they also support H2 because they are both green and observed before 3000.
(The key is to remember that grue is not a definition tied to an emerald, grue can be anything that is green observed before 3000 and blue when observed after.)
Hi Wahey,
Here, you said, "The hypotheses are rivals because, H1 claims that emeralds not observed before 3000 are green, whereas H2 predicts them to be blue." I don't think H2 or Godman's argument claim that if an emerald is not observed before 3000 it is blue. They are blue if they are observed after time(t), which in your example is 3000, but before time(t) an emerald observed or not observed is always green. So, as long as time(t) does not happen the observations can be used to support both propositions because before time(t) the emeralds, observed or not, are green.
Sorry, what I mean by unobserved is that they will be observed after (t).
So, where H1 would predict all emeralds to be green regardless of (t) H2 predicts after (t) observed emeralds will be blue (if grue).
The colour they are after (t) is irrelevant, the point is that the same evidence supports both statements despite different conclusions.
Exactly, it is irrelevant coz time(t) is always indexed to a point in future, and as long as this point in future never actualise the observation does indeed support both arguments.
That is pretty much the ultimate point, but the wording is tricky. Grue is defined such that we know definitively that all emeralds are grue now, regardless of what happens after 3000. But the point is the same, you just need to replace H1 and H2 with
H1 All emeralds will remain green after 3000; at that time they will change from grue to bleen
H1 All emeralds will remain grue after 3000; they will change from green to blue
You say you can't distinguish those two arguments merely by form. I say: Yes you can. It's really not that hard.
Your properties "green", and "blue" are axiomatic. Your set of atoms looks something like {isObserved(Emerald1), isObserved(Emerald2), isObserved(Emerald3), isObserved(Emerald4), ...} ∪ {isGreen(Emerald1), isGreen(Emerald2), isGreen(Emerald3), isGreen(Emerald4), ...}.
Your property "grue" on the other hand is not. It's a rule that can be expressed as isGrue(entity) := ( isObserved(entity) ∧ isGreen(entity) ) ∨ isBlue(entity).
In your second argument using the rule grue, before you can evaluate it, you have to eliminate the rules:
P: All observed emeralds are grue.
C: All emeralds are grue.
P: All observed emeralds are either observed and green or blue.
C: All emeralds are either observed and green or blue.
P: All observed emeralds are green.
C: All observed emeralds are green and all not observed emeralds are blue.
P: All observed emeralds are green.
C: All not observed emeralds are blue.
It's obvious that this argument is quite different from your first one.
The same goes for this silly attempt of showing that "green" is more "complex" than "grue". I can use this argument to show that something is more complex than itself by using it in an arbitrarily long disjunction of unrelated properties. If you eliminate all the rules and simplify the formular you'll end up with the simple atom "isGreen".
I love idiots on youtube who waste their time trying to refute sophisticated arguments, because they just think that highly of themselves (I bet you spent at least 30 minutes on this, ahem, gem). Bruh, none of what you said made sense. One must first understand what is being discussed before one can critique it, eh?
FruitGod - I love idiots who believe stupid arguments are sophisticated. 'Grue' involves a change, 'green' doesn't. Change is more complicated than not change. The only people confused by this are philosophers.
This is not unique to inductive logic. Compare "all chairs are furniture, X is a chair, therefore X is furniture" and "all chairs are airplanes, X is a chair, therefore X is an airplane". You can't tell from the form which is a good argument, you need more information. The same for the grue argument. So the whole argument is based on an obvious falsehood.
'Good' here doesn't mean 'good' in the normal sense: it means 'valid' in the formal logic (which, by the way, is a branch of maths, not "philosophy" in a pejorative sense) technical sense of 'has a conclusion that must be true if the premises are'. Both 'all chairs are furniture, X is a chair, therefore X is furniture' and 'all chairs are airplanes, X is a chair, therefore X is an airplane' are *valid* arguments in this sense. It's just one has a false premise. But the claim the video is making is just that validity in the technical sense depends on form alone; no one thinks that being a 'good' argument in the sense of being valid and having true or plausibly true premises depends on form alone; obviously whether the premises are true/plausible depends on what you are talking about.
There's nothing funny about 'grue' that isn't equally funny about 'green'. Consider a community of language users that use the terms 'grue' and 'bleen'. Since you are part of a community that uses 'blue ' and 'green', we have to define 'grue' and 'bleen' using the terms you know, and so to you, they will end up looking funny. But this is only skin deep. Consider explaining to this community your own color terms of 'blue' and 'green'. you'll have to use the terms they know to explain it. You'll end up having to tell them that 'blue' means: bleen before time t and grue afterward. Then they will look at you like you're an idiot and demand an explanation for why you sue such stupid color terms as 'blue' which seem to build in that stuff just changes color. He will in fact say, "'Blue' involves a change, 'Bleen' doesn't. When something's bleen, it's always bleen. Only philosophers would be confused about that." And he would be just as right as you.
So the definition of this exercise is to prove that if you make things more complicated than they need to be, that you sound more intelligent that you appear to be...or appear to be more intelligent that you actually are. Therefore if you make up words to prove your unprovable point you can prove your unprovable point.
HVALA BRATE SINANE KAKO SU TVOJI? POZDRAV IZ SRBIJE
If you buy an old computer, you can salvage copper wire out of it using power tools, but that doesn't mean copper wire is more complex than computers and power tools. Green is simpler than grue and bleen, even if you can recover the concept of green you used to define them.
These inductive arguments rely on the implied premise that an [x] object will remain [x] even after it is observed. Just explicitly say that and grue will stop breaking them.
Let simplicity guide your path.
Why doesn't it make sense to say all emeralds are grue? We can never know its unobserved form can we?
+The Next Freud that's the point. Philosophy of science during this time was dominated by individuals who wanted to show how inductive reasoning can be expressed in terms of deductive logic. Popper for example saw science as progressing via modus tollens and not via standard induction.
grue is definitely more complex than green because for grue to exist, an object has to exist in two colours. Green if observed, blue if not. meanwhile it is commonly believed that a green object will still be green if you're not looking at it. Therefore, if you argue that all emeralds have been green and will continue to be Green, you are arguing that colour remains constant. If you argue that emeralds are blue unless they are observed, you argue that colour is not constant.
It green is defined by grue and bleen, both of which contain the word green, then you've just got a tautology. That seems to me a pretty good case for green being a simpler concept.
But green also contains grue and bleen. There's no formal logical way to say which one came first.
I did NOT understand this at all.. why not show a few examples of how the argument is used? It's really hard to understand when you only speak in the abstract terms without any concrete examples of how those terms apply or don't apply.
+PIneapple29 This is impossible. Grue is a word whose only purpose is to behave differently at different positions in the argument. There are no real words that behave this way.
Actually, all real words behave this way. Green looks like what we have SO FAR observed it to look like. Chicken tastes like what we have SO FAR observed it to taste like. The word 'crocodile' seems to us, based on experience so far, to pick out a natural kind. The point of the argument is that the sum total of our experience is always insufficient to tell us whether our concepts and language actually cut reality at the seams. natural laws that seem to govern crocodiles may really be a distortion of a more general natural law that really governs brocosaxodiles. Something is a brocosaxodile if it is either broccoli, a saxophone, or a crocodile.
emerald:
- a bright green precious stone consisting of a chromium-rich variety of beryl.
- If the hue is too yellowish or too bluish, the stone is not emerald, but a different variety of beryl, and its value drops accordingly.
P: All of the numerous emeralds observed in the past have been green.
C: All emeralds, those observed and yet to be observed, are green.
- - - - -
bachelor:
- a man who is not, and has never been, married.
P: All of the numerous bachelors observed in the past have not been married.
C: All bachelors, those observed and yet to be observed, are not married.
= = = = =
Probabilistic:
- Based on or adapted to a theory of probability; subject to or involving chance variation.
Q. What is the probability of finding a non-green emerald or married bachelor?
= = = = =
GRUE:
A thing is GRUE if,
A: either it has been observed by now and it is green; or,
B: it has not been observed yet and it is blue.
Q. Can a emerald that has not been observed yet be GRUE?
No, but an Emerhire can is sure to be grue
The term "inductive logic" here and attempts to draw any parallels between it and actually formalized deductive logic don't sit well with me: inductive "logic" seems like it should simply be called probability based inductive reasoning.
I mean, I have never eaten a baby. Therefore, all babies I have eaten were trivially blue. Therefore, by inductive logic, the next baby I eat will be blue.
I thought this was about despicable me lol #idiot
Maybe this video is oversimplifying things, but the problems seems to be arising when an object property definition that is contingent on observation. Since induction is about going from the observed to the unobserved, it seems likely that this can create the same kind of self-referential paradoxes that are in Godel's completeness theorem.
I have my own problems with induction in that it assumes homogeneity between the set space of where you have taken your measurements and what you are extrapolating to. You simply have no system independent way of knowing the nothing essential has changed or that your sample is representative of the whole.
Part of the reason why deduction works in a logically tight manner is that it is restricting the set space with each step so that there is nothing new that might have different properties or follow different rules.
That was only 6 minutes?
Green = Observed and Grue OR Not Observed and Bleen
When we replace Grue and Bleen with their definitions we get
Green = Observed and Green OR Not Observed and Green.
So Green = Green.
This has not made the definition any more complicated, it just tried to obscure it.
The same thing can be done with Grue:
Grue = Observed and Green OR Not Observed and Blue.
When we replace Green and Blue with their definitions we get
Grue = Observed and Grue OR Not Observed and Grue.
So Grue = Grue.
Alternate definition :
Green : Discovered, and the color of and emerhire OR unobserved and the colour of a Sappherald.
"The fact that we usually rely on words like green, blue, emerald and sapphire rather than words like Grue, Bleen, emerhire and Sappherald is nothing more than an accident of history."
Also, we should assume that the words in our natural languages have stranger semantic properties than properties such as grue-like words. Most of our natural words have more than one meaning.
Get rekt. My philosophy-fu is stronger than your philosophy-fu :P
Annaelle Jacques-Morel
I do believe you missed the point. Definitions are just a way to give meaning to a word... it has nothing to do with "discovery". There are many metaphysical words (like grue) that have come about in order to discuss complex ideas.
Oh, no - I got the point completely right - the ultimate goal is to discuss why inductive reasoning cannot be given a purely formal account the way deductive reasoning can.
And the immediate goal was to shut down people who claim that Goodman's argument about grue was invalid because of some inherent semantic property of grueness that made it an illogical word or concept. In this case, an allegation of circularity.
Annaelle Jacques-Morel
Ah! My mistake. I misread your original post and took it as the opposite meaning. Apologies.
Grue is more comlpex. It depends upon the definition of green. It's simple (green that is).
He showed explicitly that green isn't necessarily as simple as it appears
How can the concept of Grue even be true? Doesn't positing the truth of Grue beg the question? (Owing to the fact that it has an antecedent dependent on an unobserved [and unobservable] variable)
Maybe there is no perfect definition of _complexity_, but only an idiot would say that a description of a colour which contains the concept *green*, the concept *blue* and then a *condition* is interchangeable with the concept *green*, and only a moron would suggest that { a colour that is *grue* (*green* while *observed* and *blue* if yet *unobserved*) if *already observed* OR *bleen* (*blue* while *observed* and *green* if yet *unobserved*) if *yet unobserved* } can be substituted to *green* because it's just a different perspective on the same thing.
I didn't get it from the video, but I hope that Goodman was being ironic.
Argument 1: All Observed A are Green => All A are Green => All Non-observed A are Green.
Definition of set B: All Observed B are Green AND All Non-observed B are Blue.
Argument 2: All Observed A are B => All A are B.
Author states that antecedent of argument 2 (All Observed A are B) is true. But it's not since if set A belongs to set Green and set B belongs to set Green than it just means Green is a super-set of A and B. But in no way it implies A is equivalent to B or they even intersect. So it's another Fakeadox.
The answer is actually quite simple. Neither of the arguments is valid. A valid form needs additional premise about invariance of colour, which needs justification/evidence on its own. The first argument seems valid, because there is assumed pre-existing precedent about colour green being independent of date of first observation. Such precedent does not exist for grue. Note that the puzzle is not "why the first argument IS valid and the second is not?" - the puzzle is "why the first argument SEEMS valid while the second does not?"
I have a horrible feeling that sone day, could be tomorrow, could be years from now, I will be faced with a situation where I am tasked with looking at green or blue objects and will use Grue but no one will understand.
Why do they talk about deductive logic and then use inductive logic?
Just what about this isn't deductive? Grue works on exact rules and definitions. There is no probability involved in the puzzle.
@@lightningandodinify deduction cannot be used like that. If the premise is "all observed astronauts are human" then you can't conclude "therefore all unobserved astronauts are also human." that is induction. To assume characteristics from one set onto another. Deduction works more like:
"P1:every astronaut on the Apollo missions was human.
P2:Buzz Aldrin was on the Apollo missions.
P3:buzz aldrin was an astronaut
C: buzz aldrin was human"
If you agree that all the premises are true, then it is impossible to disagree with the conclusion.
In the first example you could get an incorrect answer despite the premise being true. In this case some astronauts (which you were not aware of) were mice or chimpanzees.
@@lloydnicholls1439 none of that is relevant. The idea here to create a definition for induction that can be defended through formal logic. Deduction is only relevant as a means to explain induction. Grue shows that even with exact form (remember that the content of variables don't matter for deduction) induction cannot be explained through logic. The statement "all unobserved emeralds will be green" suddenly stops making sense when we substitute green for grue or even the disjunctive definition of green (grue + bleen). This is not possible for any true formal account. We all "know" that ampliative inferences work, but it seems that we still have no way of creatibg a valid and functional explanation what we're even doing.
@@lightningandodinify I understood the point of the video. I just felt the use of the term "deductive" logic was incorrect as I have come to understand the word. Deductive logic is simple. It's either valid or invalid and if it's valid, then conclusion follows necessarily. Inductive reasoning becomes complicated because we're are dealing with strong evidence and weak evidence, good arguments and poor ones. You should look up the "raven paradox" for another interesting problem with inductive reasoning.
@@lloydnicholls1439 i know about the raven case. I think Bayes' theorem can solve it. As for deduction, the project was to make induction seem reasonable because it always looks like a strangely poor argument unless we substitute the variables with common sense cases (like emeralds being green or copper being conductive). The "natural kinds" argument seems okay as a response to grue. It would argue that examples like copper's conductivity is "law-like" and thus projectible through induction, but the counter examples are "accidental" and their frequency is not projectible. The problem is in defining what is law-like in this way.
*sigh* I’m just a bored man trying to dip my toe in philosophy and this video is already making me feel stupid 😂
Ok, so, a grue object is green if observed, and blue if not. If emeralds are grue, then any unobserved emerald is blue. BUT, the moment we observe it it becomes green. After all, we've observed it so it must be green. If not, then our definition of grue is wrong for we would have observed a contradiction to the definition of grue. Similar with bleen. Blue if observed, and green if not.
The paradox arises because our definition includes an observer. Emeralds don't, as far as we know, magically change color once observed. And if they do magically change, it still doesn't change our observations about them. They're green when we observe them. They're also grue if they magically change from blue to green when we observe them.
I find that most paradoxes appear when we don't take one step further back and look at our definitions. If the definitions are poorly defined, then induction doesn't work properly. That was Goodman's point. The concrete definition "all emeralds are green" is not the same as "observed emeralds are green, but unobserved ones are blue and therefore all emeralds are grue." Again, we can never observe an unobserved grue object and not break the definition of grue unless the object magically changes color.
The Schroedinger's Cat thought experiment has a similar flaw. That cat is clearly either dead or alive because the cat itself is an observer in the experiment.
Most of those arguments seem to fail simply because they make absolute statements about what is true. You need to be very very careful about what you say in absolute terms, as chances are at some point you're going to be found incorrect. At this point in my life, I think gravity might be only thing I'd be willing call an absolute, and having said that, I now expect someone to one day prove my statement wrong.
An emerald is by definition green. A chemically similar mineral with a different color gets a different name.
not only is the first argument wrong as Jim Smith points out, but it is also an untenable position to assume you can classify as of yet unobserved things into categories a priori.
how is it that "grue" is considered a simple predicate in the same way that "blue" or "green is. if "grue" represents two different states isn't it by nature less simple than either "blue" or "green" and a poor substitution for this example?
Not when you introduce bleen to define green through grue and bleen. Green becomes the more conplex and disjunctive term then. I dont think this puzzle can be solved. I think Goodman was right in thinking that a formal account of induction is impossible. I believe induction requires an abandoning of formal support. Im in the camp that this isn't a vulnerability for induction but rather a special challenge for applying logic to induction. Our intuitive support for induction definitely makes sense, a formal account might just be incomprehensible if we found one.
This is all based on humans conceptualize of linear time. But if time is not linear and the past, present and future happens all at once that would ultimately challenge the paradox.
We only know that emeralds are grue after they have been observed, and can only make a prediction about whether emeralds will be grue once they are observed.
Example:
All emeralds that have been observed are grue.
Therefore, all emeralds that will be observed will be grue.
Any assertions about the state of emeralds before they are observed are baseless.
Just because all emeralds have been grue once they were observed does not mean that they were grue before they were observed, and therefore, it does not necessarily follow that all emeralds are grue.
We can not say what the state of reality is for things outside of our observed experience.
Unobserved emeralds are outside of our observed experience.
Therefore, we can not say what the state of reality is for unobserved emeralds.
What we really mean when we say things like "All emeralds are green" is that all emeralds that will be observed, will be green when they are observed.
How do we know that emeralds aren't purple when they aren't being observed, or that we aren't in the matrix and they just disappear when nobody is looking? We don't, and can't know that.
What the puzzle of grue does is bring attention to the fact that we don't experience reality directly, but only through our perception. When we typically make definitions about the nature of what we consider reality, it's taken for granted that it applies to our observed experience. This puzzle breaks that.
Also, defining Green in terms of Grue and Bleen doesn't make sense.
Grue: Items that are unobserved and blue, and items that are observed and green.
Bleen: Items that are observed and blue, and items that are unobserved and green.
Green: grue and observed, and unobserved and bleen.
Green:(grue and observed) + (unobserved and bleen)
Green:(If something is grue and observed, then it is green by the definition of grue) + (If something is bleen and observed, then it is green by the definition of bleen)
Green:(green) + (green)
Green: green and green
Green: green
With the new definition of green, there is nothing being observed to determine if an object is green. Instead, the definition depends on the word itself.
Here is an actual definition, for comparison.
Green: The color between blue and yellow on the spectrum of visible light. It is evoked by light with a predominant wavelength of roughly 495-570 nm.
With the new definition, green is somehow supposed to be determined by observing the emeralds, but not seeing the color green. It completely removes the word "green" from the color "green", changing the meaning of the word.
Green is observed, grue is deduced.
Observed emeralds are observed to be green.
Observed emeralds are deduced to be grue.
Emeralds have never been observed to change color after time t, so it is likely that they were the same color before time t.
If emeralds were green before time t, then we can deduce that they were not grue before time t.
If all observed emeralds were not grue before time t, we can assume that all emeralds are not grue before time t.
Dafuq did i just watch?!
Generic Internetter exactly how I feel😂😂😑😅
ffs how am I ever supposed to understand a philosophical text like this if I don't even understand a simple video explaining it
This is a faulty argument in as much as it requires creating no existent words to make its case. Is this really the state of philosophical study in 2019? As a person considering studying philosophy I really am dissuaded from doing so if faulty arguments are being heralded as “gotcha” statements to disprove something.
Your gross misunderstandings about what constitutes "faulty" reasoning means that you should probably stay away from philosophy and all STEM fields. You won't be missed 😃
OK, so I haven't studied logic in anyway, so I'm probably about to crap out of my mouth, but I'm going to do it anyway. I think the problem isn't that grue is more complex than green, but that grue specifically refers to whether or not a thing has been observed, while green does not. Because of that, they are not equivalent when used in a sentence that specifically refers to whether or not a thing has been observed.
«Grue» is a logical tool to help Goodman show that there cannot be such a thing as a purely formal account of inductive logic.
You can reject that grue is «as simple» as green, but then, you still have to show that there can be a formal account of inductive logic.
It doesn't help that, when you say that grue «is more complex» than green, you are appealing to the content semantic content of a problematic word to help an account of logic that says you shouldn't have to appeal to the content of words to build a logical system, thereby fatally undermining yourself.
i literally just thought of blue and green
I immediately see the solution to Mr. Goodman’s problem. Where you state the premise “All emeralds observed in the past have been grue.” you making an implied mistake that is easy to spot. Since being already observed is a prerequisite of an emerald being grue, it would be more accurate to state “all emeralds so far observed became grue as soon as they were observed, so we assumed that they must have been not grue until the observation was made. The assumption was reasonable, because we saw nothing about the observation that would change the color, and observations of the same kind have never changed the color of things before.” There was an implicit falsehood in the premise, as you stated it, because you failed to state that it became grue as soon as you observed it. That is different than color, or green, because we ordinarily assume that color doesn’t change just because you looked at it. But grue is exactly the opposite. If you merely correct that one premise, you see it easily resolved the problem. Certainly, if you had observed many emeralds in the past, you would have certainly noticed if observing them changed their color. So if you merely include the thoroughly implied premise that things don’t change color just because you observe them, you are back to sound inductive reasoning. For example, you could made the alternative premise, “all emeralds in the past became grue as soon as they were observed.” And you would be good again. (Most inductive arguments can be made into deductive arguments, if you just include qualifiers about your certainty of every premise. But the problem does touch upon one of the big problems of 20th century physics. We take it for granted in observing nature that it is possible to make observations of it without changing it, and draw conclusions, because in an everyday experience, we can do that. But in many fields of 20th century physics, people realized you can’t do that. It didn’t destroy inductive reasoning, but it made it necessary to make many implicit premises explicitly known.
The premise : All Emeralds have been GRUE is false.
The Emeralds were NOT observed and were green : thus NOT GRUE.
The premise should be : All Emeralds ARE GRUE once observed.
OR : All Emeralds are NOT GRUE until they are observed.
grue is what a call my dogs...i know that much.
Grue is more complex than green because it describes different properties of an object in different points in the time continuum. Like 'mountain' is more complex than 'slope'. 'Mountain' has different properties in different points in the space continuum (positive slope vs negative slope), while 'slope' does not.
You can define 'slope' in 'mountain' terms, but the difference still holds.
Sag ol abi. Cok yardim ettin
Vay amk rastgele felsefe videolarını seyrediyordum şansa Türk geldi.
But once grue is observed it's green
May be if an emerald is not green is not a emerald
I have a new term. Pave
it is a particle if it has been observed and a wave if it has not been observed yet.
All electrons are Pave.
This is more likely than all electrons are particles..
What are you trying to say? Likelihood has nothing to do with the grue puzzle. It's that fact that we have no formal concept with which we can define induction (or any ampliative inference for that matter).
THE OF GRUE
...PUZZLE...
Goodman defines GRUE as "all emeralds are observed to be green OR have not yet been observed and are blue". And then states that premise (1) "all emeralds Observed are grue" is True. And then says the conclusion (2) that "all emeralds are grue" is not true (thereby demonstrating that syllogistic form alone is not sufficient for proof).
With the first statement (1) we only have to evaluate the first part of the definition of GRUE: "A or B", since A is true B can be ignored, it does not apply. In (2) since we are supposedly dealing with unobserved emeralds (the condition of A are not met), we have to evaluate B and we find that is a statement that depends on the future - we have something unobserved and then we observe it - there is an event happens in time, and that event takes us from the unknown to the known. By the definition of Grue we are led into believing that the next emerald (unobserved) has to be blue - then we observe it and find it is not blue. This is an absurd. Making a claim about the unobserved is absurd. The absurdity does not play out in the premise (1) so we ignore it, and say yes, the premise is true. In (2) it does play out and we see we are not dealing with a valid statement. Deductive logic cannot include statements about the unknown and the changeable. Goodman is basically executing a slight-of-hand, a trick.
The CAT is right - GRUE is a different order of complexity than Green. Grue makes a statement about the known and unknown. Whereas in a deductive syllogism, the premises are always about the known. That Goodman thinks he proves that Green is the more complex term by introducing another to-be-determined definition, BLEEN, is bordering on ridiculous.
It's fairly intuitive that induction cannot be reduced to syllogism. But Goodman's attempt to prove this, Fails.
What I get out of this video is that it might be interesting to look at if there are any kinds of logic that work with future states.
Our entire language is based on the assumption that we know who is talking. It is not so strange to think that we could have a natural language based on the assumption that we know whether or not we can see the things we are talking about.
In such a language, predicates such as green-ness and chair-ness would seem weird.
We would instead have predicates such as grue and chable (a chair if it is discovered, and a table otherwise)
The fact that we have words such as green and emerald and chair in our natural language is a mere accident of history, with no philosophical relevance.
Interesting idea. Not sure I agree with the assumption we always know who is talking - - look at any random written material with no author... Language tends to include articles for what is assumed, and they are optional but they are there. For example in Spanish the "I" is often dropped. But you can include it.
The fact that we don't always actually know who is talking in fact is not incompatible with the notion that our language assume that we do.
I think our language assumes you know who I am. Is a valid proposition in English.
But to formalize such a proposition is complex.
Such as :
There is a Bry Boss
There is a Annaelle
Bry Boss and Annaelle speak a common language.
Suppose a P such as : When Annaelle is talking to Bry Boss, it is known to Bry Boss that it is Annaelle who is talking.
There is a built-in assumption in Bry Boss' and Annaelle's language such that it assumes P to be true.
Also, remember that I don't have to be that convincing - I have to be just convincing enough that you would accept to surrender all hope that inductive reasoning cannot be given a completely formal account the way deductive reasoning can.
If you are very certain that there can be such a thing as a completely formal account of inductive reasoning, then I have to be more convincing than your certitude.
If your certitude is weak, you ought not make that particularly hard.
If emeralds really are grue, then I think the next one we find will appear green, because grue things are green when observed. Maybe we can leave behind a blue light sensor next to the grue emerald and then look away, and then see what the sensor detected, but maybe grue objects are sensor savvy and will only be blue when the property of blueness cannot have any effect on anything else in reality at all what so ever.
This is basically a tree falling in the forest problem.
So functionally, a grue emerald is the same as an always-green emerald. So I'll just use Occam's Razor and live as if the emeralds are always green.
this is silly. if green = that silly definition, it incorporates 'grue' which itself used 'green' in its definition; its circular. I would most certainly side with the cat. further, how can we declare something to be anything (for example, blue), if we have not yet observed it? the definition of grue itself is a fallacy- it claims to know something it cannot possibly know, which is later accepted as a truth condition in one's rejection of the 'bad' argument. i swear, ever since kant people have been obsessed with turning things on their heads. maybe green is more complex - lol?
The analysis you have done is faulty in that the premises you declare are in fact not premises.
"All emeralds observed thus far are green" is not a premise in the context of the argument you present. A premise would rather be: "All emeralds are green".
Furthermore, "grue" is not a property but merely a shorthand way of building the disjunction you mention, into the argument.
The whole thing is a mess of category errors and is thus without merit as either a phenomenon or a tool of instruction. I am surprised it has become part of the curriculum.
Well, the definition of green as "grue or bleen" is recursive because the definitions of gure and bleen both contain green. So the more complicated definition clearly doesn't make sense. It can be either simplified to the original green, or it's recursive and therefore useless.
If you define green as reflecting certain wavelengths or something like that, than that's clearly the simplest possible definition by far and therefore the best.
This is not a good argument because an emerald is a beryl that is green. If the beryl was blue it would be an aquamarine. Therefor this argument fails on the definition of emerald.
It's still a good argument because it successfully disproves that inductive reasoning can be given a purely formal account.
The form of the argument may be good but this example fails because it's premise can not be true
Does not matter. The argument achieves its goal. It is sufficient.
Maybe it is, but it hasn't been proven yet, not on this video. It's like saying a given mathematical theorem is true even before it's been proven (e.g. Fermat's last theorem), it may be so but unless you proove it I'm not gonna take your word as true.
The "definition of emerald" is established via induction. The argument dejustifies induction. The point is that whatever physical processes we assume produce greenness in beryls may in fact produce grueness in them instead, and we simply have insufficient experience to judge between the hyphothesis that process x creates greenness in beryls and the hypothesis that process x creates grueness, (or grinkness or grackness, etc.) in beryls.
Can this idea be communicated without making up a bullshit term just to do it? Grue/Bleen my butt, explain this with real words that have a known meaning.
My brain trying to decide weigh this thing by fighting with itself over whether the unknown traits of an imaginary color might have relevance to comparing them with the known properties of a known color and it's just pissing me off. This is inductive nonsense, it seems. I wish Wittgenstein had bothered to make up a better language instead of just criticizing the ones we already use. >
if you can't grasp the concept of abstract thinking, this channel may be over your head... can't really help you
NothingIsSacred "...make something up to explain something real."
the literal definition of abstract thinking.. it is very clear you cannot grasp it at all
The argument is actually well served by using a "bullshit" term. If the argument had pointed out that induction can't tell us the difference between two subtly different terms that both seemed reasonable, it wouldn't be clear that there was any bad problem with induction. It's the fact that induction can't tell us the difference between an ordinary predicate and a more clearly fanciful one that illustrates that there's a problem with induction.
WTF! "BOOM"