What an interesting puzzle. So, the problem with the 'bite the bullet' approach is that without any observations of ravens at all, you have no useful data in which to ground your hypothesis. No number of observations of shoes is really going to add support. Popper is unsatisfying because I repeated observations of ravens does lend support to the idea that all ravens are black. Though I support a more bayesian interpretation there. In a certain sense, Popper is right because I don't think you can ever reach 100% certainty that all ravens are black, but you can easily reach 0% certainty in the same conclusion. So, your context driven approach seems like it's better than either of the other two. But it doesn't seem very formal. What is 'context' exactly there? To some extent, it doesn't seem that different from the first idea. Very few observations of non-black objects are going to be helpful, even if you don't know that they aren't ravens before you observe them. Mostly that's because ravens are a very small subset of the number of different things you could observe.
hey Jade , nice to meet you in this video I found out what name goes with that beautiful "up and atom" girl , I like you and I would love to meet you but we are worlds apart .....
I think, I can solve it ●In a finite (isolated) system We got more and more white things non of them are raven (In common condition we search thing and examine its colour and in this we search colour and examine the thing so, in opposite black thing "can be" raven) ●So in a finite system (with finite number of things and type of things)getting more and more white things not raven decreases the probability of getting a white raven. so yes it affects. And we do not use it because our world have so much things and variety of things that counting opposite doesn't effect much and it's not an isolated system.
That is because dictionary definitions are incomplete at best, and fails to account for common use. "Your next XX hours" and "have a nice day" have extra meanings attached to them beyond the dictionarydefinitions, and they might also be regional. This means that they're not 100% logically equivalent in reality
ua-cam.com/video/eep4_0JaaG8/v-deo.html well the English language is just stupid in general, everything we say is 100% in context. Check out that video for only a few examples, and remember... their our know rules.
Popper’s answer works; but so does Hempel’s: Suppose the number of objects is finite. If we looked at all non-black things and found them to be non-ravens, that would make the probability of all ravens being black = 1.0 (i.e., 100%). Each observation of a non-black non-raven increases the probability by the following increment: 1 / (number of non-black things). By contrast, each observation of a raven increases the probability by this increment: 1 / (number of ravens). The number of non-black things is bigger than the number of ravens by a huge factor, and the incremental increase in probability when non-black things are observed is smaller by the same factor.
The bigger issue is that even if it were mathematically and logically correct, it's not useful. A philosophy of science which allows you to make claims about ravens without ever observing a raven is inherently flawed. The purpose of a scientific philosophy is to guide what experiments we design and inform what counts as "evidence". Hempel's answer is significantly less useful than Popper's in a practical sense.
Exactly. If you had two boxes on a table labelled "black things" and "non-black-things", every sample you draw out of the boxes incrementally supports your hypothesis. But, once you open up the experiment to "boxes" of indefinite size, each confirming sample proves little. That's why medical research (for instance) focuses on "outlier" populations for sample diversity and focuses on falsifiable mechanisms like (by analogy) "If you modify the blackness gene in test ravens their offspring have drastically different tail and beak shapes and can no longer mate with ravens, therefore all ravens must be black."
This is a functionally true but still technically unsound approach. You'd have to somehow demonstrate that you have seen all non-black things, and that's inherently unverifiable. You can only *wager* that you have, and that's precisely Popper's point --- we can never say a thing is *true,* (some, such as myself, might argue that tautologies are an exception,) but you can say it is false or *wager* that it is true.
I commented about the same thing, in a finite system, statistical data gathered with repetitive discovery of a NEW raven that is black tips the scale and pits impossible odds against the notion of non black ravens existing. So if all ravens have proved to be black, we have refuted that there exists a non black raven and eliminated falsifiability, and with 100% certainty, PROVEN that all ravens are black.
Reminds me of Einstein's statement "No amount of experimentation can ever prove me right; a single experiment can prove me wrong." Finding vast numbers of black ravens (or white shoes) doesn't prove anything, but finding a single blue raven proves the hypothesis wrong.
Maybe the confusion is that testing a hypothesis is not the same as PROVING a hypothesis. The white shoe doesn't prove anything, but it tests the hypothesis successfully.
So does a black raven. You can prove it by getting ALL non-black objects and seeing them ALL not being ravens. It's the same as getting ALL ravens and seeing them all being black.
@@jursamaj Logically, observing the white shoe does actually increase the probability of ravens being black. Practically, it is useless, since the the change in probability from observing a white shoe is small enough to be insignificant.
Jeffrey Suen observing all none black things does not prove that ravens EXIST. By observing all non black things you can only claim “All black things are black.” In the other hand if you observe all ravens you can claim 2 things. 1- “ravens exist”, 2”ravens are all black”. So 2 statements are not logically “the same”. They are just not against each other. In this video I don’t see a paradox. What I see is a bullshit and low IQ scientists.
When your statement includes "all", you cannot call any observation conclusive evidence unless you can observe all of the population. If only one raven is non-black, you are almost certain to never encounter it, and all your black raven observations are meaningless. This all changes when you replace the absolute statement with one of proportionality. "Ravens tend to be black" is a much easier hypothesis to test. The shoe being white is extremely weak bayesian evidence for the original hypothesis, but it does not register in our intuition because there are functionally infinite non-black objects in the universe, so the strength of that evidence is negligible. It's not that the shoe isn't bayesian evidence, it's that you'd have to observe every non-black object in the universe to draw a conclusion from it, so its not functional evidence.
It still wouldn't have any bearing on the colour of ravens. Imagine you could list and observe all non-raven objects in the universe. That still wouldn't give us any new information on ravens.
@@palimpsestransparent You're right, given the scenario you describe, but that's not how the experiment was set up in the video. You're not observing a new not-raven. you're observing a new "non-black object". When that thing you observe is a shoe, that's one less non-black thing in the universe that isn't a raven. It reduces the odds by a minuscule amount that there are any ravens among the non-black objects.
@@jamzfive I see what you mean, but the reduction in probability is simply negligible. The number of different objects is absurdly high and the amount of each one of them too. To state that observing a non-black object increases the probability of all ravens being black seems to me a misuse of logic.
@@palimpsestransparent that's functionally what I said in my original comment. The thing that's not registering for you is the strangeness that it is technically evidence supporting that "all nonblack objects are not ravens" because you have increased the number of non-black, non-raven objects in your sample by 1. You're right that it's negligible, but it's still technically weak evidence. The cognitive dissonance this creates is why they call it a paradox, though I don't agree with that label since it's a problem of understanding the technicality, not a conflict of two knowable facts. This whole thing is more of a brain-tease than a useful thought experiment imo.
20 years ago I had nightmares about that third person... Is that about a movie or something? I just can't verify if there is no common esperience, please help me... Where do we imagine that from?
The problem is that "all ravens are black" is not a scientific hypothesis. It doesn't generate a valid null hypothesis, so it can't be tested. Strictly speaking, every observation of a non-black, non raven _does_ increase the probability that the hypothesis is correct, but the prior probability of that observation approaches 1. So the influence it has on accepting your hypothesis approaches zero. Thus it is not a hypothesis, it's a conjecture, as the information needed to decide it will always be incomplete. To demonstrate this further, just restate the hypothesis as "the probability of finding a non-black raven is less than x". The paradox disappears, as it is obvious that by far the best way to push down the upper limit on the estimate of x is to observe ravens and not white shoes.
Whats important though is that observation of white shoes does still support the hypothesis that observing a non black raven is less then x. It just does so by an amount that is below a meaningful amount.
@@e4Bc4Qf3Qf7 Exactly. But the statement "all ravens are black" is an absolute. You can't prove this with observation, only make an estimate of the upper limit of x. The "paradox" relies on the the fact that the number of non-black non ravens is absurdly high, so it seems ridiculous that observing them gives you any information at all. If you think of a sack full of poker chips of different colours and denominations, and your conjecture is that there are no purple $200 chips in the sack, then it's clear that any chip you draw out of any colour or denomination other than purple $200 increases your chances of being right.
To start with "all ravens are black" is to imprecise. Does it mean all currently existing ravens in this forest, all currently existing ravens everywhere, or all existing ravens everywhere in the past and future? A more precise hypothesis (that avoids the time and location specifics) would be "ravens can only have the color black". To prove that, you wouldn't count black ravens, you would look at what makes ravens black. By proving that the mechanism that makes ravens black can't possibly produce any other color (and proving that there is no possible alternative mechanism), you would prove that all ravens have to be black.
@@goranandersson3544 Yes, you've hit the nail on the head. Observations of the colour of ravens don't lead to a theory of raven colour. This is what I mean by saying that "all ravens are black" is not a scientific hypothesis.
"Your Honor, the Prosecution would now like to call to the stand a series of 8 thousand completely unrelated witnesses who happen to be not guilty of murder. Thereby we shall provide proof for the statement that 'All people who are not guilty of murder are not the defendant' which is logically equivalent to 'The defendant is guilty of murder.'" *AN ETERNITY LATER* "Your Honor, the Defence calls Ted Bundy to the stand..."
But if they were completely unrelated witnesses is that unrelated to each other or to the murder? If unrelated to the murder or knowledge of it, why would they even be on the stand for questioning in the first place? Plus, why would Ted Bundy be there? (I do remember who he was)
This seems like a clever counterexample, but it actually works. If you go through everyone else in the world and prove that they aren't the murderer then the person who is on trial must be guilty by process of elimination.
@@matthewgingerich3942 Unless, the murder rate of the entire world is currently a zero with 1 single outstanding defendant; but you had other defendants in the past who all got acquitted. Hmmmm.
White ravens actually exist. I wonder how many white shoes have to be counted to prove that...or rather to disprove that 'all ravens are black'. Being the lazy person I am, who does not like to infer things, I would only be counting ravens and avoid shoes alltogether.
"All swans are white" makes me think of black ones. Similarly for just about any proposition of this particular logical form. So why do logical theorists of scientific method and reasoning persist in using it as a model? It bears such little relationship to actual scientific discourse and endeavour.
I agree with Carl Hempel. Observing non-black objects that aren't ravens does support the hypothesis that all ravens are black. The reason it's unintuitive is that the amount of information received is astronomically small. It is all about the size of the sets. If you think about it, you can prove that all ravens are black in two ways: 1 - Observing every raven and confirm that they are all black. 2 - Observing every non-black thing and confirming none of them are ravens. They are both possible, but since the set of all ravens is minuscule compared to the set of all non-black stuff, the information gained from spotting a pair of white shoes if negligible.
Whatever instigates the death of me, but fails, makes me stronger. ~Hypothesis I'm not yet dead, and will not likely die, provided fixed rules perpetually apply to every level of reality. ~Theorem As things exist, I'm as certain as I can be that I will too. ~Law Hey guys, while you each have the ability to know something--you'll never actually know for certain what you know exactly. Also, fixed rules don't exist perpetually, so... ~Quantum Physics
@Adam Filinovich The sentence by xXxLolerTypxXx is logically equivalent to the original hypothesis. Also equivalent would be: Any 'thing' will kill Punya or make Punya stronger (inclusive or, i.e., there could be things which kill Punya and make Punya stronger). In predicate logic: FORALL x: NOT is_killing(x) IMPLIES makes_stronger(x) FORALL x: is_killing(x) OR makes_stronger(x) FORALL x: NOT makes_stronger(x) IMPLIES is_killing(x) To falsify the hypothesis one only needs to find a thing which is NOT killing Punya AND NOT making Punya stronger.
@Adam Filinovich Yes, but as I said, these are equivalent (NOT A) --> B (NOT B) --> A A OR B i.e.: (NOT strength) --> death. And indeed, things/events that kill you can make you either stronger or do not make you stronger without contradicting the hypothesis.
I am discovering your channel with great delight. You chose to address the most profound and difficult questions in science philosophy, and still address them with such fluidity and simplicity. You are amazing.
Those two statements may be logically equivalent, but they aren't equivalent sets. these are just two different perspectives which has it's own fatal traps. Consider the following riddle: Three knights enter an inn to get a room. They go to the desk and the innkeeper tells them that a room costs 15 gold coins. Each knight pays 5 gold coins and the bellboy shows them to their room. After several minutes, they decide that the room isn't worth 15 gold coins and they go and complain to the desk. The bellboy takes the complaint and goes and tells the innkeeper while the knights go back to their room. The innkeeper decides that the knight's return business is valuable so he gives 5 gold coins to the bellboy and tells him to give them to the knights. On his way, he realizes that he can't divide the coins equally among three knights, so he pockets two coins and gives three coins to the knights. "Great!", says one of the knights. "Now it only cost us four coins each!." Now if the knights paid 4 coins each, or 12 coins, and the bellboy kept 2 coins, that's only 14 coins! Where did the other coin go? This story mixed two perspectives. The coins paid and the coins received. If you just stick to one perspective, where the coins ended up, then the innkeeper has ten, the knights have three, and the bellboy has two. So, if there is a set of all ravens and the theory is that every element of that set is black, why is it a paradox that a shoe is outside the set is where it is supposed to be? The answer is the perspective of 'support'. Does support mean logically true, or does it mean it makes a positive contribution to the theory? The concept of positive contribution is not fact, but opinion. One may say that a white shoe doesn't contribute to the theory and another might say that after 10,000 black ravens, another black raven doesn't contribute either. The paradox exists only due to perception. If the problem is restricted to set theory, then testing whether a black raven belongs to the proposed set and a white shoe does not belong are the same thing. Finding an error would be different. In fact, every test either 'confirms' or 'contradicts' the theory. Should we draw the line between a test inside the set and a test outside the set, or between a confirming or contradicting test?
That was sneaky! It took me a while to figure out that "The knights paid 4 coins each, or 12 coins and the bellroy kept two, so the inkeeper has 10 coins."
@@PhilippeCarphin You have no idea how many physicists get fooled as well by this kind of problem. Most of our scientific discoveries have errors in logic just like this. We do more trial and error discoveries than thought experiment discoveries. We humans have a nasty tendency of creating emotional opinions and pass them off as scientific fact.
A nice thought experiment. However you are simply double counting. From all perspectives there are only a total of 15 coins. There are no missing coins. The knights pay 12 coins total = 10 coins to the innkeeper + 2 coins as a S&H fee to the bellboy. Each knight pays 12/3 coins = 4 coins = 10/3 coins to the farmer + 2/3 coins to the bellboy You can't double count the coins the bellboy has in his possession. Please redo your set math or redraw your Venn Diagram. Even Karl Popper thinks this is bad Maths. Logical equivalence is not perspective, and does not facilitate double counting of finite objects.
The solution is P[All ravens are black/We have never seen a black raven]=P[We have never seen a black raven/All ravens are black]xP[All ravens are black]/P[We have never seen a black raven] :-)
counter examples can rule out things. But it is true we will never now anything to be true because axioms cannot be proven. We can only know things to be false.
@MetraMan09 Also, there are more non-black objects than ravens: even if there were non-black raven, then picking a non-black object is unlikely to be a raven. So it's really not a 50/50 probability! Basically, in the bayesian reasoning, looking for ravens and check their colors is “worth” more than looking for non-black objects and check whether they are ravens: you will change your assumptions more in the first case than the other. I think that this weakens the difference of approach between Popper and bayesianism 😊
Logical Equivalence: "Your beautiful face makes time stand still." = "Your face could stop a clock."* *Note: after the second statement, it is a good idea to run away.
Looking at the clock face looks as though it needs either: winding or a new battery, visit to the jeweller's for repair, or perhaps a new clock? Due to the fact the clock has stopped !
I'm not a scientist at all, but I what about this hypothesis. "All school buses in the United States are yellow." In my decades in the public school all school buses I observed were yellow. But, I certainly did not see all existing school buses. Howver, I might be able to indirectly observe all of them by contacting all manufacturers who produce them and asking if every bus they build is yellow. In the case of ravens, we can't track down every single existing raven, so we can't prove they are always black. It's just my uninformed opinion.
You are committing a fallacy of equivocation. Those two statements are not equivalent, unless the second statement is also a metaphor, which isn't problematic at all.
Nice video. More about the context: the relevance of a white shoe can’t be known as we have no idea of the number of non-raven things. So we can’t know what the sample significance is. So the shoe doesn’t add knowledge about ravens. Science is almost always about statistics.
This seems like the correct resolution to the "paradox". I think the confusion comes from the fact that, at the time, most scientists did not have a proper grounding in statistics.
If you could observe 100% of the set of all ravens, you could perfectly verify whether all of them are black. Likewise, if you could observe 100% of the set of all non-black things, you could also verify whether or not all ravens are black. Since the set of non-black things is staggeringly larger than the set of all ravens, it does support the theory, but at a massively reduced ratio. Also, so long as there is potentially one or more unobserved member of each set, you cannot say with certainty whether or not all ravens are black. This is a problem, as there really isn't a good way to tell if you've finished observing everything in one of the sets anyways.
This is close to how I think of it. I think in terms of 'information'. If we could observe 100% of all things, we would know with certainty if our hypothesis is correct. As we have not observed 100% of all things, every new observation, no matter how trivial, is increasing our knowledge and therefore has some influence on our confidence in every hypothesis. The real question I think is the value - observing the white shoe contributes so little to our confidence that we probably would agree it's not worth the effort, ie the informational value provided by the observation doesn't exceed the value we could get using our resources to make different observation. I see no paradox, the statements are perfectly valid, they just aren't very useful. Logic doesn't care about usefulness, but we do.
I was thinking the same thing. The number of non-black things even limited to just Earth may as well be infinite as far as our ability to observe and categorize them goes. Therefore any observation of one does support the idea that all Ravens are black, but only by an infinitely small amount. It's close enough to zero there is a perceived paradox but it does technically have an impact, just very small
To illustrate her final point: imagine you heard about a Blue Valley, where everything in the valley is blue. Would it make sense to go to that valley and see if you can find any ravens there? Why yes, it would.
The bias towards novelty and results that change the paradigm is exactly where the current publication crisis came from. If the only results that matter are ones that challenge current understanding, then there's a significant risk that nothing is ever tested more than once which completely misses the notion that not all experiments are done perfectly, and that published conclusions can be misguided or outright wrong. White shoes matter. Even if they only stand to confirm what "everyone knows", results that feel mundane reinforce that fact that a lot of science should be straightforward and unsurprising, because giving the impression that counterintuitive ideas are the norm is how you get flat earthers and electric universe types who fundamentally question the basis of most of modern science. While simple, basic chemistry experiments may not immediately lead to the discovery of a grand unifying theory of everything, consistent reproducibility is the bedrock foundation to the claim that the scientific method works. ETA: The scope of the observations is also relevant, however. It's all too easy to draw some pretty silly conclusions relying too heavily on logic, and not all that happens in the empirical world is "logical" as we understand it (see: quantum mechanics, human behavior, etc). Conclusions drawn from observations also need to be questioned in addition to the observations themselves, because again, the scientific method's most important result is reproducibility. Logic that goes beyond what is shown empirically is a whole separate issue, and moves away from empiricism and into belief (which is not a bad thing; at the end of the day, we're all simply choosing to believe our senses are valid, and I've yet to see anyone prove that to be the case absolutely).
I agree most with the first explanation. The subset of all things that are not ravens is practically infinite, so any supporting observation of a specific subset of that subset has a negligible impact on the hypothesis. While the two statements are the same from a logical standpoint, they are not the same from a logistical standpoint.
A white shoe is an example of a 'trivial support'. It does not invalidate the 'all ravens are black' theory. It is rather like the trivial solution to an equation that is a true solution but isn't useful. I think the thought here is that the white shoe is a paradox because it isn't useful, which is incorrect. If y=A*sin(kx) is a sine wave of frequency of 2*pi*k, then y=0 fits the definition of a sine wave of any frequency, or rather, A=0. Do you say that y=0 is not a sine wave because it is flat, or that it is a sine wave of zero amplitude? Y=0 fits the definition of a sine wave but it isn't very useful. I think the dilemma here is that we aren't stating the full definition because it seems trivial. What if I redefined the definition as 'all ravens are black AND all non-black items are non-ravens'. Now the shoe fits!
However, (A implies B) if and only if (not B implies not A). Saying that all ravens are black is exactly the same as saying that all non black things are not ravens. So yes, seeing a white shoe supports the hypothesis. The question becomes: by how much? In measure theory, we can see how a measure on the set of all things that exist can be used to determine that, in fact, albeit one single white shoe has probably measure zero or close to zero, the integral over the whole set of non-black things yields the same result as the measure over the set of ravens. This means, observing all non-black things would indeed be enough to confirm the hypothesis, even if the single element we observe yields zero (an infinitesimally small) support to it. A sine wave of null amplitude is a null measure element in the set of all sine waves. It's the same idea.
@@hydraslair4723 what you said makes no sense and is not relevent. Bijections weren't implied here and you can't integrate over a set. It has nothing to do with what I said. It looks like you threw together a bunch of math terms to look like you know what you are talking about.
@@mikechilders you can't integrate over a set? Are you sure you know what you're talking about? You know that when you evaluate a definite integral, you do that over a set, right? The set might be an interval of real numbers, in which case you get the ordinary integration of real functions, while the notion of measure generalises this to arbitrary sets. I suggest you check out some measure theory. Dismissing my claims because you don't understand them is not the way to go. It is also a powerful basis for statistics and probability, something you might be interested in. "No bijections were implied here". If you assume that not(not(A)) = A, this is all you need to know to derive that (A implies B) is the same as (not B implies not A). I'm sure there are more ways to derive it, out there, without assuming that, but I can't think of any at the moment.
@@hydraslair4723 I'm not going to entertain your delusions. You can't integrate over a set of black ravens and white shoes. And that has nothing to do with my comment anyway so I'm ignoring you from now on. You don't have a firm grasp on reality and are too socially inept to have a conversation.
@@mikechilders Hey fella! Learn how to engage intelligently on a public forum or you will be justifiably and roundly mocked for your own social ineptitude. You just demonstrated that your assertion applies to you and not Hydra's Lair: Your first reply to him was agressive, slightly insulting and purely deterministic -- "you're wrong" in 3 different regards without explaining why. He calmly (almost politely) pointed out your misunderstanding of the maths theory he was citing and explained (supported) his use of it in his original statement. You came back to again say simply that he is wrong with no support or explanation of your assertion but this time more clearly insultingly so, thereby demonstrating your own lack of ability in argumentation, discourse and scientific comprehension and analysis, and therefore not only your own lack of social ability (meaning that we can't have a useful conversation with you) but also your own lack of understanding of the subject on which you try to converse (maths, or perhaps logic, or both) Go read some basic philosophy (logic in particular) then join a local debating group to learn how to argue and make social intercourse. Then we might determine if you know enough about maths to debate you or rather educate you.
I think the problem here is that we don't actually fully, completely agree with the beginning statement, which is "Observations of A with property B, support the hypothesis that all A are B". I think this should be restricted when the number of elements of A is finite. Thus, for the case of ravens, since we BELIEVE they are finite, we find it intuitive that Observation of raven with property black, supports the hypothesis that all ravens are black. If we look at the second case, I don't think many of us agree that Observations of non-black things being non raven, supports the hypothesis that all non-black things are ravens, since non-black things are infinite, or so we BELIEVE. Some may argue that in actual science, we actually use the first one, not with my restriction. Although you are absolutely correct since scientific induction is used, I believe that we use it because we believe in the uniformity of laws and matter. For example, when Newton did his gravitational laws, we found that all nearby galaxies follow the same thing; thus we believed in Newtonian gravitational laws that it works in all the universe, even the non-observable universe. Thus, someone will say that science used the first statement, Observations of A with property B, support the hypothesis that all A are B. I would argue the only reason we did that is the we believe that matter should all work in the same way and the only reason we extrapolated that law to the non-observable universe is because of our belief, other than that we don't have any good reasons to believe that Newtonian gravity works. To also add to it, when we make a discovery in the human body, or see how the embryo grows; we don't look at all mothers wombs to check if all humans are like that; we believe all humans are the same 😂😂. BTW, believing that all matter works in the same way isn't insane; I am just stating that we have to recognize that we BELIEVE IT. Some of the ideas was inspiration from the comment of Mark Peterson.
I remember being told once that in some formal logical systems, the absence of a property is not itself considered a property. Apparently, this solves a lot of paradoxes, which is why it's used some of the time. It's a useful path out of a few things. It even appeals a bit to intuition - at least, it does to me. :)
I don't know if this is what Carl Hempel believed, but this is my theory. Observing a white shoe does support the hypothesis that all ravens are black, but only to an extremely minute degree. Think about it: if you want to prove the hypothesis that all ravens are black, you basically have two approaches. One, you can observe every raven in the universe, and if all of them are black, you have succeeded. Two, you can observe every non-black thing in the universe, and if none of them are ravens, then you have also succeeded. In practice, of course, we will never be able to observe every raven or every non-black thing, and will never be able to firmly prove the black raven hypothesis. But there are far, far, far more non-black things in the universe than there are ravens. This means that observations of black ravens will probably be at least dozens of orders of magnitude more effective in suggesting that all ravens are black than observing a non-black thing that is not a raven. So, we can't really do a lot of indoor ornithology, since we would literally need to observe at least trillions of distinct things in order to obtain the same level of evidence as observing one raven. Of course, this is assuming that you're just picking non-black objects at random and observing their color. Context does matter, and specifically seeking out a white shoe or other non-raven object does nothing to support your hypothesis. On the other hand, we can narrow and refine our search significantly if we only observe in contexts where we would expect ravens to be found. For example, maybe we only look at things that are around the size of a raven, or maybe we only look at things near the surface of the earth. Maybe we only look outside, since ravens are much more likely to be outside. Still, supporting the black raven hypothesis with this approach will be many orders of magnitude more difficult than just looking for ravens.
Popper’s method was the method I’ve been taught through college. You never seek to confirm, you seek to refute either the hypothesis or the null hypothesis.
Surely the paradox only occurs because of the "potentially incorrect" statement that "all ravens are black". It should be "MOST ravens are black" or "VIRTUALLY ALL ravens are black" or even "every KNOWN raven is black". As we have never observed the whole set or ravens to be able to confirm the original statement then allowing for some uncertainty would seem to be the way to go. I am no philosopher but my gut tells me there will always be some sets for which one can make statements that are as certain as the original raven statement. However most sets are probably not so clear cut and from that we end up with a potential Raven Paradox. My thinking here has been influenced by the subtle change in my perspective on many things since I stumbled across Bayesian Models and Bayesian Statistics and how what feels intuitively right is not always so. "It ain't what you don't know that gets you into trouble but what you know "for sure" that just ain't so". As a former systems analyst by trade it never ceased to amaze me how often we make statements like "all ravens are black" when in reality there is often a " ... except when ..." clause to the statement. On a gross, day to day basis this may not be an issue if we do not allow for the possible exceptions. If only one in one million ravens are not black, then many observers will never see a non-black raven. But it would not make the statement "all ravens are black" true. Love the channel.
There is also a definition problem. What is a raven in the first place? What set of properties define a raven? Can we accept a raven that has 4 legs... or that would be a different animal? Classification is a hard subject.
A statistician would call the statement "all ravens are black" the null hypothesis, and then perform tests to determine whether or not to reject the null hypothesis. At the end the confidence in the decision to reject the null hypothesis or not would be computed. This is functionally the same as saying all ravens are most likely black, or something like that, but I think it's a much cleaner and easier way of phrasing it
There's a logical trick to ensure that your statement is correct: all TRUE ravens are black. What, you've got a white raven? Well, it's not a TRUE raven.
I believe it does. A white shoe definitely implies that A. It is a white object. B. It is not a raven. Which does support our "All ravens are black" statement. However, the support given by it is essentialy infinitesimal so practically useless. Thus, if we look at the support of evidence as a quantitative quantity, instead of qualitative quantity Even if it supports "All ravens are blue" or red or something hypothesis, it doesn't matter. However, if we observe say, a dark raven then its support for our hypothesis is magnitudes larger than that of observing a white shoe. So, our scientific method stays safe.
This is wrong. There is no paradox here: The statement "Observations of white shoe with property not ravens" is CONSISTENT with the hypothesis. It does not SUPPORT the hypothesis. For something to support the hypothesis, it must have weight, something of substance to support it. As such the statement is only consistent with the hypothesis but offers nothing else to the evidence to back up the hypothesis. So: Observations of white shoe with property not ravens support the hypothesis that ravens are black. Isn't true. Think about it: It does NOT support the hypothesis. It is only consistent with the hypothesis. Logic isn't binary. Just because it doesn't refute it doesn't mean that it supports it. It can also be consistent with it without supporting it. Observations of white shoe with property not ravens is consistent with the hypothesis that ravens are black. Observations of ravens with property black supports the hypothesis that ravens are black. This is correct.
Except that a statement logically implies and is implied by its contrapositive-e.g. "if it is raining, then I have my umbrella" logically implies "If I do not have my umbrella, then it is not raining." So "If an object is a raven, then it is black" logically implies and is implied by "If an object is non-black, then it is non-raven." So anything that *supports* the claim "If an object is non-black, then it is non-raven" supports the claim "If an object is a raven, then it is black" (which is equivalent to "all ravens are black"). But, if "Observation of white shoe with property not ravens support the hypothesis is consistent with the hypothesis that ravens are black" (ie does not support it) but "observation of ravens with property black supports the hypothesis that ravens are black," then the observation of a statement does not support its contrapositive, but the observation of a statement supports itself. So under your system, contrapositives (which *must* follow from one another) aren't equivalent, which would be absurd.
I think part of the problem is that there is no separation of equivalent and inverse here. "I hope you enjoy your day" is the same as "I wish that this day gives you joy." But the inverse is " I hope that any moment you do not enjoy is outside of today. " The whole cafe at noon example was just rephrasing the same thing, but the raven statements were the inverse of each other.
Logic is binary. Observation is not. Why does white shoe not support the hypothesis, and a black raven does? Both are consistent. How much "support" do you need to call the hypothesis 100% true?
Pure logic IS binary. And there is no such thing as evidence. You either have proof or you don't. The problem with this whole thing is that science does not use pure logic, it's intherently probabilistic. In pure logic though, if you were able to find every object that wasn't black and none were Ravens, that would be just as good a proof as finding every Raven and finding that none of them are black. In practice both finding every non-black object and every Raven are impossible though, so it's just not a question you can answer.
I think the paradox arises from the first sentence. "Observing black Ravens supports the hypothesis that all Ravens are black" this isn't really true if you think about it, or it's at least an over simplification. Let's change the example. Observing white towels supports the hypothesis that all towels are white. Well, you can observe white towels all your life but of course that doesn't mean non-white towels don't exist. So saying "observing black ravens supports the hypothesis that all Ravens are black" is just as wrong as saying "observing white shoes supports the hypothesis that all ravens are black". I think my explanation is somewhat similar to the second one in this video.
observing white towels does prove that towels are white, and the more you observe, the more likely it is. Just because you can never reach 100% doesn't mean that each white towel proves it in a small way.
Carl Hempel is absolutely right. The observation of a white shoe not being a raven does support the theory that all ravens are black. Even if by an infinitesimal amount. The argument regarding a couch sitting ornithologist isn't sound, even if it is reasonable. Machine learning works much the same way in this regard. Trillions of negative results can add up to meaningful data.
I think the reason this is a paradox is because the premise sounds well formulated, but isn't. Finding a black raven doesn't support the hypothesis that all ravens are black because the position isn't about any individual black raven. It's about all ravens, including hypothetical non-black ravens. "All" is a qualifier that modifies the subject. The white shoe doesn't support its hypothesis for the same reason. The confusion I think is because we see it more clearly when it's a white shoe and not a raven. The white shoe on its own tells us nothing, but all non-black things, which a white shoe is a part of, can disprove the hypothesis because at least a single non black raven must be included in this group for it to be false. Basically the only discrete constituents of the subject of "all ravens" or "all non-black things" that matter are ravens that disprove the rule . Any other individual member, even if it is a raven, doesn't really matter.
First logic statement is exclusive to ravens. Equivalent logical statement is inclusive of all observable objects. So they are not equally useful hypotheses.... Then Comes the fallout.
I was thinking something similar. The observations are only of the population you are sampling from and don’t necessarily extend outside of it. If I wanted to study if there were any wild elephants it would be dumb to only look in Canada and Antarctica since my sample would never be a “fair” representation of all elephants. When you are looking for a non-black raven the abundance of non-black objects means you need a bigger sample size for the same level of confidence. You would also have to make sure that you could observe non-black ravens which means you can’t just look at the items in your house if you know you don’t have any birds.
I think the answer to this question depends on whether you assume the set of all things to be finite or infinite. If you assume it to be finite, then obersving non-block ravens does in fact support you theory of all ravens being black since this means that there are less ravens that could be black (As long as you know at least A raven that is black and haven't observed any ravens that arent). Theoretically you could therefore confirm you threory by obersving everything that is not a raven until all that is left are ravens which you know to be black. If you assume the set of all things to be infinite then obersving a non-raven would NOT confirm your theory, but neither would oberving black ravens. Since even if you find one more black raven, there are still infinetly more ravens that could be non-black. I mean, there are many mathematical concepts where we have not found a proof for them being right, but we have tried a lot of numbers for which we know it is right. Yet we can't really say that this confirms the theory since there is still an inifite ammount of numbers for which the rule could be wrong. If you assume your set in question to be inifinte just finding examples of your theory being right does not confirm it in general I would say. Not that what consitiutes a "Thing" or "All" in that context does not really matter and can be defined on a case by case manner. For example, you might say that all ravens are black in the context of earth, and that as a "thing" you mean animals. So by "Set of all things" I dont mean it in the sense of just all of the universe, rather those are things that depend on the context of your theory and is meant in a more abstract way.
I only just found your channel. Thank you for your insight, your descriptiveness, your delivery that made me smile, and your ability to not talk down to someone while explaining difficult topics. You earned my subscription today :)
Agent Stache Also here's one way both a raven and writing desk are alike I found a few years ago: both the English word raven and the first English word of the two English words writing desk, start with the r sound. They do not start with the same letter, but they start with the same sound.
The problem is that you intuitively think of all non-black things as an infinitely large group. If you consider the groups as represented at 3:45 to be finite, it should make perfect sense that a non-black object decreases the chance of finding a non-black raven, because there is one less object that could be a non-black raven.
I think the main problem is that observing a white shoe doesn't "support" the notion that all ravens are black, it merely fails to contradict it. As you mention in the video, it also fails to contradict the notion that all ravens are blue, purple, or green with pink polka dots (OK, maybe you didn't actually mention *all* of those ;-) so can it truly be said to "support" all of those notions simultaneously? The appropriate opposite of "all ravens are black" is not "everything which is not black is not a raven", it's "no raven exists which is not black", which restricts your scope of examination and experiment to "the set of all ravens" which is the correct scientific approach.
I disagree. Imagine you were presented with all non-black objects in the Universe and none of them were a raven. You could then say with confidence that all ravens are black.
@@mina86 but that's not what's happening here. You're being presented with *one* non-black object, not all of them. Just seeing one does nothing to support the notion: how confident would you be that you had found *all* non-black objects? Just one missing non-black object would destroy your proof. Also, simply finding all the non-black objects does nothing to confirm the existence of ravens in the first place…
@@PhilBoswell I Agree, but with every non-black object that you see, you become more and more confident about the given hypothesis. Also, finding all the non-black objects(and finding out none of them are ravens) may not confirm the existence of ravens, but the observation is still logically equivalent to your hypothesis.
@@PhilBoswell, you're also not presented with all ravens when you test the hypothesis by observing all ravens. That's why observing a black raven *supports* the hypothesis (but does not prove it). So does observing a white shoe except in this case increase in confidence is minuscule in comparison. Finally, if there are no ravens, hypothesis that all ravens are black is trivially true.
What about things like Constructive Logic, where the statements "All ravens aren't NOT black" and "All ravens are black" cannot be equated, thus removing the paradox altogether (since the observation of a white shoe only supports the former statement)? I feel like this best suits the desires of both those hoping for falsifiability AND the ability to support a statement in the positive. Additionally, a lot of logicians, mathematicians, and computer scientists have already been moving in this direction, so the groundwork for using Constructive reasoning in practice is already there.
There appears to be no paradox here to me: you can indeed state that any observation of a non-black thing that is not a raven is I tiny little bit of evidence towards a hypothesis that all items non-black are not ravens. The hidden ‘mistake’ in thinking is that people apparently falsely assume all pieces count the same, but they do not. Restating “all ravens are black “ to “all non-black things are not ravens” vastly increases the amount of things that fall into your category of investigation - so every bit of evidence is proportionately less significant in proving your hypothesis. Stating your hypothesis as “all ravens are black” is just way more efficient. The bigger actual flaw in logical empiricism is that pointed out by Karl Popper: you can never claim to have observed _all_ ravens in the world, let alone the universe, much less all times past, present and future. Therefore, a categorical statement such as “all ravens are black” can never be truly verified. It can only ever be falsified. If I remember correctly, Popper, in The Logic of Scientific Discovery, not only states that categorical propositions (or hypotheses) should be formulated as a falsifiable statements, but also states they should be formulated in a way to make falsification as ‘easy’ or efficient as possible [edit: just continued watching and I see response 1 says the same. The only thing to add (as I did above) is that it makes sense to formulate your hypothesis in the most efficient way: that avoids many wasted hours spent on ornithology in your living room. Also, the fact that something goes against our instincts is _in_ _no_ _way_ an argument against it. Any scientist should know this]
Claiming what future technologies can and can't do does not refute anything. Saying we currently can't know all ravens black may be accurate, but making bold assumptions about an unknown future does not add anything valid to the argument and definitely does not show a flaw.
My conclusion: Vengeance and Deduction are two dishes that are best served cold. Deduction is always hindered by the fact that all premises have to totally, absolutely, unequivocally true to have real confidence in the conclusion. The instant when you introduce even a chance that the premises are not true (like here, when you introduce the concept of hypothesis) then you introduce a chance that the conclusions are false, and it might be anywhere from an almost academic concern to a total disaster. In a more practical example, if you ask a million people if they will vote for candidate A, out of a universe of 1.1 million voters, and you get a 60% of "yes" answers, you then bet your house on the result that candidate A will be elected, but there is a big chance that 300000 voters who answered "yes" don't bother to actually go to the booth and vote, and you lose your house. When you deduct from less than certain premises (like "60% of the voters will vote for A") your conclusions might be wildly inconclusive.
I don't think there is any paradox at all. The problem is that the logic doesn't take into account how much a discovery supports the hypothesis. Finding a white shoe does actually improve the probability that all ravens are black. However, there are so many "non-black" things, that the change in probability is practically useless. That's where the perceived paradox comes from. If we could observe all "non-black" things we could absolutely determine if ravens are all black, but that would require infinitely more observations than if we simply observed all ravens.
I was thinking the same thing. The number of non-black things even limited to just Earth may as well be infinite as far as our ability to observe and categorize them goes. Therefore any observation of one does support the idea that all Ravens are black, but only by an infinitely small amount. It's close enough to zero there is a perceived paradox but it does technically have an impact, just very small
Great video! We run into this problem a lot in Psychology actually, believe it or not. Psychology is something that is very difficult to quantify, so psychologists spend lot of time and effort doing correlational study after correlational study trying to induce what cause and effect relationships might exist between complex emotional states. In many cases we cannot confirm a hypothesis, but can confirm that other disconfirming hypotheses are not true. Does this confirm the other hypothesis? That is why I always liked Popper and his approach, it makes the most sense and allows us to do away with the endless correlational studies and useless data points. That said however I always liked Feyerebend and agree whole heartedly that science doesn't necessarily have to be done a certain way, if that were the case we would be artificially limiting the skills and talents that the human mind offers to the pursuit of scientific endeavors.
The observation of a white shoe adds to your knowledge of the set of ALL non-black objects. Taken to the extreme if we were to observe the full set of ALL non-white objects we would, on seeing no ravens in that set, correctly conclude that all ravens (if such a thing existed) would have to be black. Thus observing any one non-black object provides evidence that all ravens are black, but it is diluted by the quantity of all non-black objects. I think this falls more in line with the first response to the paradox.
I think this ties closely into Platos alagory of the cave. If all you've ever seen where black shadows on a white wall, you would think everything that moves is black (including "ravens" which would ofcourse only be their shadows). In this case, seeing a white shoe would definitely give you a lot of information about ravens, as it opens up the possibility for black to be used as a distinguishing label for moveable objects in the first place.
I feel like explanation #1 makes the most sense. Observing a white shoe does add to the certainty that all ravens are black, just by a very, very, very small amount and that is where language gets confusing.
I've heard this before and I really don't know why it's a puzzle,,, what about a black shoe,, its black, but it's not a raven, this refutes all non black things are not ravens, because 'all non black things are not ravens' would be the same as saying all non-non black things ARE ravens, in turn, it's saying all black things are ravens,,, and we know that isn't true,,, because my shoes are black,,, so the conclusion is,, people were just idiots spouting crap back then
White shoe Black raven. Jade wears a black t-shirt with a strange “spaghetti bird” (mainly black) And when she wears white.. I heard bird noises in the back! Also “an hypothesis is never wrong until it is” (a tl;dr version of Popper). So a white shoe kinda solidifies the hypothesis. Looking at the ceiling solidifies the hypothesis. Oh God the quarantine it’s just a big experiment!
A: If it's a raven, it's black B: If it's not black, not a raven Every observation of A or B support A or B BUT because there are hella lot of not black things than there are ravens, any support to B you may wish to translate as support to A decreases by that much. Also, to absolutely establish A by A you need to find all ravens, but to do it by B? you need to find ALL non black stuff which SEEMS a lot harder. Both of these things decieve your brain into thinking there's no way a white shoe could prove all ravens are black!! So in conclusion I'm going with the first guy I guess 😅 lol
@@gonzalolarghero5594 No, just gathering all nonwhite things won't be enough, you'll also have to prove that what you have is indeed 'all' nonwhite things
@@mbrusyda9437 I'm not saying we're actually gonna do it lol I'm just saying one task seems harder than another. (and if you gather all non white things that means you've already proved that you gathered all otherwise you won't be able to say you gathered all)
@@aryajpegasus that's my problem with that interpretation, is it ever possible to prove that you have checked all of A? If it's not then whatever implications of it is irrelevant and you're defaulting to the third interpretation
"All ravens are black" is just a stand in for "all A's are B's". It doesn't really matter whether it's true or not for the example to work since we're trying to falsify it anyway
@@SteveGouldinSpain I used to observe an albino blackbird on my way to school. From simple genetics I worked out when I should start seeing albino descendants, excitedly telling the biology teachers, who sadly informed me that most albinos don't find mates and rarely have any descendants. I never saw any more white blackbirds in the next 40 years of looking ;-(
@@SteveGouldinSpain And albino clergy ( who don't get to mate by choice ). Maybe my teachers were wrong and albinism is about to sweep the planet. You have just made me recall seeing an albino African, as I walked through the Rubaga section of Kampala ( in 1970). Just about the most sad sight of my life ( perhaps showing how lucky I have been.)
@@japeking1 yes I understand Albino Africans are much sought after by Witch Doctors for bush medecine - they just hack off an arm or a leg as takes their fancy. It's a bit like having a rabbits foot for good luck, though equally as bad luck for the albino as for the rabbit.
I think the most useful answer is Carl Hempel's; the white shoe does support the black raven hypothesis but to a miniscule degree, to the point that it is no longer intuitive. By observing many, many, many objects (not just ravens and shoes) we have built up a system that we can use to classify some objects and hypothesise that all ravens are black, or all shoes are solid. Every time we observe any object, it either reaffirms our classification system or undermines it to some degree. We believe that things have colour because of the properties of those things that affect the reflection of photons, and everything we see that has the colour we expect based on its properties, affirms the entire system in a tiny way. Every time I see a white shoe I know that my eyes are operating and photons are still being reflected by things, which shores up my confidence that I can observe the colour of ravens. If we were shown an object that undermined one aspect of the system, it would to a lesser extent cause us to lose faith in the rest of the system too. The extent to which that confidence is lost in other parts of the system depends on how closely they're related to the part that's been undermined. If I saw a red raven, then my faith in my understanding of raven DNA should probably be questioned, but it's unlikely that it will cause me to wonder whether I can make a shoe out of hydrogen. Conversely (see what I did there?) before the Higgs boson was found there were physicists saying that if the LHC didn't find it, we should throw out the Standard Model entirely and come up with something new.
So a hypothesis was given of the form "all elements of set M have property p". And the idea was then to check the hypothesis empirically by drawing a random sample out of M and check for p. Then two logically equivalent formulations of the same hypothesis (but with different M and p) were given, along with two real world examples of "drawing a sample". In one case, it was very intuitive that this added support for the hypothesis, in the other case it was highly unintuitive -> Paradox. I think the answer to the paradox depends on how the white shoe example was given: If you looked at a shop window and saw a white shoe, then thats not a random sample out of M (there are never ravens behind shop windows). If you looked at a truely random non-black thing, then this would increase the likelihood of the hypothesis, but only by a very tiny amount (because the set of non-black things is much larger then the set of ravens).
OMG I love this channel. The narrative is so well constructed that every time I think if a response or question it is addressed in the very next phrase.
Second explanation is correct. Science is ONLY falsifying hypotheses, usually mutually exclusive, collectively exhaustive hypotheses with hypotheses that we're actually interested in. To scientific method the "all ravens are black" hypothesis, we have to FALSIFY the alternative: that some ravens aren't black. Since we can't falsify that theory, "all ravens are black" isn't a scientifically known hypothesis. It's purely conjecture.
I think my feelings are that logically equivalent statements don’t address relevance. Non-black non-ravens is just too broad a category to give meaningful statements. But I also feel like my decision is purely practical; I’m not sure how I’d address the abstract/philosophical question. Truth may be objective, but the pursuit of it is human, so I think it’s difficult to define exactly the line of “relevance”. That said, I also believe a falsification is much more valuable than a support/confirmation. Falsification is the only way to be sure. But being sure isn’t the most important thing, either. In any case, this has got me thinking. Keep up the excellent work!
@@gmcgarveyut To *prove* that statement you would need to look at every coloured object in the universe and check none of them were ravens. But even a single observation of a white shoe still *supports* the hypothesis, just not very much because it is just one of trillions of non-black objects.
@@gmcgarveyut Fine then. If one white shoe "isn't significant enough" to count as support, what about the observation of a million white shoes? Why should observing a million white shoes tell me anything about ravens? The paradox doesn't go away. No matter how small the evidence contributed by a single observation is, as long as it's non-zero I can make it "significant" by making enough observations.
The error is in 4:49. If you replace "non-black things" with a white shoe, you have to do this in both instances of A. So the second part of the sentence is it supports the hypothesis that all white shoes are not ravens, which is correct. (Unless I'm mistaken about ravens.)
It does, in a miniscule way, but I'm not really seeing how it could be instructive and/or useful. For example - All protons have a positive charge. My flashlight contains batteries. Both statements are true but how does one, in any meaningful or useful way, support or detract from the other? At any rate, I enjoy your videos. Thanks!
Agreed, that was my first thought as well. And even then a raven still isn't black! We just perceive them as such since color/light absorption and reflection is also a thing... it would be like saying leaves are green, we perceive them as such because they reflect green light better than any wavelength
For the sake of this thought experiment I assume first that you cannot just look it up, then get a decent sample size, preferably from multiple different regions of the planet. Then hopefully find a non-black raven. In the case on non-black things and looking for a raven among them, it would take an even LARGER sample size(at least a trillion times more) because there are more non-black things than ravens. In short, while both data-points would be evidence, ravens are just better evidence.
@@cazhalsey8877 that's what we mean when we say something has a color. But you are right in pointing it out anyway, as people tend to forget that, so the occasional reminder is helpful. :)
I swear I remember feeling like the claim (that a white shoe is evidence that all ravens are black) did NOT make sense a few months ago, I'm not sure what changed, but I think this make sense now, here're my thoughts If I observe a not-black not-raven, such as a white shoe, yes that's evidence that all ravens are black. But how? Let's assume we live in a world where almost all ravens are black. If I randomly select things from the set of all ravens, I'm unlikely to find anything that's not black. Hypothesis confirmed, right? Let's say that almost all not-black things are also ravens. Therefore, the way to disprove the hypothesis is easy: randomly select something from the set of all not-black things. It's likely a raven, so hypothesis disproven in few tries, even though almost all ravens are black. This is why good science doesn't JUST consider things that "prove" a hypothesis, nor JUST things that falsify a hypothesis, you actually need to use both data sets. In the case that all ravens are black, limiting yourself only to the set of all not-black things can just as well "prove" that all ravens are blue or green or any color. In this case, you must consider data from the set of all ravens, not just the set of all not-black things. In the case that most ravens are black, and most not-black things are ravens, limiting yourself only to the set of ravens can "prove" that all ravens are black, when they aren't. I think the trick here might be selection bias, and why this clashes with our intuition of how the real world works. How exactly DO you select from the set of all ravens, or the set of all not-black things, in the REAL world? By first, constructing them from the set of things near you, i.e. looking around! If it were true that most ravens are black, and most not-black things are ravens, surely we would've seen some not-black ravens by now, given the extreme number of not-black things we see every day. Therefore we must live in a world where: 1) All (or most) ravens are black 2) zero (or few) not-black things are ravens Observing ravens, AND observing not-black things, helps support this claim. Failing to observe not-black things leaves open the possibility that most not-black things are ravens (Ex. if most ravens are black, and most not-black things are also ravens, then saying all ravens are black by only observing ravens) failing to observe ravens leaves open the possibility most or all ravens are black (Ex. if all ravens are black, like when Nelson Goodman "proved" that all ravens are blue by only observing not-black things, which are never ravens in this case. It might've been true, but only if by coincidence alone that all ravens were blue, instead of black) Now if you'll excuse me, I'm gonna go lie down while I untie the knot that my brain has become.
My view is this. The set of ravens is a finite set. The set of non-black objects is an infinite set. So the two sets cannot be regarded as equivalent. Therefore, the observation of a white shoe cannot be regarded as supporting the hypothesis that all ravens are black.
A white shoe *does indeed support* the hypothesis, even though by an amount so miniscule, it doesn't really matter. why? In order to conclude that the hypothesis is 100% correct, we'd have to look at all "things" (∀x ...). If we had looked at all of them and saw that none where non-black ravens, we would have verified our hypothesis. Looking at anything (including a shoe) brings us closer to that goal. The problem is, that one shoe is a pretty small fraction of all atoms we'd have to look at, so it doesn't help by a whole lot really..
My thoughts exactly, and I couldn't disagree with Hempel's interpretation (indeed, I don't think this is a paradox at all). What you really want is a more specific hypothesis, such as "among birds in a particular geographic region, all ravens are black". This leads to a more focused observation strategy, and you stand a better chance (ha) of getting statistically useful results.
No it does not. If I was locked in a black box and thrown in a black hole with some Legos. I could build new non-black things and slowly "prove" that "All Ravens are black" without access to the world
@@georgplaz True but this wasn't matter this was "non-black things" and a lego car is a different thing compared to a lego house even though there are made of the same pieces
My answer will be, no, instead no observation can never conclude anything because no observation is done on the fullest of any context, further it just tells us about the whether probability of occuring of an event is low or high that's all, and this statement also makes sense when you observe the events in Quantum level of reality and that's why Heisenberg uncertainty creeps in, it's kind of scary but the reality somehow keeps itself non-predictable at the most fundamental level. Very interesting video by the way, it's been an intellectual pleasure, and please tell your views too, what you think about it.Thank you..👍👍😊😊
A similar scientific hiccup I remember being mentioned by Martin Gardner: Imagine the hypothesis "All men are shorter than twelve feet tall". Every piece of data collected supports the hypothesis. Then we discover a man eleven-and-a-half feet tall. That does support the hypothesis but at the same time makes it a bit less certain.
Oh and we used to call niggers the blue people too. Black is after all a property of hair and garments, dark or green was properties of the sea, white was a property of clouds and snow, while pale was a property of bones and sick people. I mean if you showed someone a chart of the Norse colors, no one would truly understand them. Specially the several kinds of pale..
@@livedandletdie what I dont understand is all these American nazis playing wannabe viking in prison. More than half of you aren't even Scandanavian. Would rather listen to lame skinhead thrash instead of legit metal. And they follow a man who killed himself instead of facing his enemies in combat. I assume you do too by the language. That's why you will never know what it means to be one of us, just stop trying. People like you give SJWs shit to talk about. You're such a rough edged "viking" here on youtube..LOL Now what you said about colors was a fine addition to the conversation, but why bring N bombs into it unless you're some fake nazi who thinks hes a viking?
An object being not black should not increase your confidence that all ravens are black, because the second hypothesis is unfalsifiable, due to the fact that the group of all non-black things is unobservable, while the group of all ravens is. In fact it should, if anything, decrease your confidence because it means that non-black objects exist, therefore increasing the probability that there is a non-black raven. And the more non-black colours that exist, the lower your confidence should be, if you're going that route.
Such a great video! Such a clear explanation, I loved it. Please do a followup with the Bayesian method. I hope you keep making lots of great videos in the future, lots of success!
Given the shoes that these illustrated ravens are fabulous, and all these illustrated are black, then all black illustrated ravens are fabulous (If A -> C. If A -> B. Therefore B -> C) Wait, that's not logically sound. Does that make me a bird brain?
But this isn’t really how we classify things. In science we do the observation first and then define the terms based on what is observed. Ravens are defined by many features, and we name that group because of the traits. Defining something before we observe it is more of an artistic practice than a scientific one.
@@longlostwraith5106 If A is "All ravens are black" and C is "All non-black things are not ravens" they are equivalent. Observing non-black things and observing ravens are both attempts to _disprove_ the hypothesis by finding a non-black bird among the ravens or by finding a raven among the non-black objects. The failure to find a raven among "non-black objects" gives a tiny statistical bump to the probability that no non-black ravens exist. It'll be a much smaller bump that observing a black raven gives, simply because the number of non-black objects is immense compared with the number if ravens: It includes each individual object in the universe that is big enough to reflect light with a color: each grain of (non-black) sand, for example. The problem with observing non-black objects to disprove whether all ravens are black is that it's significantly less efficient than observing the ravens directly, and that is what our intuition captures.
I would say that propositional logic is just a tool that chacks, let's say, "the road of an argument" and tells you if it's broken at some point. But it does not show you other "roads" or arguments that merge into the same main road. So, to make it clear, the point were the argument fails is when you invert your argument with negation, and then your isolated again with another negation, because it is not isolated anymore. I'll explain myself: when you say "all ravens are black", you're saying just that, it's isolated. But if you say "all non-black are non-ravens" you're including a lot more arguments like "all ravens are blue", "all ravens are green", or even "all ravens are dead" that could follow the same logic. So, when you turn the sentence back and say "observations of non-black being non-raven supports that ravens are black", would be true, but not more true than "supports that ravens are blue" or "dead". And then, you isolated this argument and determine the color of the raven with it, when actually, this argument supports all colors for ravens equally. Idk if I'm explaining myself 😅, I would be happy to answer any question o read reputations
There is no paradox. I'm pretty sure I'm not an idiot (but I could be wrong) and there is nothing contradictory about the two statements. I suspect this video was written by a freshman college student who got a B- in a logic class last semester.
that was interesting... but technically... wouldn't having bigger data set always help? some data might be irrelevant to the thing you're trying to (dis)prove ... but it still should be better to have it ... (if you ignore the problem with having to sort out what is relevant and what is not)
I agree, especially if one of the parameters for finding ravens would include; "Large Black Bird". Albino ravens would be overlooked unless you were to use parameters that did not include a color in the description. Everyone knows what a raven is until they see one, maybe it's a crow.
I do not think that more data on shoe color would increase confidence, because there's no place on the data sheet for "shoe color." . In other words, logic and science are different, in part because science is a process, not a static set of conditions and axioms. .
The observation of a white shoe neither supports nor refutes the hypothesis simply because a shoe is not a raven, and is thus not relevant to the claim. If it were to be seen as supporting evidence, this view would be a circular argument. Imagine that we have only ever seen a single raven and this raven's color was black. If one develops the "all ravens are black" hypothesis, and then observes a purple flower, if he concludes that the flower supports his viewpoint, he is confirming his suspicions by reference to his suspicions. It's the "This book is accurate because the book says that it is accurate" approach. So, one cannot use non-ravens as evidence of the claim. Thus, the only supporting evidence which can exist is another black raven.
The general public don't discern the nuances of hypothesis, theory and axiom. The example here is equivalent to the "All swans are white" fallacy, because there are black swans.
"All swans are black" is logically correct (because the proposition doesn't contradict itself), but empirically incorrect (there are indeed black swans).
@@CocTheElf That is correct with a large enough sample size... Or more accurately with the proper samples. A scientist could study ravens for his/her entire life and only find black ravens to study, thus concluding that all ravens are black. He/she might even turn this conclusion into a doctrine and use it to bad mouth the people who believe they've seen white ravens, citing that "there isn't any scientific evidence supporting the existence of white ravens) simply because the scientist is ignorant of their existence. There are examples of white ravens but they are exceptionally rare. And so the Raven Paradox is a perfect example of how the Black Swan fallacy can/has corrupted the scientific method. "...one of just four albino ravens in the entire world." www.audubon.org/news/rare-albino-raven-murdered
"the universe is flat" because that is consistent with observations thus far... This is a claim that underlies many other theories. And there are many such claims in the sciences.
The hypothesis "all ravens are black" would normally be tested as you first describe in the video, by searching for ravens to see if any of them are not black. You could say that there exists a finite set of {all ravens} and we could search it for ravens with the property (not black). If we manage to find every raven in the set and none of them have the property (not black) we would have proven our hypothesis. This way each new observation of a black raven further supports the original hypothesis. However there is also another way we could test our hypothesis. What if we imagine a set of {all non-black things}. This set, while very large in size, would also be finite. We could therefore alternatively search this set to prove our hypothesis. If we manage to find every non-black thing, and none of them are ravens, we would prove that all ravens must be black. If we then observe a lot of non-black things, and none of them are ravens, it would give credibility to the hypothesis. For each new non-black non-raven thing we find the chance of a non-black raven existing would get smaller (since the set of all non-black things is finite in size). Therefore, in a roundabout way, you could argue that finding a white shoe further supports the hypothesis that all ravens are black.
The way I like to think of logical equivalence between two statements is that if one is true, then the other is true, and if one is false, then the other is false. Great video!
In certain (many?) situations, one of those statements is more useful than its equivalent. Given there is an almost infinite number of objects (since each object can be broken down into many different sub-units, including the quarks and leptons of its individual atoms and every possible combinations of the sub-units, and this applies to every object in the universe), of which a near-infinite number would not be black, but there is a much smaller number of objects that happen to be ravens (about 16 million). So, empirically, the process of checking 16 million ravens is much more useful that checking the number of non-black objects. In fact, it wouldn't take long before you found a raven that is not completely black (two of the nine species have a white patch and one is brown) and eventually a white raven (not albino, but leucistic) hence disproving your theory. My main point is that just because they are logically equivalent, they are not equally useful. (Just like the cafe at noon example, one way of putting it is much simpler and hence easier to use). A logical empiricist would surely focus on the most useful of any collection of logically equivalent propositions.
Does the observation of a white shoe support the hypothesis that all ravens are black?
Also, there is a special message for you at 12:33 :)
Your videos are awesome like always...
I dont have a specific complement... ☺☺☺☺
What an interesting puzzle.
So, the problem with the 'bite the bullet' approach is that without any observations of ravens at all, you have no useful data in which to ground your hypothesis. No number of observations of shoes is really going to add support.
Popper is unsatisfying because I repeated observations of ravens does lend support to the idea that all ravens are black. Though I support a more bayesian interpretation there. In a certain sense, Popper is right because I don't think you can ever reach 100% certainty that all ravens are black, but you can easily reach 0% certainty in the same conclusion.
So, your context driven approach seems like it's better than either of the other two. But it doesn't seem very formal. What is 'context' exactly there? To some extent, it doesn't seem that different from the first idea. Very few observations of non-black objects are going to be helpful, even if you don't know that they aren't ravens before you observe them. Mostly that's because ravens are a very small subset of the number of different things you could observe.
hey Jade , nice to meet you in this video I found out what name goes with that beautiful "up and atom" girl , I like you and I would love to meet you but we are worlds apart .....
I think, I can solve it
●In a finite (isolated) system
We got more and more white things non of them are raven
(In common condition we search thing and examine its colour and in this we search colour and examine the thing so, in opposite black thing "can be" raven)
●So in a finite system (with finite number of things and type of things)getting more and more white things not raven decreases the probability of getting a white raven. so yes it affects.
And we do not use it because our world have so much things and variety of things that counting opposite doesn't effect much and it's not an isolated system.
How and Why did you came up with new creepy eyed channel logo???🤔🤔
Logical equivalence is hilarious.
"Have a nice day" sounds nice
"Enjoy your next 24 hours" sounds threatening lol
Ahahhaha this is gold
That is because dictionary definitions are incomplete at best, and fails to account for common use. "Your next XX hours" and "have a nice day" have extra meanings attached to them beyond the dictionarydefinitions, and they might also be regional. This means that they're not 100% logically equivalent in reality
ua-cam.com/video/eep4_0JaaG8/v-deo.html well the English language is just stupid in general, everything we say is 100% in context. Check out that video for only a few examples, and remember... their our know rules.
Forgive me, Father, I have sinned.
I'm sorry, Daddy, I was naughty.
:-P
Not all days are 24 hours.
Popper’s answer works; but so does Hempel’s: Suppose the number of objects is finite. If we looked at all non-black things and found them to be non-ravens, that would make the probability of all ravens being black = 1.0 (i.e., 100%). Each observation of a non-black non-raven increases the probability by the following increment: 1 / (number of non-black things). By contrast, each observation of a raven increases the probability by this increment: 1 / (number of ravens). The number of non-black things is bigger than the number of ravens by a huge factor, and the incremental increase in probability when non-black things are observed is smaller by the same factor.
Exactly my thought.
Team Hempel! Move on folks, no paradox to see here!
The bigger issue is that even if it were mathematically and logically correct, it's not useful. A philosophy of science which allows you to make claims about ravens without ever observing a raven is inherently flawed. The purpose of a scientific philosophy is to guide what experiments we design and inform what counts as "evidence". Hempel's answer is significantly less useful than Popper's in a practical sense.
Exactly. If you had two boxes on a table labelled "black things" and "non-black-things", every sample you draw out of the boxes incrementally supports your hypothesis. But, once you open up the experiment to "boxes" of indefinite size, each confirming sample proves little. That's why medical research (for instance) focuses on "outlier" populations for sample diversity and focuses on falsifiable mechanisms like (by analogy) "If you modify the blackness gene in test ravens their offspring have drastically different tail and beak shapes and can no longer mate with ravens, therefore all ravens must be black."
This is a functionally true but still technically unsound approach. You'd have to somehow demonstrate that you have seen all non-black things, and that's inherently unverifiable. You can only *wager* that you have, and that's precisely Popper's point --- we can never say a thing is *true,* (some, such as myself, might argue that tautologies are an exception,) but you can say it is false or *wager* that it is true.
I commented about the same thing, in a finite system, statistical data gathered with repetitive discovery of a NEW raven that is black tips the scale and pits impossible odds against the notion of non black ravens existing. So if all ravens have proved to be black, we have refuted that there exists a non black raven and eliminated falsifiability, and with 100% certainty, PROVEN that all ravens are black.
Reminds me of Einstein's statement "No amount of experimentation can ever prove me right; a single experiment can prove me wrong." Finding vast numbers of black ravens (or white shoes) doesn't prove anything, but finding a single blue raven proves the hypothesis wrong.
Maybe the confusion is that testing a hypothesis is not the same as PROVING a hypothesis. The white shoe doesn't prove anything, but it tests the hypothesis successfully.
So does a black raven
I disagree. The only observations that test the hypothesis are observations of ravens, since the hypothesis is about ravens.
So does a black raven. You can prove it by getting ALL non-black objects and seeing them ALL not being ravens. It's the same as getting ALL ravens and seeing them all being black.
@@jursamaj Logically, observing the white shoe does actually increase the probability of ravens being black. Practically, it is useless, since the the change in probability from observing a white shoe is small enough to be insignificant.
Jeffrey Suen observing all none black things does not prove that ravens EXIST. By observing all non black things you can only claim “All black things are black.” In the other hand if you observe all ravens you can claim 2 things. 1- “ravens exist”, 2”ravens are all black”. So 2 statements are not logically “the same”. They are just not against each other.
In this video I don’t see a paradox. What I see is a bullshit and low IQ scientists.
When your statement includes "all", you cannot call any observation conclusive evidence unless you can observe all of the population. If only one raven is non-black, you are almost certain to never encounter it, and all your black raven observations are meaningless. This all changes when you replace the absolute statement with one of proportionality. "Ravens tend to be black" is a much easier hypothesis to test. The shoe being white is extremely weak bayesian evidence for the original hypothesis, but it does not register in our intuition because there are functionally infinite non-black objects in the universe, so the strength of that evidence is negligible. It's not that the shoe isn't bayesian evidence, it's that you'd have to observe every non-black object in the universe to draw a conclusion from it, so its not functional evidence.
I came to say something like this, but you said it perfectly.
It still wouldn't have any bearing on the colour of ravens. Imagine you could list and observe all non-raven objects in the universe. That still wouldn't give us any new information on ravens.
@@palimpsestransparent You're right, given the scenario you describe, but that's not how the experiment was set up in the video. You're not observing a new not-raven. you're observing a new "non-black object". When that thing you observe is a shoe, that's one less non-black thing in the universe that isn't a raven. It reduces the odds by a minuscule amount that there are any ravens among the non-black objects.
@@jamzfive I see what you mean, but the reduction in probability is simply negligible. The number of different objects is absurdly high and the amount of each one of them too. To state that observing a non-black object increases the probability of all ravens being black seems to me a misuse of logic.
@@palimpsestransparent that's functionally what I said in my original comment. The thing that's not registering for you is the strangeness that it is technically evidence supporting that "all nonblack objects are not ravens" because you have increased the number of non-black, non-raven objects in your sample by 1. You're right that it's negligible, but it's still technically weak evidence. The cognitive dissonance this creates is why they call it a paradox, though I don't agree with that label since it's a problem of understanding the technicality, not a conflict of two knowable facts. This whole thing is more of a brain-tease than a useful thought experiment imo.
I think that doing science with all of Salad Fingers' relatives is where your whole experiment went awry.
The salad finger people were extremely distracting.
I love them
It didn't go awry. It's a good video
OMG. That's what it is.... I couldn't place it! The non-black object should have been a rusty spoon!
hahaha fucking he man - it does give that vibe!
"Suppose a person -"
**increasingly terrifying people appear**
Fuck, that girl was creepy af
you said a terrifying person appears?
Assume a spherical person...
20 years ago I had nightmares about that third person... Is that about a movie or something? I just can't verify if there is no common esperience, please help me... Where do we imagine that from?
The scariest was her; that smile was far too wide...
The problem is that "all ravens are black" is not a scientific hypothesis. It doesn't generate a valid null hypothesis, so it can't be tested. Strictly speaking, every observation of a non-black, non raven _does_ increase the probability that the hypothesis is correct, but the prior probability of that observation approaches 1. So the influence it has on accepting your hypothesis approaches zero. Thus it is not a hypothesis, it's a conjecture, as the information needed to decide it will always be incomplete.
To demonstrate this further, just restate the hypothesis as "the probability of finding a non-black raven is less than x". The paradox disappears, as it is obvious that by far the best way to push down the upper limit on the estimate of x is to observe ravens and not white shoes.
Whats important though is that observation of white shoes does still support the hypothesis that observing a non black raven is less then x. It just does so by an amount that is below a meaningful amount.
@@e4Bc4Qf3Qf7 Exactly. But the statement "all ravens are black" is an absolute. You can't prove this with observation, only make an estimate of the upper limit of x. The "paradox" relies on the the fact that the number of non-black non ravens is absurdly high, so it seems ridiculous that observing them gives you any information at all.
If you think of a sack full of poker chips of different colours and denominations, and your conjecture is that there are no purple $200 chips in the sack, then it's clear that any chip you draw out of any colour or denomination other than purple $200 increases your chances of being right.
To start with "all ravens are black" is to imprecise. Does it mean all currently existing ravens in this forest, all currently existing ravens everywhere, or all existing ravens everywhere in the past and future? A more precise hypothesis (that avoids the time and location specifics) would be "ravens can only have the color black". To prove that, you wouldn't count black ravens, you would look at what makes ravens black. By proving that the mechanism that makes ravens black can't possibly produce any other color (and proving that there is no possible alternative mechanism), you would prove that all ravens have to be black.
@@goranandersson3544 Yes, you've hit the nail on the head. Observations of the colour of ravens don't lead to a theory of raven colour. This is what I mean by saying that "all ravens are black" is not a scientific hypothesis.
@@e4Bc4Qf3Qf7 exactly
"Your Honor, the Prosecution would now like to call to the stand a series of 8 thousand completely unrelated witnesses who happen to be not guilty of murder. Thereby we shall provide proof for the statement that 'All people who are not guilty of murder are not the defendant' which is logically equivalent to 'The defendant is guilty of murder.'"
*AN ETERNITY LATER*
"Your Honor, the Defence calls Ted Bundy to the stand..."
But if they were completely unrelated witnesses is that unrelated to each other or to the murder? If unrelated to the murder or knowledge of it, why would they even be on the stand for questioning in the first place? Plus, why would Ted Bundy be there? (I do remember who he was)
@@weepingwillow-ud6xl he's a famous serial killer.
This seems like a clever counterexample, but it actually works. If you go through everyone else in the world and prove that they aren't the murderer then the person who is on trial must be guilty by process of elimination.
@@matthewgingerich3942 Unless, the murder rate of the entire world is currently a zero with 1 single outstanding defendant; but you had other defendants in the past who all got acquitted. Hmmmm.
this is a disturbingly similar perversion of logic which resulted in mis-carriages of justice- see ua-cam.com/video/bVG2OQp6jEQ/v-deo.html
"All ravens are black" *Immediately thinks about albino ravens*
AtrophyBelladonna lol exactly
What about the South African ravens with white patches in their feathers..those are not black and less exotic than albino ravens.
White ravens actually exist. I wonder how many white shoes have to be counted to prove that...or rather to disprove that 'all ravens are black'. Being the lazy person I am, who does not like to infer things, I would only be counting ravens and avoid shoes alltogether.
" ... except those that are not ..."
"All swans are white" makes me think of black ones. Similarly for just about any proposition of this particular logical form. So why do logical theorists of scientific method and reasoning persist in using it as a model? It bears such little relationship to actual scientific discourse and endeavour.
Snakes don't have armpits.
Or do they? I must observe my shoe to figure this out.
You'd have to observe something with an armpit
Snake -> no armpits = armpits -> not a snake
You need to count how many things have armpits and aren't snakes to prove it
Rapid シ enter John Hammond. He has cloned an extinct snake. It grows arms.
Te nis shu
Well actually some snakes have been found with vestiges of limbs so you could say that those snakes had arm pits.
I agree with Carl Hempel. Observing non-black objects that aren't ravens does support the hypothesis that all ravens are black. The reason it's unintuitive is that the amount of information received is astronomically small.
It is all about the size of the sets. If you think about it, you can prove that all ravens are black in two ways:
1 - Observing every raven and confirm that they are all black.
2 - Observing every non-black thing and confirming none of them are ravens.
They are both possible, but since the set of all ravens is minuscule compared to the set of all non-black stuff, the information gained from spotting a pair of white shoes if negligible.
Whatever doesn't kill me makes me stronger
~Hypothesis
So whatever doesn't make you stronger will kill you?
So far today trillions of things have not killed me. Why am I getting no stronger?
Whatever instigates the death of me, but fails, makes me stronger.
~Hypothesis
I'm not yet dead, and will not likely die, provided fixed rules perpetually apply to every level of reality.
~Theorem
As things exist, I'm as certain as I can be that I will too.
~Law
Hey guys, while you each have the ability to know something--you'll never actually know for certain what you know exactly. Also, fixed rules don't exist perpetually, so...
~Quantum Physics
@Adam Filinovich The sentence by xXxLolerTypxXx is logically equivalent to the original hypothesis. Also equivalent would be: Any 'thing' will kill Punya or make Punya stronger (inclusive or, i.e., there could be things which kill Punya and make Punya stronger). In predicate logic:
FORALL x: NOT is_killing(x) IMPLIES makes_stronger(x)
FORALL x: is_killing(x) OR makes_stronger(x)
FORALL x: NOT makes_stronger(x) IMPLIES is_killing(x)
To falsify the hypothesis one only needs to find a thing which is NOT killing Punya AND NOT making Punya stronger.
@Adam Filinovich Yes, but as I said, these are equivalent
(NOT A) --> B
(NOT B) --> A
A OR B
i.e.: (NOT strength) --> death.
And indeed, things/events that kill you can make you either stronger or do not make you stronger without contradicting the hypothesis.
"A Hiccup on the Scientific Method"
Flat earthers: **Heavy Breathing**
Right behind the religious apologists...
@@jarrod752 oh yes lol
science is just a theory
Science derived from theories, therefore your statement is accurate.
@@QuizmasterLaw So you don't know what either of those words mean, got it
I am discovering your channel with great delight. You chose to address the most profound and difficult questions in science philosophy, and still address them with such fluidity and simplicity. You are amazing.
Those two statements may be logically equivalent, but they aren't equivalent sets. these are just two different perspectives which has it's own fatal traps. Consider the following riddle:
Three knights enter an inn to get a room. They go to the desk and the innkeeper tells them that a room costs 15 gold coins. Each knight pays 5 gold coins and the bellboy shows them to their room.
After several minutes, they decide that the room isn't worth 15 gold coins and they go and complain to the desk. The bellboy takes the complaint and goes and tells the innkeeper while the knights go back to their room.
The innkeeper decides that the knight's return business is valuable so he gives 5 gold coins to the bellboy and tells him to give them to the knights. On his way, he realizes that he can't divide the coins equally among three knights, so he pockets two coins and gives three coins to the knights. "Great!", says one of the knights. "Now it only cost us four coins each!."
Now if the knights paid 4 coins each, or 12 coins, and the bellboy kept 2 coins, that's only 14 coins! Where did the other coin go?
This story mixed two perspectives. The coins paid and the coins received. If you just stick to one perspective, where the coins ended up, then the innkeeper has ten, the knights have three, and the bellboy has two.
So, if there is a set of all ravens and the theory is that every element of that set is black, why is it a paradox that a shoe is outside the set is where it is supposed to be? The answer is the perspective of 'support'. Does support mean logically true, or does it mean it makes a positive contribution to the theory?
The concept of positive contribution is not fact, but opinion. One may say that a white shoe doesn't contribute to the theory and another might say that after 10,000 black ravens, another black raven doesn't contribute either. The paradox exists only due to perception. If the problem is restricted to set theory, then testing whether a black raven belongs to the proposed set and a white shoe does not belong are the same thing. Finding an error would be different. In fact, every test either 'confirms' or 'contradicts' the theory. Should we draw the line between a test inside the set and a test outside the set, or between a confirming or contradicting test?
That was sneaky! It took me a while to figure out that "The knights paid 4 coins each, or 12 coins and the bellroy kept two, so the inkeeper has 10 coins."
@@PhilippeCarphin You have no idea how many physicists get fooled as well by this kind of problem. Most of our scientific discoveries have errors in logic just like this. We do more trial and error discoveries than thought experiment discoveries. We humans have a nasty tendency of creating emotional opinions and pass them off as scientific fact.
Thanks for the riddle, it was a good one!
A nice thought experiment. However you are simply double counting. From all perspectives there are only a total of 15 coins. There are no missing coins.
The knights pay 12 coins total = 10 coins to the innkeeper + 2 coins as a S&H fee to the bellboy.
Each knight pays 12/3 coins = 4 coins = 10/3 coins to the farmer + 2/3 coins to the bellboy
You can't double count the coins the bellboy has in his possession. Please redo your set math or redraw your Venn Diagram. Even Karl Popper thinks this is bad Maths. Logical equivalence is not perspective, and does not facilitate double counting of finite objects.
You pulled a sneaky.
The Bayesian solution seems to me to be the correct one. Nothing is certain and nothing is ruled out. Can’t wait for new videos!
The solution is P[All ravens are black/We have never seen a black raven]=P[We have never seen a black raven/All ravens are black]xP[All ravens are black]/P[We have never seen a black raven] :-)
so... nothing is true, everything is permitted?
counter examples can rule out things. But it is true we will never now anything to be true because axioms cannot be proven. We can only know things to be false.
@MetraMan09 Also, there are more non-black objects than ravens: even if there were non-black raven, then picking a non-black object is unlikely to be a raven. So it's really not a 50/50 probability! Basically, in the bayesian reasoning, looking for ravens and check their colors is “worth” more than looking for non-black objects and check whether they are ravens: you will change your assumptions more in the first case than the other. I think that this weakens the difference of approach between Popper and bayesianism 😊
@@peterbonnema8913 Double check that middle sentence. xD
Logical Equivalence: "Your beautiful face makes time stand still." = "Your face could stop a clock."*
*Note: after the second statement, it is a good idea to run away.
Looking at the clock face looks as though it needs either: winding or a new battery, visit to the jeweller's for repair, or perhaps a new clock? Due to the fact the clock has stopped !
I'm not a scientist at all, but I what about this hypothesis. "All school buses in the United States are yellow." In my decades in the public school all school buses I observed were yellow. But, I certainly did not see all existing school buses. Howver, I might be able to indirectly observe all of them by contacting all manufacturers who produce them and asking if every bus they build is yellow. In the case of ravens, we can't track down every single existing raven, so we can't prove they are always black. It's just my uninformed opinion.
You are committing a fallacy of equivocation. Those two statements are not equivalent, unless the second statement is also a metaphor, which isn't problematic at all.
@ilove bigbrother Yes, "non-ugly" would have been a 'good' choice.
Nice video. More about the context: the relevance of a white shoe can’t be known as we have no idea of the number of non-raven things. So we can’t know what the sample significance is. So the shoe doesn’t add knowledge about ravens. Science is almost always about statistics.
But if it can be known, like in particle/astro physics then that does tell us something.
@@Xeridanus Yes!
This seems like the correct resolution to the "paradox". I think the confusion comes from the fact that, at the time, most scientists did not have a proper grounding in statistics.
Problem with this paradox as I see it is that "white" is not equivalent to "not black". White is not black, but not black is not necessarily white.
Absolutely. If we knew there are only 10 non-black objects and we found 10 white shoes, everything else (including ravens!) must be black.
If you could observe 100% of the set of all ravens, you could perfectly verify whether all of them are black. Likewise, if you could observe 100% of the set of all non-black things, you could also verify whether or not all ravens are black. Since the set of non-black things is staggeringly larger than the set of all ravens, it does support the theory, but at a massively reduced ratio.
Also, so long as there is potentially one or more unobserved member of each set, you cannot say with certainty whether or not all ravens are black. This is a problem, as there really isn't a good way to tell if you've finished observing everything in one of the sets anyways.
This is close to how I think of it. I think in terms of 'information'. If we could observe 100% of all things, we would know with certainty if our hypothesis is correct.
As we have not observed 100% of all things, every new observation, no matter how trivial, is increasing our knowledge and therefore has some influence on our confidence in every hypothesis.
The real question I think is the value - observing the white shoe contributes so little to our confidence that we probably would agree it's not worth the effort, ie the informational value provided by the observation doesn't exceed the value we could get using our resources to make different observation.
I see no paradox, the statements are perfectly valid, they just aren't very useful. Logic doesn't care about usefulness, but we do.
I was thinking the same thing. The number of non-black things even limited to just Earth may as well be infinite as far as our ability to observe and categorize them goes. Therefore any observation of one does support the idea that all Ravens are black, but only by an infinitely small amount. It's close enough to zero there is a perceived paradox but it does technically have an impact, just very small
To illustrate her final point: imagine you heard about a Blue Valley, where everything in the valley is blue. Would it make sense to go to that valley and see if you can find any ravens there? Why yes, it would.
The logical conclusion I can draw from this video is that white shoes are pure evil
Mine was |truth> = |black raven> + |white shoe>
ua-cam.com/video/lnGHB-kI2ZM/v-deo.html
The bias towards novelty and results that change the paradigm is exactly where the current publication crisis came from. If the only results that matter are ones that challenge current understanding, then there's a significant risk that nothing is ever tested more than once which completely misses the notion that not all experiments are done perfectly, and that published conclusions can be misguided or outright wrong.
White shoes matter. Even if they only stand to confirm what "everyone knows", results that feel mundane reinforce that fact that a lot of science should be straightforward and unsurprising, because giving the impression that counterintuitive ideas are the norm is how you get flat earthers and electric universe types who fundamentally question the basis of most of modern science. While simple, basic chemistry experiments may not immediately lead to the discovery of a grand unifying theory of everything, consistent reproducibility is the bedrock foundation to the claim that the scientific method works.
ETA: The scope of the observations is also relevant, however. It's all too easy to draw some pretty silly conclusions relying too heavily on logic, and not all that happens in the empirical world is "logical" as we understand it (see: quantum mechanics, human behavior, etc). Conclusions drawn from observations also need to be questioned in addition to the observations themselves, because again, the scientific method's most important result is reproducibility. Logic that goes beyond what is shown empirically is a whole separate issue, and moves away from empiricism and into belief (which is not a bad thing; at the end of the day, we're all simply choosing to believe our senses are valid, and I've yet to see anyone prove that to be the case absolutely).
hear, hear
I agree most with the first explanation. The subset of all things that are not ravens is practically infinite, so any supporting observation of a specific subset of that subset has a negligible impact on the hypothesis. While the two statements are the same from a logical standpoint, they are not the same from a logistical standpoint.
0:51 Salad Fingers sciencing rusty spoons.
She's even talking like salad fingers, it's slightly unsettling
That is exactly what I wanted to comment on.
XD haven't seen that in years
Brad Cozine my exact thoughts
yeah ngl there were some creepy animations here! that white shoe dude. nightmare fuel!
A white shoe is an example of a 'trivial support'. It does not invalidate the 'all ravens are black' theory. It is rather like the trivial solution to an equation that is a true solution but isn't useful. I think the thought here is that the white shoe is a paradox because it isn't useful, which is incorrect.
If y=A*sin(kx) is a sine wave of frequency of 2*pi*k, then y=0 fits the definition of a sine wave of any frequency, or rather, A=0. Do you say that y=0 is not a sine wave because it is flat, or that it is a sine wave of zero amplitude? Y=0 fits the definition of a sine wave but it isn't very useful.
I think the dilemma here is that we aren't stating the full definition because it seems trivial. What if I redefined the definition as 'all ravens are black AND all non-black items are non-ravens'. Now the shoe fits!
However, (A implies B) if and only if (not B implies not A). Saying that all ravens are black is exactly the same as saying that all non black things are not ravens. So yes, seeing a white shoe supports the hypothesis.
The question becomes: by how much?
In measure theory, we can see how a measure on the set of all things that exist can be used to determine that, in fact, albeit one single white shoe has probably measure zero or close to zero, the integral over the whole set of non-black things yields the same result as the measure over the set of ravens. This means, observing all non-black things would indeed be enough to confirm the hypothesis, even if the single element we observe yields zero (an infinitesimally small) support to it.
A sine wave of null amplitude is a null measure element in the set of all sine waves. It's the same idea.
@@hydraslair4723 what you said makes no sense and is not relevent. Bijections weren't implied here and you can't integrate over a set. It has nothing to do with what I said. It looks like you threw together a bunch of math terms to look like you know what you are talking about.
@@mikechilders you can't integrate over a set? Are you sure you know what you're talking about?
You know that when you evaluate a definite integral, you do that over a set, right? The set might be an interval of real numbers, in which case you get the ordinary integration of real functions, while the notion of measure generalises this to arbitrary sets.
I suggest you check out some measure theory. Dismissing my claims because you don't understand them is not the way to go.
It is also a powerful basis for statistics and probability, something you might be interested in.
"No bijections were implied here". If you assume that not(not(A)) = A, this is all you need to know to derive that (A implies B) is the same as (not B implies not A). I'm sure there are more ways to derive it, out there, without assuming that, but I can't think of any at the moment.
@@hydraslair4723 I'm not going to entertain your delusions. You can't integrate over a set of black ravens and white shoes. And that has nothing to do with my comment anyway so I'm ignoring you from now on. You don't have a firm grasp on reality and are too socially inept to have a conversation.
@@mikechilders Hey fella! Learn how to engage intelligently on a public forum or you will be justifiably and roundly mocked for your own social ineptitude. You just demonstrated that your assertion applies to you and not Hydra's Lair:
Your first reply to him was agressive, slightly insulting and purely deterministic -- "you're wrong" in 3 different regards without explaining why. He calmly (almost politely) pointed out your misunderstanding of the maths theory he was citing and explained (supported) his use of it in his original statement. You came back to again say simply that he is wrong with no support or explanation of your assertion but this time more clearly insultingly so, thereby demonstrating your own lack of ability in argumentation, discourse and scientific comprehension and analysis, and therefore not only your own lack of social ability (meaning that we can't have a useful conversation with you) but also your own lack of understanding of the subject on which you try to converse (maths, or perhaps logic, or both)
Go read some basic philosophy (logic in particular) then join a local debating group to learn how to argue and make social intercourse. Then we might determine if you know enough about maths to debate you or rather educate you.
Me to myself: I am pretty intelligent,
Me to myself after this video: AH my stupidity, it's unchallengeable.
I've spent more time trying to think of a "Nevermore!" joke than actually analyzing the paradox
All ravens are black, qouth the white raven... nevermore
finding a white shoe increases the support for the hypothesis only a minuscule amount, never more.
Qouth the white raven: "'WTF?' I mean, 'Nevermore!'"
Nevermore will I wear white shoes
An Albino Raven.
Exactly, a non-black raven. That such a thing exists falsifies the hypothesis. Non-black ravens are the *only* thing that matters.
Popper would be proud
An Albino black shoe
www.audubon.org/news/rare-albino-raven-murdered
All ravens are black is just an example of a hypothesis, it's not one we actually think is true.
I think the problem here is that we don't actually fully, completely agree with the beginning statement, which is "Observations of A with property B, support the hypothesis that all A are B". I think this should be restricted when the number of elements of A is finite. Thus, for the case of ravens, since we BELIEVE they are finite, we find it intuitive that Observation of raven with property black, supports the hypothesis that all ravens are black. If we look at the second case, I don't think many of us agree that Observations of non-black things being non raven, supports the hypothesis that all non-black things are ravens, since non-black things are infinite, or so we BELIEVE.
Some may argue that in actual science, we actually use the first one, not with my restriction. Although you are absolutely correct since scientific induction is used, I believe that we use it because we believe in the uniformity of laws and matter. For example, when Newton did his gravitational laws, we found that all nearby galaxies follow the same thing; thus we believed in Newtonian gravitational laws that it works in all the universe, even the non-observable universe. Thus, someone will say that science used the first statement, Observations of A with property B, support the hypothesis that all A are B. I would argue the only reason we did that is the we believe that matter should all work in the same way and the only reason we extrapolated that law to the non-observable universe is because of our belief, other than that we don't have any good reasons to believe that Newtonian gravity works. To also add to it, when we make a discovery in the human body, or see how the embryo grows; we don't look at all mothers wombs to check if all humans are like that; we believe all humans are the same 😂😂.
BTW, believing that all matter works in the same way isn't insane; I am just stating that we have to recognize that we BELIEVE IT.
Some of the ideas was inspiration from the comment of Mark Peterson.
I remember being told once that in some formal logical systems, the absence of a property is not itself considered a property. Apparently, this solves a lot of paradoxes, which is why it's used some of the time. It's a useful path out of a few things. It even appeals a bit to intuition - at least, it does to me. :)
It might be useful. But the lack of a property being a property has its place. Such as saying a man is poor
When I look at her, I think of everything but science. Science and women just don't mix.
@@seanleith5312 umm what?
@@solsol2733 what the fuck
@@johndwolynetz6495 I think you are responding to the wrong guy.
"All swans are white" was a true statement until 1697 when the sample size increased and proved it wrong.
Same as ravens,now, too are proven not all black.
Aside your passively brilliant videos and pedagogy, your animations are ADORABLE OMG!
Good to see zombies taking an interest in the scientific method rather than just eating brains.
That's where the brains _are_
They ate a little too many brains
They're growing your brain to eat it. Don't fall for it! Wake up sheeple!
They have been beaten by plants so much for so long (10 years by now), so they have repented.
@@loganstrong5426 resist science, and your brains won't be farmed by zombies for food!
Albino ravens exist, and that supports our hypothesis that all alien birds are green.
I don't know if this is what Carl Hempel believed, but this is my theory. Observing a white shoe does support the hypothesis that all ravens are black, but only to an extremely minute degree. Think about it: if you want to prove the hypothesis that all ravens are black, you basically have two approaches. One, you can observe every raven in the universe, and if all of them are black, you have succeeded. Two, you can observe every non-black thing in the universe, and if none of them are ravens, then you have also succeeded.
In practice, of course, we will never be able to observe every raven or every non-black thing, and will never be able to firmly prove the black raven hypothesis. But there are far, far, far more non-black things in the universe than there are ravens. This means that observations of black ravens will probably be at least dozens of orders of magnitude more effective in suggesting that all ravens are black than observing a non-black thing that is not a raven. So, we can't really do a lot of indoor ornithology, since we would literally need to observe at least trillions of distinct things in order to obtain the same level of evidence as observing one raven.
Of course, this is assuming that you're just picking non-black objects at random and observing their color. Context does matter, and specifically seeking out a white shoe or other non-raven object does nothing to support your hypothesis. On the other hand, we can narrow and refine our search significantly if we only observe in contexts where we would expect ravens to be found. For example, maybe we only look at things that are around the size of a raven, or maybe we only look at things near the surface of the earth. Maybe we only look outside, since ravens are much more likely to be outside. Still, supporting the black raven hypothesis with this approach will be many orders of magnitude more difficult than just looking for ravens.
Popper’s method was the method I’ve been taught through college. You never seek to confirm, you seek to refute either the hypothesis or the null hypothesis.
or both hypotheses
Surely the paradox only occurs because of the "potentially incorrect" statement that "all ravens are black". It should be "MOST ravens are black" or "VIRTUALLY ALL ravens are black" or even "every KNOWN raven is black". As we have never observed the whole set or ravens to be able to confirm the original statement then allowing for some uncertainty would seem to be the way to go.
I am no philosopher but my gut tells me there will always be some sets for which one can make statements that are as certain as the original raven statement. However most sets are probably not so clear cut and from that we end up with a potential Raven Paradox.
My thinking here has been influenced by the subtle change in my perspective on many things since I stumbled across Bayesian Models and Bayesian Statistics and how what feels intuitively right is not always so.
"It ain't what you don't know that gets you into trouble but what you know "for sure" that just ain't so".
As a former systems analyst by trade it never ceased to amaze me how often we make statements like "all ravens are black" when in reality there is often a " ... except when ..." clause to the statement. On a gross, day to day basis this may not be an issue if we do not allow for the possible exceptions. If only one in one million ravens are not black, then many observers will never see a non-black raven. But it would not make the statement "all ravens are black" true.
Love the channel.
There is also a definition problem. What is a raven in the first place? What set of properties define a raven? Can we accept a raven that has 4 legs... or that would be a different animal? Classification is a hard subject.
you have stumbled onto the difference between induction and dedication as they function in logic (not electrical engineering )
A statistician would call the statement "all ravens are black" the null hypothesis, and then perform tests to determine whether or not to reject the null hypothesis. At the end the confidence in the decision to reject the null hypothesis or not would be computed. This is functionally the same as saying all ravens are most likely black, or something like that, but I think it's a much cleaner and easier way of phrasing it
mudfooted.com/white-ravens-qualicum-beach/
There's a logical trick to ensure that your statement is correct: all TRUE ravens are black. What, you've got a white raven? Well, it's not a TRUE raven.
I believe it does. A white shoe definitely implies that A. It is a white object. B. It is not a raven. Which does support our "All ravens are black" statement. However, the support given by it is essentialy infinitesimal so practically useless. Thus, if we look at the support of evidence as a quantitative quantity, instead of qualitative quantity Even if it supports "All ravens are blue" or red or something hypothesis, it doesn't matter. However, if we observe say, a dark raven then its support for our hypothesis is magnitudes larger than that of observing a white shoe. So, our scientific method stays safe.
This is wrong. There is no paradox here:
The statement "Observations of white shoe with property not ravens" is CONSISTENT with the hypothesis. It does not SUPPORT the hypothesis. For something to support the hypothesis, it must have weight, something of substance to support it. As such the statement is only consistent with the hypothesis but offers nothing else to the evidence to back up the hypothesis.
So:
Observations of white shoe with property not ravens
support the hypothesis that ravens are black.
Isn't true. Think about it: It does NOT support the hypothesis. It is only consistent with the hypothesis. Logic isn't binary. Just because it doesn't refute it doesn't mean that it supports it. It can also be consistent with it without supporting it.
Observations of white shoe with property not ravens
is consistent with the hypothesis that ravens are black.
Observations of ravens with property black
supports the hypothesis that ravens are black.
This is correct.
If you lived in a nearly empty island, observing non-black objects to be non-ravens would be significant, albeit less efficient.
Except that a statement logically implies and is implied by its contrapositive-e.g. "if it is raining, then I have my umbrella" logically implies "If I do not have my umbrella, then it is not raining." So "If an object is a raven, then it is black" logically implies and is implied by "If an object is non-black, then it is non-raven." So anything that *supports* the claim "If an object is non-black, then it is non-raven" supports the claim "If an object is a raven, then it is black" (which is equivalent to "all ravens are black").
But, if "Observation of white shoe with property not ravens support the hypothesis is consistent with the hypothesis that ravens are black" (ie does not support it) but "observation of ravens with property black supports the hypothesis that ravens are black," then the observation of a statement does not support its contrapositive, but the observation of a statement supports itself.
So under your system, contrapositives (which *must* follow from one another) aren't equivalent, which would be absurd.
I think part of the problem is that there is no separation of equivalent and inverse here. "I hope you enjoy your day" is the same as "I wish that this day gives you joy." But the inverse is " I hope that any moment you do not enjoy is outside of today. "
The whole cafe at noon example was just rephrasing the same thing, but the raven statements were the inverse of each other.
Logic is binary. Observation is not.
Why does white shoe not support the hypothesis, and a black raven does? Both are consistent.
How much "support" do you need to call the hypothesis 100% true?
Pure logic IS binary. And there is no such thing as evidence. You either have proof or you don't. The problem with this whole thing is that science does not use pure logic, it's intherently probabilistic.
In pure logic though, if you were able to find every object that wasn't black and none were Ravens, that would be just as good a proof as finding every Raven and finding that none of them are black. In practice both finding every non-black object and every Raven are impossible though, so it's just not a question you can answer.
I think the paradox arises from the first sentence. "Observing black Ravens supports the hypothesis that all Ravens are black" this isn't really true if you think about it, or it's at least an over simplification.
Let's change the example. Observing white towels supports the hypothesis that all towels are white. Well, you can observe white towels all your life but of course that doesn't mean non-white towels don't exist.
So saying "observing black ravens supports the hypothesis that all Ravens are black" is just as wrong as saying "observing white shoes supports the hypothesis that all ravens are black".
I think my explanation is somewhat similar to the second one in this video.
I thought that too, I think this conclusion is a logical support for Karl Popper's statement
observing white towels does prove that towels are white, and the more you observe, the more likely it is. Just because you can never reach 100% doesn't mean that each white towel proves it in a small way.
But if observing black ravens doesn't support the hypothesis that all ravens are black, then what DOES support the hypothesis?
I really like the format you make your videos, But I absolutly LOVE the animations! they are brilliant and creepy and hilarious. They are awesome!😆
Carl Hempel is absolutely right. The observation of a white shoe not being a raven does support the theory that all ravens are black. Even if by an infinitesimal amount.
The argument regarding a couch sitting ornithologist isn't sound, even if it is reasonable. Machine learning works much the same way in this regard. Trillions of negative results can add up to meaningful data.
It supports it with the proviso that there's a finite set of possible objects.
But it's such a small amount that it doesn't qualify as support.
The boots on Ravens is so cute
I think the reason this is a paradox is because the premise sounds well formulated, but isn't. Finding a black raven doesn't support the hypothesis that all ravens are black because the position isn't about any individual black raven. It's about all ravens, including hypothetical non-black ravens. "All" is a qualifier that modifies the subject. The white shoe doesn't support its hypothesis for the same reason. The confusion I think is because we see it more clearly when it's a white shoe and not a raven. The white shoe on its own tells us nothing, but all non-black things, which a white shoe is a part of, can disprove the hypothesis because at least a single non black raven must be included in this group for it to be false.
Basically the only discrete constituents of the subject of "all ravens" or "all non-black things" that matter are ravens that disprove the rule . Any other individual member, even if it is a raven, doesn't really matter.
5:22 while you like bird science, I much prefer bird law
I have no idea why you would think that way, considering that bird law in this country is not governed by reasoning
I knew a person who was an expert in the bird law... his name was Charlie... he was also a fullonrapist. :)))
First logic statement is exclusive to ravens.
Equivalent logical statement is inclusive of all observable objects.
So they are not equally useful hypotheses.... Then Comes the fallout.
The first statement isn't exclusive to ravens, it's inclusive to all colored things since it entails they can't be ravens if they're not black.
I was thinking something similar. The observations are only of the population you are sampling from and don’t necessarily extend outside of it. If I wanted to study if there were any wild elephants it would be dumb to only look in Canada and Antarctica since my sample would never be a “fair” representation of all elephants. When you are looking for a non-black raven the abundance of non-black objects means you need a bigger sample size for the same level of confidence. You would also have to make sure that you could observe non-black ravens which means you can’t just look at the items in your house if you know you don’t have any birds.
Agreed.
I think the answer to this question depends on whether you assume the set of all things to be finite or infinite.
If you assume it to be finite, then obersving non-block ravens does in fact support you theory of all ravens being black since this means that there are less ravens that could be black (As long as you know at least A raven that is black and haven't observed any ravens that arent). Theoretically you could therefore confirm you threory by obersving everything that is not a raven until all that is left are ravens which you know to be black.
If you assume the set of all things to be infinite then obersving a non-raven would NOT confirm your theory, but neither would oberving black ravens. Since even if you find one more black raven, there are still infinetly more ravens that could be non-black. I mean, there are many mathematical concepts where we have not found a proof for them being right, but we have tried a lot of numbers for which we know it is right. Yet we can't really say that this confirms the theory since there is still an inifite ammount of numbers for which the rule could be wrong. If you assume your set in question to be inifinte just finding examples of your theory being right does not confirm it in general I would say.
Not that what consitiutes a "Thing" or "All" in that context does not really matter and can be defined on a case by case manner. For example, you might say that all ravens are black in the context of earth, and that as a "thing" you mean animals. So by "Set of all things" I dont mean it in the sense of just all of the universe, rather those are things that depend on the context of your theory and is meant in a more abstract way.
I only just found your channel. Thank you for your insight, your descriptiveness, your delivery that made me smile, and your ability to not talk down to someone while explaining difficult topics. You earned my subscription today :)
My brown writing desk is not a raven, but it's _like_ a raven, in a way I'm having difficulty determining.
Perhaps it’s because they both produce flat notes
Agent Stache Also here's one way both a raven and writing desk are alike I found a few years ago: both the English word raven and the first English word of the two English words writing desk, start with the r sound. They do not start with the same letter, but they start with the same sound.
@@Reubentheimitator6572 Lewis Carroll would be proud (as would th mad hatter)
@@daviddunmore8415 That line isn't in the book. It was improvised by Ed Wynn in the Disney film.
David Dunmore Thank you for the compliment David. I've wished to be complimented for that realization for a long while.
The problem is that you intuitively think of all non-black things as an infinitely large group. If you consider the groups as represented at 3:45 to be finite, it should make perfect sense that a non-black object decreases the chance of finding a non-black raven, because there is one less object that could be a non-black raven.
I think the main problem is that observing a white shoe doesn't "support" the notion that all ravens are black, it merely fails to contradict it.
As you mention in the video, it also fails to contradict the notion that all ravens are blue, purple, or green with pink polka dots (OK, maybe you didn't actually mention *all* of those ;-) so can it truly be said to "support" all of those notions simultaneously?
The appropriate opposite of "all ravens are black" is not "everything which is not black is not a raven", it's "no raven exists which is not black", which restricts your scope of examination and experiment to "the set of all ravens" which is the correct scientific approach.
I disagree. Imagine you were presented with all non-black objects in the Universe and none of them were a raven. You could then say with confidence that all ravens are black.
@@mina86 but that's not what's happening here. You're being presented with *one* non-black object, not all of them. Just seeing one does nothing to support the notion: how confident would you be that you had found *all* non-black objects? Just one missing non-black object would destroy your proof.
Also, simply finding all the non-black objects does nothing to confirm the existence of ravens in the first place…
@@PhilBoswell I Agree, but with every non-black object that you see, you become more and more confident about the given hypothesis.
Also, finding all the non-black objects(and finding out none of them are ravens) may not confirm the existence of ravens, but the observation is still logically equivalent to your hypothesis.
@@PhilBoswell, you're also not presented with all ravens when you test the hypothesis by observing all ravens. That's why observing a black raven *supports* the hypothesis (but does not prove it). So does observing a white shoe except in this case increase in confidence is minuscule in comparison.
Finally, if there are no ravens, hypothesis that all ravens are black is trivially true.
Phil Boswell
Agree.
Believe this is conflict of “scientific method” vs “logical progression”.
or
apples vs oranges
What about things like Constructive Logic, where the statements "All ravens aren't NOT black" and "All ravens are black" cannot be equated, thus removing the paradox altogether (since the observation of a white shoe only supports the former statement)?
I feel like this best suits the desires of both those hoping for falsifiability AND the ability to support a statement in the positive. Additionally, a lot of logicians, mathematicians, and computer scientists have already been moving in this direction, so the groundwork for using Constructive reasoning in practice is already there.
I read the comments to find out if this idea was written already. Glad to see I'm not the only one with this same logic.
There appears to be no paradox here to me: you can indeed state that any observation of a non-black thing that is not a raven is I tiny little bit of evidence towards a hypothesis that all items non-black are not ravens. The hidden ‘mistake’ in thinking is that people apparently falsely assume all pieces count the same, but they do not.
Restating “all ravens are black “ to “all non-black things are not ravens” vastly increases the amount of things that fall into your category of investigation - so every bit of evidence is proportionately less significant in proving your hypothesis. Stating your hypothesis as “all ravens are black” is just way more efficient.
The bigger actual flaw in logical empiricism is that pointed out by Karl Popper: you can never claim to have observed _all_ ravens in the world, let alone the universe, much less all times past, present and future. Therefore, a categorical statement such as “all ravens are black” can never be truly verified. It can only ever be falsified. If I remember correctly, Popper, in The Logic of Scientific Discovery, not only states that categorical propositions (or hypotheses) should be formulated as a falsifiable statements, but also states they should be formulated in a way to make falsification as ‘easy’ or efficient as possible
[edit: just continued watching and I see response 1 says the same. The only thing to add (as I did above) is that it makes sense to formulate your hypothesis in the most efficient way: that avoids many wasted hours spent on ornithology in your living room. Also, the fact that something goes against our instincts is _in_ _no_ _way_ an argument against it. Any scientist should know this]
Claiming what future technologies can and can't do does not refute anything. Saying we currently can't know all ravens black may be accurate, but making bold assumptions about an unknown future does not add anything valid to the argument and definitely does not show a flaw.
My conclusion: Vengeance and Deduction are two dishes that are best served cold.
Deduction is always hindered by the fact that all premises have to totally, absolutely, unequivocally true to have real confidence in the conclusion. The instant when you introduce even a chance that the premises are not true (like here, when you introduce the concept of hypothesis) then you introduce a chance that the conclusions are false, and it might be anywhere from an almost academic concern to a total disaster.
In a more practical example, if you ask a million people if they will vote for candidate A, out of a universe of 1.1 million voters, and you get a 60% of "yes" answers, you then bet your house on the result that candidate A will be elected, but there is a big chance that 300000 voters who answered "yes" don't bother to actually go to the booth and vote, and you lose your house. When you deduct from less than certain premises (like "60% of the voters will vote for A") your conclusions might be wildly inconclusive.
Loved the creepy goofy animation 😎
Suvi-Tuuli Allan Do you know the UA-cam series Salad Fingers?
@@homberger-it yes?
My hypothesis is that all ravens utter the word, "Nevermore", if sufficiently persuaded to do so in your presence.
It is true, Ravens have the capability of speech.
I don't think there is any paradox at all. The problem is that the logic doesn't take into account how much a discovery supports the hypothesis. Finding a white shoe does actually improve the probability that all ravens are black. However, there are so many "non-black" things, that the change in probability is practically useless. That's where the perceived paradox comes from.
If we could observe all "non-black" things we could absolutely determine if ravens are all black, but that would require infinitely more observations than if we simply observed all ravens.
I was thinking the same thing. The number of non-black things even limited to just Earth may as well be infinite as far as our ability to observe and categorize them goes. Therefore any observation of one does support the idea that all Ravens are black, but only by an infinitely small amount. It's close enough to zero there is a perceived paradox but it does technically have an impact, just very small
Great video! We run into this problem a lot in Psychology actually, believe it or not. Psychology is something that is very difficult to quantify, so psychologists spend lot of time and effort doing correlational study after correlational study trying to induce what cause and effect relationships might exist between complex emotional states. In many cases we cannot confirm a hypothesis, but can confirm that other disconfirming hypotheses are not true. Does this confirm the other hypothesis? That is why I always liked Popper and his approach, it makes the most sense and allows us to do away with the endless correlational studies and useless data points. That said however I always liked Feyerebend and agree whole heartedly that science doesn't necessarily have to be done a certain way, if that were the case we would be artificially limiting the skills and talents that the human mind offers to the pursuit of scientific endeavors.
The observation of a white shoe adds to your knowledge of the set of ALL non-black objects. Taken to the extreme if we were to observe the full set of ALL non-white objects we would, on seeing no ravens in that set, correctly conclude that all ravens (if such a thing existed) would have to be black. Thus observing any one non-black object provides evidence that all ravens are black, but it is diluted by the quantity of all non-black objects. I think this falls more in line with the first response to the paradox.
I think this ties closely into Platos alagory of the cave. If all you've ever seen where black shadows on a white wall, you would think everything that moves is black (including "ravens" which would ofcourse only be their shadows). In this case, seeing a white shoe would definitely give you a lot of information about ravens, as it opens up the possibility for black to be used as a distinguishing label for moveable objects in the first place.
It's not a paradox at all, it's just language isn't a perfect representation of reality.
It is like saving up pennies to buy something that costs billions of dollars.
I feel like explanation #1 makes the most sense. Observing a white shoe does add to the certainty that all ravens are black, just by a very, very, very small amount and that is where language gets confusing.
I've heard this before and I really don't know why it's a puzzle,,, what about a black shoe,, its black, but it's not a raven, this refutes all non black things are not ravens, because 'all non black things are not ravens' would be the same as saying all non-non black things ARE ravens, in turn, it's saying all black things are ravens,,, and we know that isn't true,,, because my shoes are black,,, so the conclusion is,, people were just idiots spouting crap back then
So you're saying language is a paradox?
Bingo!
White shoe
Black raven.
Jade wears a black t-shirt with a strange “spaghetti bird” (mainly black)
And when she wears white.. I heard bird noises in the back!
Also “an hypothesis is never wrong until it is” (a tl;dr version of Popper). So a white shoe kinda solidifies the hypothesis. Looking at the ceiling solidifies the hypothesis.
Oh God the quarantine it’s just a big experiment!
A: If it's a raven, it's black
B: If it's not black, not a raven
Every observation of A or B support A or B
BUT because there are hella lot of not black things than there are ravens, any support to B you may wish to translate as support to A decreases by that much.
Also, to absolutely establish A by A you need to find all ravens, but to do it by B? you need to find ALL non black stuff which SEEMS a lot harder.
Both of these things decieve your brain into thinking there's no way a white shoe could prove all ravens are black!!
So in conclusion I'm going with the first guy I guess 😅 lol
Hm, nah, even then you'll need to prove that you've found all raven
@@gonzalolarghero5594 No, just gathering all nonwhite things won't be enough, you'll also have to prove that what you have is indeed 'all' nonwhite things
@@mbrusyda9437 I'm not saying we're actually gonna do it lol I'm just saying one task seems harder than another.
(and if you gather all non white things that means you've already proved that you gathered all otherwise you won't be able to say you gathered all)
@@aryajpegasus that's my problem with that interpretation, is it ever possible to prove that you have checked all of A? If it's not then whatever implications of it is irrelevant and you're defaulting to the third interpretation
@@mbrusyda9437 Nope never possible. But as I said twice we're not even gonna try.
I don't want to throw a spanner in the works but there are occasionally albino ravens.
"All ravens are black" is just a stand in for "all A's are B's". It doesn't really matter whether it's true or not for the example to work since we're trying to falsify it anyway
@@durellnelson2641 I know. I was being facetious. :-)
@@SteveGouldinSpain I used to observe an albino blackbird on my way to school. From simple genetics I worked out when I should start seeing albino descendants, excitedly telling the biology teachers, who sadly informed me that most albinos don't find mates and rarely have any descendants. I never saw any more white blackbirds in the next 40 years of looking ;-(
@@SteveGouldinSpain And albino clergy ( who don't get to mate by choice ). Maybe my teachers were wrong and albinism is about to sweep the planet.
You have just made me recall seeing an albino African, as I walked through the Rubaga section of Kampala ( in 1970). Just about the most sad sight of my life ( perhaps showing how lucky I have been.)
@@japeking1 yes I understand Albino Africans are much sought after by Witch Doctors for bush medecine - they just hack off an arm or a leg as takes their fancy. It's a bit like having a rabbits foot for good luck, though equally as bad luck for the albino as for the rabbit.
I think the most useful answer is Carl Hempel's; the white shoe does support the black raven hypothesis but to a miniscule degree, to the point that it is no longer intuitive. By observing many, many, many objects (not just ravens and shoes) we have built up a system that we can use to classify some objects and hypothesise that all ravens are black, or all shoes are solid. Every time we observe any object, it either reaffirms our classification system or undermines it to some degree. We believe that things have colour because of the properties of those things that affect the reflection of photons, and everything we see that has the colour we expect based on its properties, affirms the entire system in a tiny way. Every time I see a white shoe I know that my eyes are operating and photons are still being reflected by things, which shores up my confidence that I can observe the colour of ravens. If we were shown an object that undermined one aspect of the system, it would to a lesser extent cause us to lose faith in the rest of the system too. The extent to which that confidence is lost in other parts of the system depends on how closely they're related to the part that's been undermined. If I saw a red raven, then my faith in my understanding of raven DNA should probably be questioned, but it's unlikely that it will cause me to wonder whether I can make a shoe out of hydrogen. Conversely (see what I did there?) before the Higgs boson was found there were physicists saying that if the LHC didn't find it, we should throw out the Standard Model entirely and come up with something new.
Jade I absolutely love your channel! Wonderful animations, great delivery, and interesting content! Thank you for your contributions.
Your animations supplement your explanations so well!!! Love this channel :D
So a hypothesis was given of the form "all elements of set M have property p". And the idea was then to check the hypothesis empirically by drawing a random sample out of M and check for p. Then two logically equivalent formulations of the same hypothesis (but with different M and p) were given, along with two real world examples of "drawing a sample". In one case, it was very intuitive that this added support for the hypothesis, in the other case it was highly unintuitive -> Paradox.
I think the answer to the paradox depends on how the white shoe example was given: If you looked at a shop window and saw a white shoe, then thats not a random sample out of M (there are never ravens behind shop windows). If you looked at a truely random non-black thing, then this would increase the likelihood of the hypothesis, but only by a very tiny amount (because the set of non-black things is much larger then the set of ravens).
OMG I love this channel. The narrative is so well constructed that every time I think if a response or question it is addressed in the very next phrase.
Please keep up the philosophy of science videos!!! Its amazing!
Second explanation is correct. Science is ONLY falsifying hypotheses, usually mutually exclusive, collectively exhaustive hypotheses with hypotheses that we're actually interested in. To scientific method the "all ravens are black" hypothesis, we have to FALSIFY the alternative: that some ravens aren't black. Since we can't falsify that theory, "all ravens are black" isn't a scientifically known hypothesis. It's purely conjecture.
But doesn't this mean that _all_ scientific theories are purely conjecture, no matter how well established?
Observation of white shoes supports the hypothesis that people have bad taste in accessories.
a basketball player wore white shoes with white fur today
I think my feelings are that logically equivalent statements don’t address relevance. Non-black non-ravens is just too broad a category to give meaningful statements.
But I also feel like my decision is purely practical; I’m not sure how I’d address the abstract/philosophical question. Truth may be objective, but the pursuit of it is human, so I think it’s difficult to define exactly the line of “relevance”.
That said, I also believe a falsification is much more valuable than a support/confirmation. Falsification is the only way to be sure. But being sure isn’t the most important thing, either.
In any case, this has got me thinking. Keep up the excellent work!
weird, i thought falsification would lead to never ending pursuit since u can never confirm anything.
Yes, it is way too broad a category, so a white shoe doesn't support 'all ravens are black'. To support it you would need to see almost everything.
@@gmcgarveyut To *prove* that statement you would need to look at every coloured object in the universe and check none of them were ravens. But even a single observation of a white shoe still *supports* the hypothesis, just not very much because it is just one of trillions of non-black objects.
@@alexpotts6520 That's stretching the meaning of 'supports'. I think there should be some statistical significance before using 'supports'.
@@gmcgarveyut Fine then. If one white shoe "isn't significant enough" to count as support, what about the observation of a million white shoes? Why should observing a million white shoes tell me anything about ravens?
The paradox doesn't go away. No matter how small the evidence contributed by a single observation is, as long as it's non-zero I can make it "significant" by making enough observations.
The error is in 4:49. If you replace "non-black things" with a white shoe, you have to do this in both instances of A. So the second part of the sentence is it supports the hypothesis that all white shoes are not ravens, which is correct. (Unless I'm mistaken about ravens.)
It does, in a miniscule way, but I'm not really seeing how it could be instructive and/or useful. For example - All protons have a positive charge. My flashlight contains batteries. Both statements are true but how does one, in any meaningful or useful way, support or detract from the other?
At any rate, I enjoy your videos. Thanks!
I just looked up "albino ravens." Yeah, it's a thing. Checkmate. :p
That was my first instinct, too 😂
Agreed, that was my first thought as well. And even then a raven still isn't black! We just perceive them as such since color/light absorption and reflection is also a thing... it would be like saying leaves are green, we perceive them as such because they reflect green light better than any wavelength
And more exotic species such as the white necked raven.
For the sake of this thought experiment I assume first that you cannot just look it up, then get a decent sample size, preferably from multiple different regions of the planet. Then hopefully find a non-black raven.
In the case on non-black things and looking for a raven among them, it would take an even LARGER sample size(at least a trillion times more) because there are more non-black things than ravens.
In short, while both data-points would be evidence, ravens are just better evidence.
@@cazhalsey8877 that's what we mean when we say something has a color. But you are right in pointing it out anyway, as people tend to forget that, so the occasional reminder is helpful. :)
I swear I remember feeling like the claim (that a white shoe is evidence that all ravens are black) did NOT make sense a few months ago, I'm not sure what changed, but I think this make sense now, here're my thoughts
If I observe a not-black not-raven, such as a white shoe, yes that's evidence that all ravens are black. But how? Let's assume we live in a world where almost all ravens are black. If I randomly select things from the set of all ravens, I'm unlikely to find anything that's not black. Hypothesis confirmed, right?
Let's say that almost all not-black things are also ravens. Therefore, the way to disprove the hypothesis is easy: randomly select something from the set of all not-black things. It's likely a raven, so hypothesis disproven in few tries, even though almost all ravens are black. This is why good science doesn't JUST consider things that "prove" a hypothesis, nor JUST things that falsify a hypothesis, you actually need to use both data sets.
In the case that all ravens are black, limiting yourself only to the set of all not-black things can just as well "prove" that all ravens are blue or green or any color. In this case, you must consider data from the set of all ravens, not just the set of all not-black things.
In the case that most ravens are black, and most not-black things are ravens, limiting yourself only to the set of ravens can "prove" that all ravens are black, when they aren't.
I think the trick here might be selection bias, and why this clashes with our intuition of how the real world works. How exactly DO you select from the set of all ravens, or the set of all not-black things, in the REAL world? By first, constructing them from the set of things near you, i.e. looking around! If it were true that most ravens are black, and most not-black things are ravens, surely we would've seen some not-black ravens by now, given the extreme number of not-black things we see every day. Therefore we must live in a world where:
1) All (or most) ravens are black
2) zero (or few) not-black things are ravens
Observing ravens, AND observing not-black things, helps support this claim.
Failing to observe not-black things leaves open the possibility that most not-black things are ravens
(Ex. if most ravens are black, and most not-black things are also ravens, then saying all ravens are black by only observing ravens)
failing to observe ravens leaves open the possibility most or all ravens are black
(Ex. if all ravens are black, like when Nelson Goodman "proved" that all ravens are blue by only observing not-black things, which are never ravens in this case. It might've been true, but only if by coincidence alone that all ravens were blue, instead of black)
Now if you'll excuse me, I'm gonna go lie down while I untie the knot that my brain has become.
Interesting choice in background music. I don't know the last time I heard a 9:8 beat.
Edit 4:30
It vascilates from 9/8 to 7/8, giving an overall syncopated 4/4 beat.
I thought you were going to end the video showing an albino raven. I love the rick-and-morty style puzzled faces by the way.
My view is this. The set of ravens is a finite set. The set of non-black objects is an infinite set. So the two sets cannot be regarded as equivalent. Therefore, the observation of a white shoe cannot be regarded as supporting the hypothesis that all ravens are black.
A white shoe *does indeed support* the hypothesis, even though by an amount so miniscule, it doesn't really matter.
why? In order to conclude that the hypothesis is 100% correct, we'd have to look at all "things" (∀x ...). If we had looked at all of them and saw that none where non-black ravens, we would have verified our hypothesis. Looking at anything (including a shoe) brings us closer to that goal. The problem is, that one shoe is a pretty small fraction of all atoms we'd have to look at, so it doesn't help by a whole lot really..
My thoughts exactly, and I couldn't disagree with Hempel's interpretation (indeed, I don't think this is a paradox at all). What you really want is a more specific hypothesis, such as "among birds in a particular geographic region, all ravens are black". This leads to a more focused observation strategy, and you stand a better chance (ha) of getting statistically useful results.
No it does not. If I was locked in a black box and thrown in a black hole with some Legos. I could build new non-black things and slowly "prove" that "All Ravens are black" without access to the world
@@44fippe of course you can't count any matter twice. so after looking at each lego piece once, you are done with your observations.
@@georgplaz True but this wasn't matter this was "non-black things" and a lego car is a different thing compared to a lego house even though there are made of the same pieces
@@44fippe I think you still missed my point
My answer will be, no, instead no observation can never conclude anything because no observation is done on the fullest of any context, further it just tells us about the whether probability of occuring of an event is low or high that's all, and this statement also makes sense when you observe the events in Quantum level of reality and that's why Heisenberg uncertainty creeps in, it's kind of scary but the reality somehow keeps itself non-predictable at the most fundamental level. Very interesting video by the way, it's been an intellectual pleasure, and please tell your views too, what you think about it.Thank you..👍👍😊😊
A similar scientific hiccup I remember being mentioned by Martin Gardner: Imagine the hypothesis "All men are shorter than twelve feet tall". Every piece of data collected supports the hypothesis. Then we discover a man eleven-and-a-half feet tall. That does support the hypothesis but at the same time makes it a bit less certain.
Karl Popper has my vote.
But a statement of falseness of a proposition is equivalent to a proposition of truth of some inverted statement
Fun fact: the old Norse described ravens as blue
Huginn and Muninn approve of this message and have taken it to Odin for you.
Oh and we used to call niggers the blue people too. Black is after all a property of hair and garments, dark or green was properties of the sea, white was a property of clouds and snow, while pale was a property of bones and sick people.
I mean if you showed someone a chart of the Norse colors, no one would truly understand them. Specially the several kinds of pale..
@@livedandletdie what I dont understand is all these American nazis playing wannabe viking in prison. More than half of you aren't even Scandanavian. Would rather listen to lame skinhead thrash instead of legit metal. And they follow a man who killed himself instead of facing his enemies in combat. I assume you do too by the language. That's why you will never know what it means to be one of us, just stop trying. People like you give SJWs shit to talk about. You're such a rough edged "viking" here on youtube..LOL
Now what you said about colors was a fine addition to the conversation, but why bring N bombs into it unless you're some fake nazi who thinks hes a viking?
An object being not black should not increase your confidence that all ravens are black, because the second hypothesis is unfalsifiable, due to the fact that the group of all non-black things is unobservable, while the group of all ravens is.
In fact it should, if anything, decrease your confidence because it means that non-black objects exist, therefore increasing the probability that there is a non-black raven. And the more non-black colours that exist, the lower your confidence should be, if you're going that route.
Such a great video! Such a clear explanation, I loved it. Please do a followup with the Bayesian method. I hope you keep making lots of great videos in the future, lots of success!
Given the shoes that these illustrated ravens are fabulous, and all these illustrated are black, then all black illustrated ravens are fabulous
(If A -> C. If A -> B. Therefore B -> C)
Wait, that's not logically sound. Does that make me a bird brain?
But this isn’t really how we classify things. In science we do the observation first and then define the terms based on what is observed. Ravens are defined by many features, and we name that group because of the traits. Defining something before we observe it is more of an artistic practice than a scientific one.
I've got a fourth answer to the Raven paradox:... That is not a paradox!, that's just saying A !=B, hey look a C.
Except you've already proven that A = C
@@juliavanderkris5156 No, you haven't. A sentence that contains C is not equivalent to C.
@Cheeson Toast
Time flies like an arrow.
Fruit flies like a banana.
@@longlostwraith5106 If A is "All ravens are black" and C is "All non-black things are not ravens" they are equivalent. Observing non-black things and observing ravens are both attempts to _disprove_ the hypothesis by finding a non-black bird among the ravens or by finding a raven among the non-black objects. The failure to find a raven among "non-black objects" gives a tiny statistical bump to the probability that no non-black ravens exist. It'll be a much smaller bump that observing a black raven gives, simply because the number of non-black objects is immense compared with the number if ravens: It includes each individual object in the universe that is big enough to reflect light with a color: each grain of (non-black) sand, for example.
The problem with observing non-black objects to disprove whether all ravens are black is that it's significantly less efficient than observing the ravens directly, and that is what our intuition captures.
@@longlostwraith5106 And right now, I'd like a beer.
I would say that propositional logic is just a tool that chacks, let's say, "the road of an argument" and tells you if it's broken at some point.
But it does not show you other "roads" or arguments that merge into the same main road.
So, to make it clear, the point were the argument fails is when you invert your argument with negation, and then your isolated again with another negation, because it is not isolated anymore.
I'll explain myself: when you say "all ravens are black", you're saying just that, it's isolated. But if you say "all non-black are non-ravens" you're including a lot more arguments like "all ravens are blue", "all ravens are green", or even "all ravens are dead" that could follow the same logic. So, when you turn the sentence back and say "observations of non-black being non-raven supports that ravens are black", would be true, but not more true than "supports that ravens are blue" or "dead". And then, you isolated this argument and determine the color of the raven with it, when actually, this argument supports all colors for ravens equally.
Idk if I'm explaining myself 😅, I would be happy to answer any question o read reputations
That's interesting. Makes a lot of sense!
iv seen a white raven... not sure if it disputes the paradox
Hearsay is inadmissible.
There is no paradox. I'm pretty sure I'm not an idiot (but I could be wrong) and there is nothing contradictory about the two statements. I suspect this video was written by a freshman college student who got a B- in a logic class last semester.
that was interesting...
but technically... wouldn't having bigger data set always help?
some data might be irrelevant to the thing you're trying to (dis)prove ... but it still should be better to have it ...
(if you ignore the problem with having to sort out what is relevant and what is not)
I agree, especially if one of the parameters for finding ravens would include; "Large Black Bird". Albino ravens would be overlooked unless you were to use parameters that did not include a color in the description. Everyone knows what a raven is until they see one, maybe it's a crow.
I do not think that more data on shoe color would increase confidence, because there's no place on the data sheet for "shoe color."
.
In other words, logic and science are different, in part because science is a process, not a static set of conditions and axioms.
.
The observation of a white shoe neither supports nor refutes the hypothesis simply because a shoe is not a raven, and is thus not relevant to the claim. If it were to be seen as supporting evidence, this view would be a circular argument. Imagine that we have only ever seen a single raven and this raven's color was black. If one develops the "all ravens are black" hypothesis, and then observes a purple flower, if he concludes that the flower supports his viewpoint, he is confirming his suspicions by reference to his suspicions. It's the "This book is accurate because the book says that it is accurate" approach. So, one cannot use non-ravens as evidence of the claim.
Thus, the only supporting evidence which can exist is another black raven.
Shes physically pretty but her intelligence makes her gorgeous 😍😍😘
The general public don't discern the nuances of hypothesis, theory and axiom.
The example here is equivalent to the "All swans are white" fallacy, because there are black swans.
That's the entire point.
"All swans are black" is logically correct (because the proposition doesn't contradict itself), but empirically incorrect (there are indeed black swans).
@@CocTheElf That is correct with a large enough sample size... Or more accurately with the proper samples.
A scientist could study ravens for his/her entire life and only find black ravens to study, thus concluding that all ravens are black. He/she might even turn this conclusion into a doctrine and use it to bad mouth the people who believe they've seen white ravens, citing that "there isn't any scientific evidence supporting the existence of white ravens) simply because the scientist is ignorant of their existence.
There are examples of white ravens but they are exceptionally rare. And so the Raven Paradox is a perfect example of how the Black Swan fallacy can/has corrupted the scientific method.
"...one of just four albino ravens in the entire world."
www.audubon.org/news/rare-albino-raven-murdered
@@tomharner83 It isn't. As it refers to an object in experience, any kind of principle must necessarily adhere to the realm of possibility.
"the universe is flat" because that is consistent with observations thus far... This is a claim that underlies many other theories.
And there are many such claims in the sciences.
The hypothesis "all ravens are black" would normally be tested as you first describe in the video, by searching for ravens to see if any of them are not black. You could say that there exists a finite set of {all ravens} and we could search it for ravens with the property (not black). If we manage to find every raven in the set and none of them have the property (not black) we would have proven our hypothesis. This way each new observation of a black raven further supports the original hypothesis.
However there is also another way we could test our hypothesis. What if we imagine a set of {all non-black things}. This set, while very large in size, would also be finite. We could therefore alternatively search this set to prove our hypothesis. If we manage to find every non-black thing, and none of them are ravens, we would prove that all ravens must be black.
If we then observe a lot of non-black things, and none of them are ravens, it would give credibility to the hypothesis. For each new non-black non-raven thing we find the chance of a non-black raven existing would get smaller (since the set of all non-black things is finite in size).
Therefore, in a roundabout way, you could argue that finding a white shoe further supports the hypothesis that all ravens are black.
The way I like to think of logical equivalence between two statements is that if one is true, then the other is true, and if one is false, then the other is false. Great video!
In certain (many?) situations, one of those statements is more useful than its equivalent. Given there is an almost infinite number of objects (since each object can be broken down into many different sub-units, including the quarks and leptons of its individual atoms and every possible combinations of the sub-units, and this applies to every object in the universe), of which a near-infinite number would not be black, but there is a much smaller number of objects that happen to be ravens (about 16 million). So, empirically, the process of checking 16 million ravens is much more useful that checking the number of non-black objects. In fact, it wouldn't take long before you found a raven that is not completely black (two of the nine species have a white patch and one is brown) and eventually a white raven (not albino, but leucistic) hence disproving your theory.
My main point is that just because they are logically equivalent, they are not equally useful. (Just like the cafe at noon example, one way of putting it is much simpler and hence easier to use). A logical empiricist would surely focus on the most useful of any collection of logically equivalent propositions.