CORRECTION: Throughout the section on deduction, I separated validity and soundness into two distinct concepts. I did this for explanatory reasons to give clear examples of different combinations of valid/invalid sound/unsound. But strictly speaking, an argument is sound exactly when an argument is valid AND with true premises. As such, there isn't actually such a thing as a sound argument which is not valid. I think my explanation makes the concepts clear, but I regret not summing up the section on deduction with this point.
@Another Roof Excellent video! As a mathematician I have been trying to explain this to people for years, now I have a video, to which I can point people! What was that *challenge* you mentioned at the end? Is there a link to the problem description?
That is actually an incredibly interesting thing you bring up. The concept of a "sound argument". Layman wise it is essentially when the arguments makes sense, and the conclusion following from the arguments makes sense in context from the premises and the arguments. They are obviously almost never valid, as in completely true, since we as humans and our reasoning is... well flawed... But because we are flawed we use perfect concepts to describe something imperfect, but pretty close to the concept. Like well... Perfect, valid, true, false, etc. Despite in many cases perfect is obviously wrong, since something perfect is unlikely to ever exist. Something valid has the same issue, so does true and false statements. Essentially outside of an abstract system like math, these statements will always have some level of imprecision :P
@YeYaTeTeTe The term you allude to is "logical." Logic does not care whether the premises are true or false, believed or not. Logic does not tell you whether a conclusion holds true. Logic does tell you that, under the hypothesis that the premises be true, the logically obtained conclusion would also be true. Absolute truth does not exist and is not assumed anywhere in logic.
Sherlock Holmes and Dr Watson went on a camping trip. After a good meal and a bottle of wine they lay down for the night, and went to sleep. Some hours later, Holmes awoke and nudged his faithful friend. "Watson, look up at the sky and tell me what you see." Watson replied, "I see millions and millions of stars." "What does that tell you?" Watson pondered for a minute. "Astronomically, it tells me that there are millions of galaxies and potentially billions of planets. Astrologically, I observe that Saturn is in Leo. Horologically, I deduce that the time is approximately a quarter past three. Theologically, I can see that God is all powerful and that we are small and insignificant. Meteorologically, I suspect that we will have a beautiful day tomorrow. Why, what does it tell you?" Holmes was silent for a minute, then spoke. "Watson, you imbecile. Some bastard has stolen our tent."
It would be funnier/actually clever, if the tent part didn’t just come out of nowhere. You didn’t mention they went to sleep in a tent. Maybe they are sleeping outside?
At 7:40 it would be worthwhile to point out that false premises can lead to true conclusion. E.g. "All giraffes are mortal" "Sokrates is a giraffe" "Therefore Sokrates is mortal"
@@detroitpolak9904 You must have some amazing deduction skills that you can tell so much about me from my spelling. I'm German, for Christ's sake. It's how we spell Socrates. It's an understandable mistake to make that doesn't even tell you much about my ability to spell, never mind all the rest, you dimwit.
The problem with abduction being, perhaps, the most common form of reasoning is that we humans tend to be pretty bad at judging probabilities. It's hard to identify the most likely conclusion if your likelihood estimates are noisy.
The biggest problem with abduction is confirmation bias. When we form conclusions we almost never reason to disprove our conclusion and only think of arguments that agrees with the conclusion.
Deduce, generalize and lack substance, Induce, observe and lack implementation Abduct, and well, you've got a lot more problems. Too certain someone is guilty, leaving no room for any other freedom of exception. Induction > reductive logic and uninteractability (+observation/-implementation) Abduction > probabilistic and unexceptionalism (+verdict/-possibility) Deduction > abstract statistics & stereotype. (+group/-representation)
Eh, nothing counts unless you do it in non-binary logic. Ordinary binary logic is full of paradoxes and inconsistencies, a fact Sherlock knew all too well. The so-called "informal fallacies" (such as the relevance fallacies) are only "informal" in binary logic. In 3-valued logic, the informal fallacies become formal fallacies. So when you say "FORMAL LOGIC" you really mean non-binary logic. Which is constructive, and formal, and better than binary logic. As Spock would say, "My logic is superior to your logic." Plus you know using words in all caps means you are a bot
What is there besides true and false? Paradoxes. There's a branch of logic called constructive logic, which accepts a conclusion as true only if a specific example can be constructed. Classical logic says that proving that a statement is not false is enough to prove that it is true. This idea is called the postulate of the excluded middle, since it assumes that there is nothing between true and false. But constructive logic doesn't use that postulate, since using it would mean not having a specific example to verify the conclusion. (For example, the argument for God's existence briefly discussed in the video is a valid deduction that it's impossible for some first cause not to exist, but it fails to supply a specific entity that must be the first cause. So constructive logic agrees, given that the premises are true, that a first cause can't _not_ exist, but it refuses to go so far as to say that a first cause _does_ therefore exist.) In that way, constructive logic has three truth values: true, false, and neither true nor false. This has nothing to do with probability or fuzzy logic. The third value allows constructive logic to engage directly with paradoxes without falling apart. It's possible to use it to prove that a statement like "This statement is false" is not true and is also not false, without either of those conclusions disproving the other. In classical logic, the best we can do is assert axiomatically that paradoxes don't happen, which is a bit awkward because paradoxes do in fact happen within logic itself.
@@jeremydavis3631 If you're adding a "neither true or false" value for statements like "this statement is false", for completeness shouldn't we also have a "both true and false" value that would apply to sentences like "this sentence is true"?
Just had a bit of a thought. If deductive reasoning means the conclusion necessarily follows, then deductive reasonining is ridiculously rare in general. Even if you find the bloody knife, do a DNA check and the suspects DNA is on it, and you have several witnesses, that does not "deductively" follow to him being the actual perpetrator. The witnesses can remember wrong, the DNA on the knife could've been placed there earlier, etc. So the conclusion doesn't logically follow. I like this, very very interesting video
Agreed! That's why I discuss how usually abduction and induction are the only available options. Deduction is mostly reserved for the abstract like in philosophy and mathematics. Thanks for watching and sharing your comments in the live chat!
Yes, deduction pretty much only happens with abstractions. Almost nothing in real life is certain enough to produce sound deductive arguments. It's fairly common in computer programming, and even there it's only sound as long as bit flips are not involved... which they often are....
@@KohuGaly Welcome to cosmic radiation, and nearby radiation, and radio transmitions, and... I'll just stop the list here :P Bit flips is the bane of programmers until they actually invented a way to kinda deal with it XD
We might call it rare, or we might just be using it so thoughtlessly and automatically that we do not notice it. If someone says that all the food is in the fridge, we should not need to ask where to find the eggs because we can use deductive reasoning to conclude that the eggs are in the fridge, yet that reasoning is so obvious and effortless that we do not pay attention to what we are doing.
Regarding the Sherlock Holmes scene when he was introduced to Mary: Something a lot of people miss about this scene is that he _intentionally_ got Mary's past wrong in an insulting way so that she and Watson would get up and leave. This is because he doesn't like the idea of them being together. Right after they leave, the waiters bring food to the table even though they hadn't ordered anything -- Sherlock must have ordered food before they arrived, and told the staff something like "A pair of friends are going to sit down briefly and then leave again, wait until after they leave to bring my food."
I agree with most of what you said except the last part. It's his favorite restaurant. He knows exactly how long his food will take to get there and knew he only needed x amount of time to chase them away lol I bet he got that down to the second, if not millisecond
@@taloutezero That may be possible, but I doubt it. I work at a restaurant, and in my experience it's never that precise. The time it takes for the staff to come take the customer's order, the time to relay that to the kitchen, how long it takes to prepare, how long it takes to bring it out to the table, all those times are variable depending on a lot of factors that Sherlock has no way of knowing ahead of time. Also when a customer has already placed an order and then two other people show up, the usual procedure is that the waiter will hurry over to take their orders as quickly as possible so they can start getting it prepared, because they like to bring the whole party's food all at once. (at least, that's how it worked in every restaurant I've been in) They were sitting there for quite a while and nobody came, likely because the staff had already been told that they'd be leaving again soon.
@@John73John I agree with what you said but I think its also both. He probably knew how long it would take to prepare his food. I doubt Sherlock would let his food get cold while trolling Watson and Mary so I think he told them the others wouldn't be eating AND he timed the foods preparation. In those days, would it have been easier or harder to find out which staff was on duty? I can't imagine that Sherlock has no idea who is in the kitchen of his favorite restaurant (especially on days he goes there) or how long stuff takes to make there.
@@taloutezero I don't think it's possible to conclusively deduce one way or another (see what I did there?) but it's a lot more than just "who's in the kitchen tonight?". Maybe one of the other customers ordered a complicated dish and the chef's attention was occupied for an extra couple of minutes before he could start working on your order. Maybe the waiter takes your order and then decides to visit another table and take their order as well before relaying both to the kitchen. Maybe the carriage John and Mary arrived in was a minute early or late because of some condition on the road that Sherlock didn't know about. Any one of a hundred things could happen to mess up the timing. Real life is way too complex and chaotic to make a prediction of something like that and get it right down to the second. He could get a general idea (within, say, 5 minutes on either side of a bell curve) and well within the time the food would still be hot if it's kept covered.
@@John73John I guess I'm deriving my conclusions from who he is as a person. If Sherlock Holmes has deemed a place his "favorite" out of all similar places, I judge by his self love and indulgence that part of the reasoning for him is the timeliness and predictability in their service. I could be wrong and it could be a hectic unorganized environment but considering he thinks the universe of himself, I can't imagine he would go some place prone to delays in his orders or very untimely service. I understand that reality can be chaotic and nothing is guaranteed but this is one of the few "public" (I know its a fancy reservation only place but people who aren't in his inner circle are considered public) spaces that could get Sherlock to leave his room AND dress up. I don't think my conclusion is far off.
Thank you for making this clear. It always drove me crazy that if there is a link of half a dozen steps, each with a 70% probability of being caused by the previous, then it is concluded that the solution must be so and so. In reality, we are already down to 12% probability.
Great summary. This has always bothered me about detective stories. My reaction always was "you can't know that, there are so many other explanations why that may have happened!" Abductive reasoning is of course essential for many practical solutions, but detective stories often apply it in pretty far-fetched ways that only work because the author wants it to.
yes, me too! you can think of other possible explanations, but of course in the story the detective is right and everyone is like "wow, you're a genius!" Grr.
@@DMW4 You: Source? ChatGPT: I made it up The actual issue is semantically the word "deduction" includes abductive reasoning. In fact that's the way the word is mostly used
That's why I hate Agatha Christie. The whole storyline goes on giving hints and motives, and, at the end, Poirot says IT WAS HIS COUSIN THAT DOESN'T EVEN APPEAR IN THIS BOOK
I think Doyle himself didn't like how everyone thought that holmes was a genius, and wrote a short story where watson refutes his 'deduction' with a different valid answer. He wanted people to know that sherlock was smart because he, the author, already had an answer and then wrote the path to get there, not the other way around
@@chaotickreg7024The Doctor himself may as well be a weapon. Even discounting how many times he's harmed/killed someone through his intellect and charm, he's also been throwing hands since the First Doctor. Hartnell defenestrating Roman soldiers was such a bizarre image.
I think it's worth noting that all of these types of logical reasoning are closely related. Abduction is just Deduction with the word "probably" covering for otherwise invalid or unsound reasoning. "A: Toast is made in a toaster B: This is toast conclusion: This was made in a toaster" is an unsound deductive argument, but "A: Toast is (normally) made in a toaster B: This is toast conclusion: This was (probably) made in a toaster" is a perfectly reasonable abductive argument. In addition, Abduction and Induction are also strongly connected to each other. For example, "A: The road is wet B: Rain can make the road wet C: Rain probably made the road wet" is an abductive argument, but how do we know that rain is the most likely explanation? Well, if you look at a bunch of examples of things making the road wet, you'll find that the most common one is rain. We've just concluded a general rule from a bunch of specific examples- that's induction. Nearly all abductive reasoning works this way. Induction doesn't make any predictions on it's own: it's value comes in contributing evidence to an abductive line of reasoning. Abductive lines of reasoning rely on having some knowledge of what is or isn't likely, which only induction can provide. Without using both, neither is particularly helpful. Side note, nearly everything relies on inductive and abductive reasoning. We can't be deductively sure that the universe will exist tomorrow, for example, or that the laws of physics will be at all the same. We must rely on inductive reasoning to conclude that, since the universe has continued existing every day so far, and the laws of physics have remained consistent for as long as we've been aware of, that they will remain the way they are as a general rule. And abductively, that means that the universe will probably exist tomorrow.
We cannot proof the "soundness" of deduction. Because facts and observations might always be wrong. However, the "validity" of a deductive argument can be verified. Also, in mathematics and philosophy, deduction is very much "valid" and useful tool.
Well there's also not much reason to think about if the laws of the universe stopped working. There isn't anything we could do to stop it, and we would be fucked if it happened, so there's not much reason to spend time and energy doing anything but acting as if it will continue existing.
Someone ought to mention the concept of "mathematical induction" and how it is actually a type of deduction. Maybe that's obvious to everyone, but it feels like the sort of thing that may need to be said in every discussion of the distinction between deductive and inductive reasoning.
it's weird that Mathematical Induction is the proper English term. the German term is more or less "complete induction": you start with inductive arguments, but show that it is the only induction possible, hence completing the induction to a deduction.
It’s probably called “induction” because it somewhat feels like inductive reasoning. The proof sort of emerges out of our recognition of the general pattern.
There is a sense in which mathematical induction is not deduction (and this is very confusing and there are lots of schools of thought on this): Mathematical induction is not possible in a first order finite axiomatisation, essentially it is NOT deductive in a comprehendible first-order theory. You need to impose the existence of the inference for every numeral acted on by the function symbol in the theory, and there are infinite numerals. (to be coy: it's not a premise, and it's not a valid deduction from the premises, yet the general rule is 'induced', then 'abducted' into being applicable). This doesn't prevent induction from being *constructive* though, as we can use computers (or equivalently, recursion) given infinite resources to be able to make conclusions from the infinite first order theory, but to do this we have to discard double negation elimination, and then we have issues of consistency (without DNE maybe some contradictions you could have arrived at now can't be arrived at). But, even an infinite first-order theory is not enough to constrain the suitable models of that theory, what we conclude from mathematical induction is not that the conclusion applies to *all* numerals, but just the ones are successors of our base case. Or what this is really saying is that you cannot write the conclusion of mathematical induction in first-order logic, as otherwise you need infinite terms in the single statement of your conclusion. When we make a computer evaluate the statement we are already making assumptions about the model in order to even run the program. So there is some meaning to discarding mathematical induction in some deductive scenarios. Obviously this only about first-order logic, higher order logic is its own can of worms that I can't say much about.
@MagicGonads the first-order induction schema is still true in nonstandard models of arithmetic, since of course that's what it means to be a model of PA. "For all x, P(x)" really does follow from P(0) and P(x) => P(Sx) (where P is a first-order formula with one free variable). The reason this works is that nonstandard naturals have infinitely many predecessors. Hence around nonstandard x there is a copy of *Z* akin to {..., x-3, x-2, x-1, x, x+1, x+2, ...}. The model, however, is forced to assert that it's turtles all the way down for that segment, meaning P(x) really is true. Of course, second-order induction ends up failing in such a nonstandard model, precisely because second-order logic -- basically, a logic that can see subsets of the model -- can "observe" the gap that is created. Summing things up, though, we have that mathematical induction is a deduction purely because we assume it as a premise for every first-order formula. Lastly, as for making induction constructive, there are no issues of consistency compared to PA. First-order classical PA is strictly stronger syntactically than first-order Heyting arithmetic (PA without excluded middle).
Another group of frequent ring removers are medical professionals like nurses. The ring can protect any pathogens and filth trapped under it from being washed off. So while my mother was a frequent wedding ring remover, she is not an adulterer
You also can't wear metal objects while getting an x-ray or being near an MRI machine. So that's another reason why medical professionals or just any scientists might remove their jewlery.
Good point, however the coloration difference would come (usually) from exposure to sunlight, outdoors. Therefore a nurse who presumably only takes her ring off indoors might not have a discernible untanned region.
She "may" not be an adulterer. And she "may" not be a frequent adulterer. On the other hand she could have been schtupping a couple of the neighbors and the milkman and the postman and various repairman while wearing her ring. As she could have also done in a one-night fling before you were born. Also, though I have no hard data, I believe that married men remove the rings to hide their marital status in order to have illicit sex more often.
I'm very pedantic myself, but I'm a language teacher so I'm personally pretty okay with a word having a general public meaning different from its academic meaning. I do understand what you mean though, for as incredible as it sounds, I once had to explain (or tried to explain anyway) to a creationist that "theory" in "theory of evolution" doesn't mean "hypothesis".
Hmm, "hypothesis" is not far off, since scientific theories are never proven. Newtonian dynamics are useful and taught in physics class, but that theory is nevertheless wrong. Similarly, the theory of evolution is at least likely to be incomplete. But the term "theory" is indeed not intended as "speculation".
@@landsgevaer Newtonian mechanics isn't wrong, it's incomplete. It breaks down at high speeds, but within it's boundaries it's close enough. Newton himself knew his theory was incomplete. The same applies to General Relativity, it breaks down at really small scales. To be fair though, the term "theory" has become somewhat muddied in academia. I blame string "theory" for that (more like string conjecture). Theories are hypotheses that have been tested and validated so often, it would take an enormous amount of evidence to refute them. So all theories are hypotheses, but not every hypothesis is a theory. And that's a simplification, most theories are a set of hypotheses.
@@ayumikuro3768 I would argue that Newtonian mechanics is fundamentally wrong still. It treats space and time wrong (fibre bundle vs. Minkovski space). You can't repair that by simply adding something while retaining its foundations, so I cannot call that "incomplete". I agree it is a very decent approximation, and as a framework it is very useful, but it is fundamentally wrong nevertheless. But setting all that aside, since you agree that theories are not unlike hypotheses, for the purpose of this thread we agree. Thanks. 🤝
@@landsgevaer In the debates what is usually referenced is "Darwinian evolution" as a particular theory which is straight up wrong on a number of points. What matters in science is predictive validity, and no scientific theory can be "complete" even for a small domain not least of all because things can be re-conceptualized
This calls for a new Sherlock Holmes series, where the guy is just like Saul in Better Call Saul, a faker detective, who always comes up with supposedly brilliant deductions which frequently end up being wrong, but the guy conspires creatively to make himself look good every time, in ways that one could call "amazing", achieving some level of success.
There is an old movie called without a clue.... In which Sherlock is an actor and Watson is the one who solves the crime with Sherlock being the face and voice of Watson
I would argue Sherlock Holmes does a lot of Inductive reasoning as well - depending on which interpretation of the character you are watching, I guess. In many versions of Sherlock, he spends a lot of off-camera time, and just a tiny bit of on-camera time, exhaustively studying various obscure events to form inductive conclusions about the results, unrelated to any particular case. Then later when he encounters a similar event during a case, he is already equipped to pull out a pre-considered inductive rule and apply it to the observations made. I suppose you could reasonably argue for either "induction" or "abduction" as a label for that final step, but it's the previous inductive step that occupies the character's time even though it's the last step that is shown on camera, due to being more exciting.
The problem I have with the wedding ring debunking argument, specifically in regards to how just because it's cleaner on the inside and is removed frequently, doesn't mean she's a cheater, is that it doesn't take into account the state of the rest of the jewelry she wears, nor the rest of her appearance as a whole. Sherlock explains that while she cares a lot for her appearance and the rest of her jewelry is clean, the wedding ring remains the only dirty piece of jewelry on her, implying that it's cared for less than the rest of her stuff. Why would someone of that nature care so little about her wedding ring of all things? This is what he couples with the fact she removes it frequently to ultimately come to the conclusion that she's unhappy in her marriage and cheats.
@@Sammysapphira The only aspect of it I might consider bad writing is the jumping straight to cheating angle and having a series of partners. I would probably have stopped at her being generally unhappy in her marriage as there wouldn't really be much evidence to suggest she was actively doing anything about it. But her being unhappy in her marriage is clearly illustrated in the state of the rest of her jewelry compared to the wedding ring, but people ignore that to just say Sherlock said "taking your ring off means you're cheating"
Good video, that was interesting. I'd say it's not misappropriation to call what Sherlock does "deduction" or "logical" because these words were used by people way before philosophers logicians and mathematicians formalized them to mean more specific things. I'm a physicist, and I can't really complain when crystal healers talk about "negative energies", because people used energy to mean liveliness-stuff, and generally vibe, along with 'the ability to do stuff'. It is fair to ask people nicely in your case, to say "hey, here's a better word for what you mean, now we can tell these things apart", I think most people, if you had their attention, would say sure, sounds good to me. Others will probably call you a nerd and ignore it lol
@@mawillix2018 I guess that would make me allergic to the manosphere. Makes sense, that terrible community irritates me just as much as almonds or birch pollen
20:13 "What if Sherlock isn't doing any of the three types of reasoning?" I've always seen the "whatever remains" part to actually mean "whatever remains", not just what is known to you. That would make this statement actually true, and if Sherlock isn't using any of the three types, then he must be using something else. That something else is still part of "whatever remains" in my interpretation. Though I can definitely see how it could be interpreted differently.
Well, "if I have correctly eliminated X, Y and Z, then the truth must be contained in the set of possibilities excluding X, Y and Z" is pretty solid (mostly because it gets around the possibility that one of X, Y or Z should not have been eliminated, and doesn't say anything about how broad or narrow the remaining field of possibilities is)
To me. This is simply indicating that the writer doesn't know how to write detective stories. So I look it up and... yeah. The directior doesn't like detective stories
Off the top of my head, I’d say the problem with trying to eliminate possibilities in an environment where the possibilities aren’t outset for you, is that you never know if you have in fact eliminated all other possibilities, meaning you’re still at the mercy of your own biases and/or limitations.
@@Silkie_Dragon Hence why almost all good detective stories are set in some sort of location where things can't change like a moving vehicle or a remote mansion. And in a lot of other cases there's some other key limiting factor that narrows down the possibility space.
@@Silkie_Dragonbut our limited understanding of the world does not erase the general truth of the statement itself. “If you eliminate all impossibilities, whatever is left is true” does not say anything about a human’s ability to correctly ascertain that truth. I could even break it down into a deductive argument. P1: Something happened P2: Anything that did not happen could not have possibly happened Conclusion: when you eliminate the impossible, whatever remains (…) must be the truth.
I completely agree with the conclusion, its also why a "theory" has come to mean a hypothesis instead of something that has overwhelming evidence. (I don't like to say proof outside of deductive math reasoning as it's only guaranteed to always work and be true in hypothetical math land)
@@DMW4 how? do I come over to your house and check what you asked chatgpt before asking that question? the answer chatgpt gave you says, "and there are numerous examples in the stories where he uses deductive reasoning to solve cases, as I mentioned in my previous answer." Which means this wasn't the first question. I do understand that he does employ deduction many times as it is very hard not too, but sometimes an example outside "as I mentioned in my previous answer" is quite useful...
@@DMW4 Chill dude, he just wanted to know the previous answer. Your making drama over it. To be fair I also want to know the previous message so I can understand him.
One of the things I’ve always loved about the novels is Watson admitting that a lot of the time Sherlock is actually wrong, & the instances in which he actually pulls something remarkable with his strange method he selectively presents those stories to the public. This follows logically; making huge categorical assumptions & coming to wild conclusions about mundane phenomena would make you a bit foolish more often than not.
Well, they always try to make film/TV adaptations entertaining, which sadly means turning Sherlock Holmes into a magician. But after reading the original stories by ACD I get a feeling that Holmes does use deduction, alongside the other methods. Firstly, he is introduced as a consulting detective, which means he mostly applies already solved cases to fresh ones. This gives us the idea that his reasoning must be pretty solid. Secondly, many of his conclusions are: 'you have a tattoo that could only have been made in China, therefore you have visited China'. Unlike on the silver screen, he often seeks more evidence before jumping to conclusions; but of course he also theorises a lot. That is to say, SH stories have a ridiculous amount of mistakes for a detective series, so I wouldn't be surprised if ACD didn't really know what deduction is, or wanted to give an impression that Holmes simply cannot make a mistake, by choosing the most foolproof way of reasoning. The video itself is great, and it explains the difference between the three very well, and with visual representation. Many thanks!
The video does not prove that Sherlock never used deduction. The video explained instances in which Sherlock misused the term 'deduction', but since it did not examine *all* of Sherlock's arguments or conclusions, it did not prove that Sherlock 'never' used deduction. Nor did the video prove that all unexamined instances fit into the same category as the examined instances. Therefore, ultimately, the title was clickbait.
@@KSignalEingang I agree with you. AnotherRoof's ranking is based on the degree of sensibility and reasoning used, but if you are talking about who the best "Holmes" is, then Jeremy Brett is, in my opinion too, the best of them all. He is the Sherlock Holmes of the books.
The term deduction can be used by bad faith actors just like a lot of logical fallacies so it's important to be able to dissect the elements. Thank you very much for this!
19:32 In the books Sherlock Holmes actually researches a lot of what he uses to reason when investigating. I remember faintly he testing different types of tabaco for something. Maybe that was on that UK tv show, I don't remember. I think in the books it makes clear he studies and examines a lot of behavior of things and people in his 'spare time', outside of investigations.
24:50 this is exactly what I was thinking as I was watching this section, glad you touched on it. Though I will say, the closer I get to the end of my phd the more I think its not necessarily true that abductive reasoning is *not* the approach taken by science. It is probably the one we'd like to avoid using if we could but as you say right after, its often all we have, and thats true in science as well and is often the motivator for further research, typically once the technology or theory (or funding...) becomes available. But I love this one, always up for a good math+popculture merger.
Good to hear from you again! Yeah totally agree! Abduction to me is nearly always the first step -- find the patterns and plausible explanations, then seek to investigate to prove or support later.
I believe one of the problems with Sherlock's "deductions" is everything that's not shown in the movies/episodes because it would make them 10x longer, for instance, he's constantly ruling out possibilities (with whatever reasoning, be it deduction, induction, abduction or just logic) before simplifying the results for easy "understanding" by the lesser gifted. So, the inside of the ring being clean and adulturer premise and conclusion is the last remaining possibility after he has removed the other possible possibilities (for instance frequently removed due to work reasons etc), ie the premise would actually be several pages long but simplified to a short sentance. I guess it still might not be pure deduction but it atleast explains a bit more about the process and premise.
Oh man, when you were doing the "wet road" and "rained last night" diagrams I wanted to reach through the screen to yell "Noooo! The size of those circles are misrepresentative of what would most likely happen in the real-world!" and then you went ahead and adjusted the sizes of the circles. Waves of relief washed through the ether and natural order was restored to the universe. Liked the yellow Alex easter egg. Also the old-timey reel of RDJ Sherlock to get around copyright. And the quick "formal" suit side gag. And the Denis, Fincher, and Ritchie references to incorporate your love of film into the vid. Great way of teaching deductive, inductive and abductive reasoning. The whole video was bloody excellent. RE: part 2 puzzle video I suggest you do it separately to your next planned video. For the simple reason that we get more videos. The yt algorithm is a fickle beast sometimes, with a large element of luck, so if you can do two quality videos instead of one, you're effectively doubling your chances of an algo-boost. More opportunities of engagement without impacting quality, and you're keeping the content recent + frequent with viewers.
Thanks for your comments! I've said it before elsewhere but my original channel idea was film review / analysis, and I think my desire to chat film creeped in here! Yeah still mulling over the Countdown idea. Lots to discuss. The algorithm shined on the last one, maybe I'll earn its favour again!
This is leading me to the headcanon that Sherlock doesn't actually know what the difference is between forms of reasoning - he has a great track record of pulling it off, but he's actually really bad at explaining how he arrived at his conclusions. It's already canon that Sherlock doesn't bother to learn about things that he deems irrelevant to him - like the movements of celestial bodies - maybe he doesn't care to know how his own mind works. I feel like that would fit in with his existing character flaws
I think that's just a BBC thing. In other versions that I've seen, Sherlock is pretty well-versed in general knowledge and current events. Not knowing how celestial bodies work makes him look like an uneducated pleb.
@@One.Zero.One101 In the original books he also doesn't know about astronomy (and literateratue) in the slightest, being astounded by the idea of the solar system, and there are a few other things like gardening and politics that be barely knows.
@@EthSephCW17 For anyone interested, Watson himself wrote about Sherlock's knowledge. Which goes like this: Sherlock Holmes-his limits. 1. Knowledge of Literature.-Nil. 2. Philosophy.-Nil. 3. Astronomy.-Nil. 4. Politics.-Feeble. 5. Botany.-Variable. Well up in belladonna, opium, and poisons generally. Knows nothing of practical gardening. 6. Geology.-Practical, but limited. Tells at a glance different soils from each other. After walks has shown me splashes upon his trousers, and told me by their colour and consistence in what part of London he had received them. 7. Chemistry.-Profound. 8. Anatomy.-Accurate, but unsystematic. 9. Sensational Literature.-Immense. He appears to know every detail of every horror perpetrated in the century. 10. Plays the violin well. 11. Is an expert singlestick player, boxer, and swordsman. 12. Has a good practical knowledge of British law.
Excellent video, thank you! Very well worded conclusions in last 4 mins. Even deductions can be tricky. All bachelors are unmarried men. Sarah is a bachelor of science. Therefore Sarah is an umarried man of science. Meanings are slippery and can alter from premiss to the next, sometimes subtly.
As a Sherlock Holmes fan myself (I consider Doyle's stories to be my favorite literature), I've always kind of thought this was funny. Sherlock is pretty much always just making assumptions not logically deducing facts. It doesn't hurt my enjoyment of the story or the character, though. This was an interesting dive into what each term specifically means.
@@DMW4 , ChatGPT is not an authority on anything. To illustrate this, I just went to ChatGPT and told it Sherlock Holmes doesn't use actual deductive reasoning. As you can see from the following response, it agreed. You are correct. Pure deductive reasoning is only applicable in certain contexts, such as formal logic and mathematics, where the rules of logic are well-defined and the premises and conclusions are absolute. In that sense, it is true that the deductive reasoning used by Sherlock Holmes is not the same as the pure form of deductive reasoning found in formal logic. However, it is still common to refer to Sherlock Holmes' use of logical inference as "deductive reasoning" in a broader sense. Sherlock Holmes uses deductive reasoning as a shorthand to refer to his process of elimination and logical inference, even if it does not fit the strict definition of deductive reasoning. This is likely due to the fact that deductive reasoning is a commonly understood term that conveys the idea of logical inference, even in situations that do not fit the definition of deductive reasoning. Overall, while the terminology used to describe Sherlock Holmes' methods may be imprecise, it is clear that his approach to investigation involves a combination of induction, abduction, observation, and intuition, all of which contribute to his highly effective and influential methods.
I haven't learned about what abduction is while I was in school/university. And I think we should teach about this and give it some attention not just put spotlight only on deduction and induction. Even in math when I read some math proof, it feel like proof writer already know the answer and they use deduction to proof it later. (And I always left with an unanswer question "what lead them to this answer in the first place?" and I often can't find it becuase spotlight was put on the finished product, the deductive proof itself)
First, you are the best, I really understand how set theory defines numbers now. I read Godel, Etcher, Bach, but I really didn't get the proof until you explained it. Your reference to "Pigs On The Wing", that is golden! Please keep making these!
I am so glad you explained the unsoundness of the wedding ring argument in this video, because the moment I heard it I was questioning it’s soundness but without realizing that’s what I was doing, I just figured I must not know something about how removing wedding rings effects the rings. This confusion happens a lot for me and when the argument comes from a figure of intellectual authority I will remain skeptical of it but assume I must’ve simply missed something that they know and I don’t. Now when I get that feeling I’ll do more than simply remain skeptical since they might be intentionally glossing over information to support their argument, and I’ll see if there is any reasonable explanation for the steps that I have not been shown.
The problem I have with the wedding ring debunking argument, specifically in regards to how just because it's cleaner on the inside and is removed frequently, doesn't mean she's a cheater, is that it doesn't take into account the state of the rest of the jewelry she wears, nor the rest of her appearance as a whole. Sherlock explains that while she cares a lot for her appearance and the rest of her jewelry is clean, the wedding ring remains the only dirty piece of jewelry on her, implying that it's cared for less than the rest of her stuff. Why would someone of that nature care so little about her wedding ring of all things? This is what he couples with the fact she removes it frequently to ultimately come to the conclusion that she's unhappy in her marriage and cheats.
24:50 i would argue that the abductive approach is often used in archaeology wherein there is scarce information to base conclusions on. While induction isnt foreign to this science, cases in which it can effectively be used are not common.
The problem with the : - some of b is is a - some of c is in b - therefore some of c is in a Is that the initial example would have constructed a triple nested Venn diagram, where a is entirely with b, and b entirely within c. The language kind of implied it, but not explicitly, and that's where the issue first artist. Your analysis of the Venn diagram you drew is also perfect, alongside your counter example, but I believe we may need to change how we word things to disambiguate
This channel is a golden mine, love it! Last week I was explaining formal logic at class and Sherlock Holmes came instantly as an example of deduction, that's if you take the crime scene as a closed system with relations of literary necessity. Seeing this video I think I will restrain myself to syllogisms next time to not cause any confusion hehe 😅
Oh, wow. Such a source of frustration to me. Thanks for explaining that the reason I never really understood what “deductive” means is because people almost always misuse it. I think the true meanings do matter because (in the US)… well, if people use these words at all, it’s usually some sort of power play. Like, they don’t remember anything except that deduction is supposedly the “best” type of reasoning, so they say something is deductive to imply that it’s unassailable, not that it’s sound. Whether or not I say it out loud, it’s going to be a huge help for me to be able to say, “Aha, but what you’re talking about isn’t actually deduction!”
Wow. You do have a knack for producing hugely thought-provoking videos and making the abstruse absurdly approachable! Yet another of yours I thoroughly enjoyed ...though I feel bad at having never grasped the formal differences between the types of reasoning before. But hey, my degrees are in the liberal arts, so ...par for the course, I guess😅
@@DMW4 Well, the obvious first response is, "citation required". If there are many instances of Holmes actually deducing something, let's have at least one specific instance, rather than mere assertion. ChatGPT should be better than that! Second thing to say: I don't think it matters. The significance of this video, for me, is that it lays bare the existence of three distinct types of logical reasoning and then goes on to explain how you tell one from another. In and of itself, it is sufficient to its purpose and needs no reliance on Conan Doyle specifics to make it's point.
@@DMW4 Your main point is simply wrong then. The video's title is a mere assertion, not a logical deduction, induction or abduction. The best you can say is, "it's wrong", therefore. It's not an example of a logical fallacy at all.
@@DMW4 The rather obvious point I was making is that since the title is a mere assertion and not a logical deduction, it cannot be a logical fallacy. It is merely correct or incorrect. Like your assertion that it is a logical fallacy. There's nothing logical about asserting something. Therefore mere assertions cannot be logically fallacious. As you put it, a "logical fallacy is flawed, deceptive false **argument**". If I say "the sky is polka dot pink and purple", that isn't an argument. It's a statement. It's an incorrect statement, of course. But it's not a reasoned argument.
@@DMW4 If you had confined yourself to saying it was incorrect, I wouldn't have argued with you on the point. Your claim of 'logical fallacy' was what I took issue with. I would (and did!) ask you, however, to back up *your* assertion with a citation. Which you failed to do. If Holmes frequently resorted to the use of deduction, cite me one example of him doing so. You were the one making that claim. Regardless of your source, you need to back it up. The entire video has made a good fist of explaining why your assertion is incorrect, after all. A simple citation can refute that claim.
New viewer here. I loved that you used the blackboard as a visual aid as you explained each type of reasoning. It has helped me to very clearly discern the differences between each. The examples you provided through text and speech were also very helpful. I think I have a sort of mixed learning style; I cannot solely rely on visuals, speech, text, or personal experience by themselves. Some combination of these must all come together so that I can truly understand a topic. You've done well by combining the 3 of 4 of them. Hopefully one day, I can experience these reasonings myself so I may understand fully. I hope that in the more videos I watch from you, you continue this mixed style of instruction. It fully encompasses all different learning styles at once, leaving no one unaided. Again, thanks so much. I wish you the best. I hope you do your best. So far, so good! 😁
Thanks for watching, and welcome! I actually think this video is my least diverse in terms of props and visual aids. My earlier videos are very tactile with lots of physical props. Also while "learning styles" are a bit of a myth, I think having a range of models / diagrams / aids is good so I'm glad you found it helpful!
I have a story of how someone got totally wrong conclusions because they were a Sherlock fan. Someone came up to me on a bus, said they liked Sherlock, and asked if they could check their powers of observation by drawing conclusions about me based on my appearance. I liked Sherlock too so I agreed. He said I have a cat and a dog because I had two types of pet hair on my skirt. I had two cats. He made a correct observation but drew the wrong conclusion. He then said my boots were new because they were clean. They weren’t new (or particularly clean) but I do take care of my clothes. He again drew the wrong conclusion. Unfortunately I can’t remember if he said anything else but I do remember he didn’t get anything about me right.
Honestly, before the self-promotion segment, I didn't even notice your subscriber count. The only thing that made me a little "suspicious" was that camera placement looks a little odd, but never really payed that much attention to it. Anyways, I find your videos very educational, I hope you will reach a wider audience soon!
Such an excellent breakdown and explanation of the different types of reasoning! I once used, in one of my Intro to Comp. Classes, how the BBC Sherlock is an example of deductive reasoning vs. The RDJ Sherlock being one for inductive reasoning (since that's somewhat how the films try to portray them). But yours is much better. Also -- the entire trope of the snooty smarter-than-mortals Mr. Holmes is an example of literary ratiocination if you ask me.
Thank you for caring and being pedantic! I really liked your explanation and overall approach. I'm on the "we-should-always-use-the-correct-term" side myself.
The line about "once you eliminate the impossible yada yada, whatever is left no matter how improbable is the obvious conclusion" leads me to believe that Sherlock is using the process of elimination and I'm gonna try and show that with the wedding ring example. We have a dead woman in the middle of an abandoned house looking like a suicide amidst a string of suspicious suicides, Sherlock finds her ring is polished on the inside and she is wearing a fancy coat. I think in the episode itself someone says she's far from home, Sherlock uses this to eliminate the chance that she's local so now she's a traveller. she's pretty young looking, her outfit is matching and fashionable which means she's either going for a meeting or something else within the city. Sherlock uses the added fact that the ring is polished on the inside due to frequent removal. A traveller with a fashionable matching outfit that frequently removes her ring- Therefore she's an adulterer. How he decided she's a serial adulterer is a whole other thing, but basically my point is that he takes all the things he sees and one by one eliminates them based on the facts given until it lands on the most logical reasoning. Edit: If I'm wrong I'm wrong, but I think this makes the most sense to me
@@DMW4 Maybe he does use deduction, but the answer to your question is still no. It would not be a logical fallacy. Someone being wrong rarely constitute a logical fallacy, nor is their claim necessarily a logical fallacy (which I assume is what you really meant). They may have simply got the facts wrong. This would also be the case here. To be logically fallacious, he would have to contradict himself, but he does not. You are bringing in new information to claim that he is wrong.
@alexh8754 Yeah, except its not possible in the real world to eliminate all but one possibility. So Sherlock Holmes' process of elimination cannot be deduction.
@@moth5799 john had enough money to buy 1 of 3 things from the store. he bought one of them. it was definitely not 2 or 3. therefore item one was the item john purchased. item one was the only item capable of doing such an action at a crime scene! it was a very particular antique keypad unlocker. one of one. the inventor passed away as soon as he made it and it was unseen until john bought it. good work holmes!
I wish your videos had existed when I was trying to study formal logic at uni with the world's most boring lecturer. You managed to explain this far more clearly in 30 mins than he did in an entire semester.
Let me just start by saying I absolutely loved your Pink Floyd reference! Nice video! I really liked your dicussion in the end of the viedo. I want to add that: yes, it might be problematic to use words with a spesific meaning in science to mean something else colloqially. Generally it's not a problem though. This is how language works. If words didn't evolve and change meaning we wouldn't have all these amazing and useful languages. It's not a problem when we in every day converation use the word "theory" to mean what scientists would call an hypothesis. But it IS a problem when people don't understand that theory does not mean hypothesis in scientific terms as "the theory of evolution" or "the theory of gravity". ("But that is just a theory!") That's why I always get more interested in a debate when the debattants start by making some definitions. You might not even agree on how different words SHOULD be defined, but it doesn't really matter if you just can agree on something "for now". If my opponent define atheist as someone who "hates God", that is very, very silly, but I can technically live with my opponents stupid definition, as long as I can define my self as a PNCOTEOAG (person not convinced of the existence of any gods) and use that in our debate. (Of course you never get any way if you go completely Jordan Peterson though, and ask people to define every single well defined word when people disagrees with you)
19:05: I am so glad you brought this up. SO many people just seem to not remember that what is considered "scientific fact" can change based on new evidence.
Not to be overly pedantic, but words have specific meanings, especially when discussing science. In science, a "fact" is generally understood as an observation or a measured value that has been repeatedly confirmed and accepted as true by the scientific community. For example, the statement "Water boils at 100°C at sea level" is a fact, based on repeated observation and measurement. The theory of thermodynamics helps explain why this fact holds true under specific conditions. When you use the phrase "scientific fact", it would seem you actually mean hypothesis or theory. These are open to change over time as new facts are discovered, and logical reasoning identifies incorrect assumptions and conclusions. The theory is modified, leading to correction over time. The facts themselves don't change. We could discover an entirely new interpretation of gravity that fundamentally changes the way we understand the universe, yet the scientific facts we currently have would necessarily comport with this new gravitational theory for it to be considered true. In other words, in science, a fact (accepted by repeated measurement and validation) is a form of evidence, and evidence isn't open to change.
@@icycooldrink6085 This is a great explanation. That is what I meant. I find that a lot of people forget the different between scientific theory and scientific fact. This has caused trouble in the past; the house arrest of Galileo for instance.
@@lukeleslie9648 A theory can be as fleshed out as the theory of evolution, or the theory of gravity, but they can still be classed as "theories" in science, due to their ever-expanding index of new discoveries. This becomes particularly annoying when people (usually theists) use it as a way to strong arm debates, "its a theory, therefore not real", something along the lines of that.
@@derpy9452actually the term theory in science simply refers to the total body of knowledge of a given subject. It has no relationship to whether or not there's still new things to learn. Even if provably everything to know about a subject were known, it would still be called theory, there's nothing to move beyond to.
4:10 I've never seen a Non-arabic person reflecting with this level on a term especially with a language such as English (I'm Arabic and we have such a pride with the poetry/ versatility of Arabic language) and it's amazing to observe.
It makes sense that they used the word deduction, rather than abduction. It's better to say he's amazing at deduction rather than say he amazing at abduction. Might get stares for that.
Fun fact, in German mathematical induction is called "complete induction" (vollständige Induktion) because it is induction, it just happens to be valid because you're not showing something for many numbers and conclude it must be true for the rest of them, you're showing something for _all_ the numbers.
"Once you're eliminated the impossible, whatever remains, no matter how improbably, must be the truth. So far we ruled out the possibility that the suspect walked to the crime scene, for he has no legs. Now we just need to rule out the possibility that he drove, cycled, teleported, garnered the assistance of aliens or remotely commit the crime using telekinetic powers." "Do you really think all of that is likely?" "Likely, no, but possible, yes!".
Greetings Dr McGraw, The curse of being a Mathmematician among Innumerates. Just discovered your channel. I'm a Some-College 72 year old avid reader who always had some math facility. Without Pedantry we'd all be Footless and falling on our.... Again thanks, I'm looking forward to more. All the Best, Jacques Mexico retired but no tired
I think the distinction in definitions is immensely important. I've gotten so sick of getting into arguments with people, only to realize later that the issue was actually incorrect definitions, and not a genuine disagreement. Language is important.
Regarding the last point you made that deduction in common parlance is not the same as deduction in more rigorous settings I think is trying to fight the tide. It's like how "theory" in common parlance just means "idea" while in more scientific settings a theory is much more rigorously defined and is pretty much what we'd call a done deal in day to day conversation. I understand and agree it's frustrating that jargon is used in ways directly counter to what they mean, but I don't think it's something worth expending the time or calories being bothered by.
Broadly speaking, I agree -- it's hard to fight the tide and maybe not worth the effort. My point was more that the common parlence version has seeped into arenas (like debate) in which the rigorous version should be demanded. And many people don't know the difference which is what I hope to remedy with this video.
FWIW, when explaining the more rigorous definition of "theory", I often find people get it when I bring up the notion of "music theory" - it's not the bare supposition that "music exists" or anything like that, it's a framework that allows us to talk about music in a way that's helpful to understanding and discussing the underlying "facts" of tone, rhythm, harmony, etc., and how they relate to one another.
I think efforts to educate people about the proper meaning of theory have been pretty successful though, like you don't even see creationists saying “it's just a theory” anymore so that has to be a sign of progress.
Abductive reasoning is used all the time in medicine when making a diagnosis. The patient’s symptoms rarely line up perfectly with the textbook definition of one diagnosis, but rather fall in between a few “likely” diagnoses that are arranged in order of likelihood
I didn't know what you meant until I watched your video, and now I realize I use real deductive logic in programming! Thank you for breaking down this topic!
Very nice, very clear, very instructive ! I didnt know "abduction", but maybe it's because it has a completely different name in french whereas induction and deduction are basically the same word in both
i took a course in logic, and am currently talking one in mathematical proofs, but neither of them really explained anything here past the deduction section. i also find it interesting that mathematical induction is still a form of deduction. it took me quite a while to understand why mathematical induction worked as an actual proof
@@qy9MC look up mathematical induction. it's a form of proof that uses recursion and it is actually deductive based on what he said, but it's called induction. it's quite a fun type of proof
The key distinction of a mathematical and scientific conclusion is verifiability. For a challenging math problem like finding the prime factors of a large integer, someone claiming to know the correct answer can have their answer verified with 100% confidence whether or not it was accurate. For a challenging scientific problem, the best we can do is test it and assert that we were unable to disprove it based on our current understanding.
I think it's in the Red Headed League short story where Holmes tells the client he's a clerk because the cuffs of his jacket are shiny. He could have bought the jacket at a thrift store, or borrowed it from someone. That's the example that I've always pointed to as proof that Holmes' "deductions" aren't logical.
True story: when I was six years old, my brother began teaching me how to multiply. The first thing he taught me was that 3 x 3 = 9. I asked him why, because I wanted to know. He shot back with "it doesn't matter why, 3 x 3 = 9." After watching the entire video, I'm not sure where that falls in the category of logic. All I know is, he was right, because when I got to the 3rd grade a couple of years later, they told me the same thing, also without explanation. This may have to do more with indoctrination than with logic, but even today, 47 years later, 3 x 3 is still 9. Good stuff, this math...
Sherlock in the books, it is said that he has methods to know what has more chance to implies something, when observing someone and that he has already used these methods so much that it makes him have a magical intuition, but it is never revealed what these methods are, so...
My god I love the fact that you say "I'm a mathematician... of course I'm pedantic!" As a chemist, probably my favourite part of this video. Thank you for your amazing educational work by the way :)
Correction: when the ground is wet it is often isn't from the day before because it is also wet when it is raining, and you often notice it then. That said you're quite justified still as it breaks some of Grice's Maxims when we mention such options too much. A pedantic curse of being completist in our structures. An other form of trivials for communication
You don't even need to remove the ring frequently for it to be polished! Try moving your ring nervously back and forth or pensively spinning the ring around your finger. Do that 10,000 times and you've buffed the ring smooth with your skin and hairs.
Even as a boy I slightly mistrusted the postulate from Conan Doyle via Holmes that "When you have eliminated the impossible, whatever remains, however improbable, must be the truth." I became increasingly unconvinced, as I was forced to gradually surrender the simplistic and convenient notions of youth, that it would ever be feasible to marshal ALL the alternative hypotheses to account for *known* facts (and that's setting aside their usual scarcity, in comparison to unknown and in some cases unknowable facts), let alone strictly and reliably split those hypotheses across the nebulous and hypothetical boundary between impossible and highly improbable. But even if this were possible, it seemed particularly unlikely that there would ever be only one hypothesis left on the "highly improbable" side of that boundary (unless, as often seemed the case in the Holmes stories, a woefully inadequate number of alternative hypotheses had been adduced in the first place, often only two or three) Finally the methology seems to me blatantly fallacious now you have laid out with a simple Venn diagram, in a specific instance, how Holmes' truth claim about wedding rings violates the formal definition of deduction. There is a good reason that the Holmes canon is shelved in the "fiction" section of libraries. It does make great reading, I have to admit, to pretend that the affairs and contexts of social interaction are necessarily susceptible to logical dissection with reliable prognoses. But if my happiness is ever hostage to the findings of a detective or judge, I can only hope they will not have learned their "logic" at Sherlock's knee.
The methodological flaw with this reasoning is unknown unknowns. Holmes can never ever be certain that he has removed all other possibilities because he cannot ever know that he knows everything pertaining to the case. Like maybe that ring actually had a special coating on the inside that kept it clean that Holmes has never heard about and since he isn't particularly up to date on nanoscience he doesn't even know such a thing could exist.
@@hedgehog3180 It's a compelling and plausible example of an unknown unknown. The pedant in me does nevertheless feel compelled to consider a faint plea in mitigation for Conan Doyle: Holmes did observe that the ring was dirty on the outside, and it seems rather unlikely (although of course not impossible) that the ring would lose its external protection, or never have been externally protected, and yet retain its internal coating. However, an infinite number of very unlikely things are happening every instant. There is a huge distance between "very unlikely" and "impossible", a key consideration which Holmes completely and chronically overlooks. Which is why your example transcends my pedantic quibble, and perhaps hints at one reason why such quibbles, even though they may be worth dissecting, are usually immaterial.
You’re right, of course, but the idea is that when Sherlock Holmes says, “The state of this ring indicates serial infidelity,” he has eliminated other possibilities through obscure expertise (e.g., BBC Sherlock canonically authored an article about the “The X Different Kinds of Cigarette Ash,” so when he later makes a claim about an ashtray indicating something, the viewer is to understand that he has the requisite expertise to prove that claim by necessity.). It’s a superpower that works better when it’s not explained (which is good because it can’t be explained because it doesn’t actually work irl).
Tysm for this lol! Since I was younger, Holmes & these types of male characters in general often irked me with their type of reasoning, making premises that don't necessarily follow to then, at best, guess a conclusion & look like smug genies when correct. Especially when it came to assumptions about women's sex lives. I just couldn't put my finger on why, but it felt like it wasn't deduction. The best I could formulate was "At least say it's *likely* that this is the case, or make it clear we're talking about probability." Funny that that's basically what abduction is, which is what they were doing most of time. It also explains why I liked RDJ's version of Holmes better, bc the story shows he can be off sometimes. There's an issue in general with romanticising people's conditions as them being God, like that show about a man who can ALWAYS tell when someone lies, or the one about a woman who remembers everything & never forgets, or hell even The Good Doctor. Autism and sociopathy don't make you a well of truth. Despite these conditions, you're still human.
i'm so happy to have found your channel! i took some classes in propositional logic in college way back then, you're helping me take out the rust from my brain.
The following may be better as separate comments, but I've decided to make it one comment: I remember finding that “deduce” doesn't necessarily mean deduction. I used “abduce” (invented by me) instead. (Now, I've realised that that probably was induction, so I was also wrong in that way.) I wrote about how I could end up with an incorrect definition of a word. One of the ways was by mishearing something. Someone suggested that I may have misheard “deduce” as “abduce”. I explained how I actually got this. (I couldn't remember why I thought “deduce” meant deduction) Here's an example of another one to illistrate how I used “abduce”: I saw a video where a streamer played a game. (I'll use some terms that I think are common for many games, but if you don't know, just treat them like people treat made-up words such as “gostak”.) There, they made a bingo card with various possible things they could find in the level. One of them was “elevator button”. I didn't know what it was. At some point, the streamer jumped and that had effect. They called it an elevator button. I abduced (or induced) that it meant detecting jumps. Later, it turned out that it actually meant a useless trigger I think deduction and induction are special cases of abduction. Deduction is when the method guarantees it with absolute certainty (assuming the premises are true), which is a case of high likelihood, and induction is when it's by generalising examples. In both cases, the result is likely true Here's a copypasta I've found recently: > # Smart characters written stupidly > > Why does nobody like Sherlock? Because it has smart characters written stupidly. > > Anton Chigurh from No Country for Old Men is a smartly written smart character. When Chigurh kills a hotel room full of three people he books to room next door so he can examine it, finding which walls he can shoot through, where the light switch is, what sort of cover is there etc. This is a smart thing to do because Chigurh is a smart person who is written by another smart person who understands how smart people think. > > Were Sherlock Holmes to kill a hotel room full of three people. He'd enter using a secret door in the hotel that he read about in a book ten years ago. He'd throw peanuts at one guy causing him to go into anaphylactic shock, as he had deduced from a dartboard with a picture of George Washington carver [sic] on it pinned to the wall that the man had a severe peanut allergy. The second man would then kill himself just according to plan as Sherlock had earlier deduced that him and the first man were homosexual lovers who couldn't live without eachother due to a faint scent of penis on each man's breath and a slight dilation of their pupils whenever they looked at each other. As for the third man, why Sherlock doesn't kill him at all. The third man removes his sunglasses and wig to reveal he actually WAS Sherlock the entire time. But Sherlock just entered through the Secret door and killed two people, how can there be two of him? The first Sherlock removes his mask to reveal he's actually Moriarty attempting to frame Sherlock for two murders. Sherlock however anticipated this, the two dead men stand up, they're undercover police officers, it was all a ruse. "But Sherlock!" Moriarty cries "That police officer blew his own head off, look at it, there's skull fragments on the wall, how is he fine now? How did you fake that?". Sherlock just winks at the screen, the end. > > This is retarded because Sherlock is a smart person written by a stupid person to whom smart people are indistinguishable from wizards. Induction as discussed here is also used in mathematics, although its results aren't called theorems until proven with deduction. They're usually called conjectures. It is commonly used in the study of L-objects I think a kind of deduction is similar to induction. The difference is that all the cases are considered. In Russian, it's called перебор (homonym for overkill). There are also two kinds of deduction known as induction. One is for sets defined by operations on them. One way of defining them formally is as the intersection of all sets closed under these operations. (It's possible to prove that they are themselves closed. Here's a fully formalised definition of one such set: x:∀N(∀n(∀ee∉n∨∃m(m∈N∧∀k(k∈n⇔k∈m∨∀e(e∈k⇔e∈m)))⇒n∈N)⇒x∈N). Here, I've used logical operators in a way I think makes it most clear and didn't use what I regard as shortcuts: quantors restricted to sets and identity. The latter means that I'm using a system when it isn't an elementary predicate; in such a system, the axiom of extensionality should be what is otherwise the substitution property imported from the identity package.) This meaning of induction is that every closed subset is the whole set. To me, the video mentioning that many people misunderstand it didn't explain it; I only realised what it actually is this month. There is also transfinite induction, which is basically the well-orderedness of a set formulated in a slightly different way I probably planned (very short-term) to write another point; if I remember (recall) it, I'll put it below
I think Holmes uses deduction all the time, the premises simply aren't stated in the text because he's a detective, not a maths professor. For example- Gregory (Scotland Yard detective, to Holmes): “Is there any other point to which you would wish to draw my attention?” Holmes: “To the curious incident of the dog in the night-time.” Gregory: “(But) The dog did nothing in the night-time.” Holmes: “That was the curious incident.” Here's the implied deduction- P1: Dogs don't do nothing when there's a nighttime disturbance, unless there's something curious occurring. P2: A dog did nothing during a nighttime disturbance. C: Something curious occurred. He then uses abduction to determine the nature of the occurrence, but the foundation of all of that is the initial deduction.
That's the actual problem I've always had with Holmes cases, brought to the point. I always saw at least one other possibility (usually a myriad) and never understood why the accidental cummulation of his lucky guesses made him such an ingenious detective, while usually single wrong guesses could have lead him to completely wrong paths.
The problem I have with the wedding ring debunking argument, specifically in regards to how just because it's cleaner on the inside and is removed frequently, doesn't mean she's a cheater, is that it doesn't take into account the state of the rest of the jewelry she wears, nor the rest of her appearance as a whole. Sherlock explains that while she cares a lot for her appearance and the rest of her jewelry is clean, the wedding ring remains the only dirty piece of jewelry on her, implying that it's cared for less than the rest of her stuff. Why would someone of that nature care so little about her wedding ring of all things? This is what he couples with the fact she removes it frequently to ultimately come to the conclusion that she's unhappy in her marriage and cheats.
One of the extrinsic reasons for there to be maths: "HOWTO Think". (Or howto think about one's thinking - and so be aware of the weight of current thoughts?) My terminological bugbear is the way "refuted" seems to be shifting in journalistic parlance (speakage, I mean, but Frenchified) from what it means to something like "denied emphatically" or "loudly and confidently asserted", depending on what its being used to verbally beef up with stronger sounding words. It's fine for ordinary people to be careless like that, but someone whose training is meant to start with a training in very solid language use, and knowledge of current usage (as well as clever tricks like how to notice you don't know what something means, and then look it up in a dictionary) I think we're entitled to complain. Yes, language will change, partly by slop, but that doesn't mean it's up to the journalists of our time to provide as much of that slop as possible. A journalist is meant to be left out of the language slop game. It's for the less educated rest of us, not for them. They're meant to be playing something like the pedantry game.
CORRECTION:
Throughout the section on deduction, I separated validity and soundness into two distinct concepts. I did this for explanatory reasons to give clear examples of different combinations of valid/invalid sound/unsound. But strictly speaking, an argument is sound exactly when an argument is valid AND with true premises. As such, there isn't actually such a thing as a sound argument which is not valid. I think my explanation makes the concepts clear, but I regret not summing up the section on deduction with this point.
It was clear. Though, if possible, you could annotate the video with a 2x2 table showing the impossibility of a sound and invalid argument.
@Another Roof Excellent video! As a mathematician I have been trying to explain this to people for years, now I have a video, to which I can point people! What was that *challenge* you mentioned at the end? Is there a link to the problem description?
@@reellezahl Thanks! My previous video about Countdown, Britain's Oldest* Gameshow, contained a challenge problem for viewers!
That is actually an incredibly interesting thing you bring up. The concept of a "sound argument". Layman wise it is essentially when the arguments makes sense, and the conclusion following from the arguments makes sense in context from the premises and the arguments. They are obviously almost never valid, as in completely true, since we as humans and our reasoning is... well flawed...
But because we are flawed we use perfect concepts to describe something imperfect, but pretty close to the concept.
Like well... Perfect, valid, true, false, etc.
Despite in many cases perfect is obviously wrong, since something perfect is unlikely to ever exist. Something valid has the same issue, so does true and false statements.
Essentially outside of an abstract system like math, these statements will always have some level of imprecision :P
@YeYaTeTeTe The term you allude to is "logical." Logic does not care whether the premises are true or false, believed or not. Logic does not tell you whether a conclusion holds true. Logic does tell you that, under the hypothesis that the premises be true, the logically obtained conclusion would also be true. Absolute truth does not exist and is not assumed anywhere in logic.
I think my favourite form of reasoning is abduction. That way if people try to disagree I have a hostage.
I prefer induction - you can get more power out of it and don't risk a prison sentence...
Deductions are cheaper to get though...
This comment thread is the greatest thing ever made by 3 authors in the history of mankind
@@micayahritchie7158 , aw.. I was too late to be inducted into that group...
@@rmsgrey get power out of induction. Nice.
Sherlock Holmes and Dr Watson went on a camping trip. After a good meal and a bottle of wine they lay down for the night, and went to sleep.
Some hours later, Holmes awoke and nudged his faithful friend. "Watson, look up at the sky and tell me what you see."
Watson replied, "I see millions and millions of stars."
"What does that tell you?"
Watson pondered for a minute. "Astronomically, it tells me that there are millions of galaxies and potentially billions of planets. Astrologically, I observe that Saturn is in Leo. Horologically, I deduce that the time is approximately a quarter past three. Theologically, I can see that God is all powerful and that we are small and insignificant. Meteorologically, I suspect that we will have a beautiful day tomorrow. Why, what does it tell you?"
Holmes was silent for a minute, then spoke. "Watson, you imbecile. Some bastard has stolen our tent."
from OVER them? Who??? Moriarty? Hahahahaha!
And John is so clueless! 10/10!
😂😂
Good one
i’ve never actually laughed at a comment on youtube before this 😭
It would be funnier/actually clever, if the tent part didn’t just come out of nowhere. You didn’t mention they went to sleep in a tent. Maybe they are sleeping outside?
At 7:40 it would be worthwhile to point out that false premises can lead to true conclusion. E.g. "All giraffes are mortal" "Sokrates is a giraffe" "Therefore Sokrates is mortal"
Are you implying that there are immortal giraffes?
Ohhhhhhh you're saying Socrates isn't a giraffe. That is a much more understandable mistake
@@CrockHoaxit’s alright, it’s not exactly widely known that giraffes aren’t mortal
@@detroitpolak9904 Your comment tells me that you deduction skills suck ass.
@@detroitpolak9904 You must have some amazing deduction skills that you can tell so much about me from my spelling.
I'm German, for Christ's sake. It's how we spell Socrates. It's an understandable mistake to make that doesn't even tell you much about my ability to spell, never mind all the rest, you dimwit.
The problem with abduction being, perhaps, the most common form of reasoning is that we humans tend to be pretty bad at judging probabilities. It's hard to identify the most likely conclusion if your likelihood estimates are noisy.
The biggest problem with abduction is confirmation bias. When we form conclusions we almost never reason to disprove our conclusion and only think of arguments that agrees with the conclusion.
Deduce, generalize and lack substance, Induce, observe and lack implementation
Abduct, and well, you've got a lot more problems. Too certain someone is guilty, leaving no room for any other freedom of exception.
Induction > reductive logic and uninteractability (+observation/-implementation)
Abduction > probabilistic and unexceptionalism (+verdict/-possibility)
Deduction > abstract statistics & stereotype. (+group/-representation)
Town of Salem game
@@khajiithadwares2263
My abductive reasoning infers that you are clearly a witch, because I live in the 1800s and only witches are this smart
probabilites are fun to think about, but really difficult.
AnotherRoof DESTROYS Sherlock Holmes using DEFINITIONS and FORMAL LOGIC.
Eh, nothing counts unless you do it in non-binary logic. Ordinary binary logic is full of paradoxes and inconsistencies, a fact Sherlock knew all too well. The so-called "informal fallacies" (such as the relevance fallacies) are only "informal" in binary logic. In 3-valued logic, the informal fallacies become formal fallacies. So when you say "FORMAL LOGIC" you really mean non-binary logic. Which is constructive, and formal, and better than binary logic. As Spock would say, "My logic is superior to your logic." Plus you know using words in all caps means you are a bot
@@tomholroyd7519 3 valued logic? What 3rd state is there besides "true" and "false"?
@@3snoW_he probably means statement that arent true or false, which can happen ig u wont encounter it in every life so who cares
What is there besides true and false? Paradoxes.
There's a branch of logic called constructive logic, which accepts a conclusion as true only if a specific example can be constructed. Classical logic says that proving that a statement is not false is enough to prove that it is true. This idea is called the postulate of the excluded middle, since it assumes that there is nothing between true and false. But constructive logic doesn't use that postulate, since using it would mean not having a specific example to verify the conclusion. (For example, the argument for God's existence briefly discussed in the video is a valid deduction that it's impossible for some first cause not to exist, but it fails to supply a specific entity that must be the first cause. So constructive logic agrees, given that the premises are true, that a first cause can't _not_ exist, but it refuses to go so far as to say that a first cause _does_ therefore exist.)
In that way, constructive logic has three truth values: true, false, and neither true nor false. This has nothing to do with probability or fuzzy logic. The third value allows constructive logic to engage directly with paradoxes without falling apart. It's possible to use it to prove that a statement like "This statement is false" is not true and is also not false, without either of those conclusions disproving the other. In classical logic, the best we can do is assert axiomatically that paradoxes don't happen, which is a bit awkward because paradoxes do in fact happen within logic itself.
@@jeremydavis3631 If you're adding a "neither true or false" value for statements like "this statement is false", for completeness shouldn't we also have a "both true and false" value that would apply to sentences like "this sentence is true"?
Just had a bit of a thought.
If deductive reasoning means the conclusion necessarily follows, then deductive reasonining is ridiculously rare in general. Even if you find the bloody knife, do a DNA check and the suspects DNA is on it, and you have several witnesses, that does not "deductively" follow to him being the actual perpetrator. The witnesses can remember wrong, the DNA on the knife could've been placed there earlier, etc. So the conclusion doesn't logically follow.
I like this, very very interesting video
Agreed! That's why I discuss how usually abduction and induction are the only available options. Deduction is mostly reserved for the abstract like in philosophy and mathematics. Thanks for watching and sharing your comments in the live chat!
Yes, deduction pretty much only happens with abstractions. Almost nothing in real life is certain enough to produce sound deductive arguments. It's fairly common in computer programming, and even there it's only sound as long as bit flips are not involved... which they often are....
@@AnotherRoof I was glad to watch, even if I was late :)
@@KohuGaly Welcome to cosmic radiation, and nearby radiation, and radio transmitions, and... I'll just stop the list here :P Bit flips is the bane of programmers until they actually invented a way to kinda deal with it XD
We might call it rare, or we might just be using it so thoughtlessly and automatically that we do not notice it. If someone says that all the food is in the fridge, we should not need to ask where to find the eggs because we can use deductive reasoning to conclude that the eggs are in the fridge, yet that reasoning is so obvious and effortless that we do not pay attention to what we are doing.
Regarding the Sherlock Holmes scene when he was introduced to Mary: Something a lot of people miss about this scene is that he _intentionally_ got Mary's past wrong in an insulting way so that she and Watson would get up and leave. This is because he doesn't like the idea of them being together. Right after they leave, the waiters bring food to the table even though they hadn't ordered anything -- Sherlock must have ordered food before they arrived, and told the staff something like "A pair of friends are going to sit down briefly and then leave again, wait until after they leave to bring my food."
I agree with most of what you said except the last part. It's his favorite restaurant. He knows exactly how long his food will take to get there and knew he only needed x amount of time to chase them away lol I bet he got that down to the second, if not millisecond
@@taloutezero That may be possible, but I doubt it. I work at a restaurant, and in my experience it's never that precise. The time it takes for the staff to come take the customer's order, the time to relay that to the kitchen, how long it takes to prepare, how long it takes to bring it out to the table, all those times are variable depending on a lot of factors that Sherlock has no way of knowing ahead of time.
Also when a customer has already placed an order and then two other people show up, the usual procedure is that the waiter will hurry over to take their orders as quickly as possible so they can start getting it prepared, because they like to bring the whole party's food all at once. (at least, that's how it worked in every restaurant I've been in) They were sitting there for quite a while and nobody came, likely because the staff had already been told that they'd be leaving again soon.
@@John73John I agree with what you said but I think its also both. He probably knew how long it would take to prepare his food. I doubt Sherlock would let his food get cold while trolling Watson and Mary so I think he told them the others wouldn't be eating AND he timed the foods preparation. In those days, would it have been easier or harder to find out which staff was on duty? I can't imagine that Sherlock has no idea who is in the kitchen of his favorite restaurant (especially on days he goes there) or how long stuff takes to make there.
@@taloutezero I don't think it's possible to conclusively deduce one way or another (see what I did there?) but it's a lot more than just "who's in the kitchen tonight?". Maybe one of the other customers ordered a complicated dish and the chef's attention was occupied for an extra couple of minutes before he could start working on your order. Maybe the waiter takes your order and then decides to visit another table and take their order as well before relaying both to the kitchen. Maybe the carriage John and Mary arrived in was a minute early or late because of some condition on the road that Sherlock didn't know about. Any one of a hundred things could happen to mess up the timing. Real life is way too complex and chaotic to make a prediction of something like that and get it right down to the second. He could get a general idea (within, say, 5 minutes on either side of a bell curve) and well within the time the food would still be hot if it's kept covered.
@@John73John I guess I'm deriving my conclusions from who he is as a person. If Sherlock Holmes has deemed a place his "favorite" out of all similar places, I judge by his self love and indulgence that part of the reasoning for him is the timeliness and predictability in their service. I could be wrong and it could be a hectic unorganized environment but considering he thinks the universe of himself, I can't imagine he would go some place prone to delays in his orders or very untimely service. I understand that reality can be chaotic and nothing is guaranteed but this is one of the few "public" (I know its a fancy reservation only place but people who aren't in his inner circle are considered public) spaces that could get Sherlock to leave his room AND dress up. I don't think my conclusion is far off.
Thank you for making this clear. It always drove me crazy that if there is a link of half a dozen steps, each with a 70% probability of being caused by the previous, then it is concluded that the solution must be so and so. In reality, we are already down to 12% probability.
@@DMW4 ChatGPT isn't always an accurate source. It wasn't able to actually point out a single instance of Holmes using deduction.
Remember 95% accurate is 50% accurate as it is either accurate or inaccurate
@@bestaround3323 someone who doesn't understand probability
@@tomlxyz no, that's just how it feels whenever a game says something is 95% accurate
@@tomlxyz You either missed the joke or you didn't. 50-50 chance.
Great summary. This has always bothered me about detective stories. My reaction always was "you can't know that, there are so many other explanations why that may have happened!"
Abductive reasoning is of course essential for many practical solutions, but detective stories often apply it in pretty far-fetched ways that only work because the author wants it to.
yes, me too! you can think of other possible explanations, but of course in the story the detective is right and everyone is like "wow, you're a genius!" Grr.
So you love Pitch Meetings, too 😂 ..."so the story can happen"
@@DMW4 You: Source?
ChatGPT: I made it up
The actual issue is semantically the word "deduction" includes abductive reasoning. In fact that's the way the word is mostly used
@@DMW4really? You making that thing think for you?
That's why I hate Agatha Christie. The whole storyline goes on giving hints and motives, and, at the end, Poirot says IT WAS HIS COUSIN THAT DOESN'T EVEN APPEAR IN THIS BOOK
I think Doyle himself didn't like how everyone thought that holmes was a genius, and wrote a short story where watson refutes his 'deduction' with a different valid answer. He wanted people to know that sherlock was smart because he, the author, already had an answer and then wrote the path to get there, not the other way around
My favourite "Doctor Who" quote, from Patrick Troughton in 1967 is "Logic, my dear Zoe, only allows you to be wrong with more authority."
I love the one about why he doesn't carry a weapon "because they might think I'm going to hurt them"
@@chaotickreg7024 That's just so true
@@chaotickreg7024The Doctor himself may as well be a weapon. Even discounting how many times he's harmed/killed someone through his intellect and charm, he's also been throwing hands since the First Doctor. Hartnell defenestrating Roman soldiers was such a bizarre image.
I think it's worth noting that all of these types of logical reasoning are closely related.
Abduction is just Deduction with the word "probably" covering for otherwise invalid or unsound reasoning.
"A: Toast is made in a toaster
B: This is toast
conclusion: This was made in a toaster"
is an unsound deductive argument, but
"A: Toast is (normally) made in a toaster
B: This is toast
conclusion: This was (probably) made in a toaster"
is a perfectly reasonable abductive argument.
In addition, Abduction and Induction are also strongly connected to each other. For example,
"A: The road is wet
B: Rain can make the road wet
C: Rain probably made the road wet"
is an abductive argument, but how do we know that rain is the most likely explanation?
Well, if you look at a bunch of examples of things making the road wet, you'll find that the most common one is rain. We've just concluded a general rule from a bunch of specific examples- that's induction. Nearly all abductive reasoning works this way.
Induction doesn't make any predictions on it's own: it's value comes in contributing evidence to an abductive line of reasoning. Abductive lines of reasoning rely on having some knowledge of what is or isn't likely, which only induction can provide. Without using both, neither is particularly helpful.
Side note, nearly everything relies on inductive and abductive reasoning. We can't be deductively sure that the universe will exist tomorrow, for example, or that the laws of physics will be at all the same. We must rely on inductive reasoning to conclude that, since the universe has continued existing every day so far, and the laws of physics have remained consistent for as long as we've been aware of, that they will remain the way they are as a general rule. And abductively, that means that the universe will probably exist tomorrow.
I don't know when toasters became popular, but I am certain Sherlock didn't use one.
its* own
@@JorgetePanete cretin
We cannot proof the "soundness" of deduction. Because facts and observations might always be wrong. However, the "validity" of a deductive argument can be verified.
Also, in mathematics and philosophy, deduction is very much "valid" and useful tool.
Well there's also not much reason to think about if the laws of the universe stopped working. There isn't anything we could do to stop it, and we would be fucked if it happened, so there's not much reason to spend time and energy doing anything but acting as if it will continue existing.
Someone ought to mention the concept of "mathematical induction" and how it is actually a type of deduction. Maybe that's obvious to everyone, but it feels like the sort of thing that may need to be said in every discussion of the distinction between deductive and inductive reasoning.
There are three, not two, types of reasoning: deduction, induction and abduction. Sherlock used the third. So do doctors when diagnosing.
it's weird that Mathematical Induction is the proper English term. the German term is more or less "complete induction": you start with inductive arguments, but show that it is the only induction possible, hence completing the induction to a deduction.
It’s probably called “induction” because it somewhat feels like inductive reasoning. The proof sort of emerges out of our recognition of the general pattern.
There is a sense in which mathematical induction is not deduction (and this is very confusing and there are lots of schools of thought on this):
Mathematical induction is not possible in a first order finite axiomatisation, essentially it is NOT deductive in a comprehendible first-order theory.
You need to impose the existence of the inference for every numeral acted on by the function symbol in the theory, and there are infinite numerals.
(to be coy: it's not a premise, and it's not a valid deduction from the premises, yet the general rule is 'induced', then 'abducted' into being applicable).
This doesn't prevent induction from being *constructive* though, as we can use computers (or equivalently, recursion) given infinite resources to be able to make conclusions from the infinite first order theory, but to do this we have to discard double negation elimination, and then we have issues of consistency (without DNE maybe some contradictions you could have arrived at now can't be arrived at).
But, even an infinite first-order theory is not enough to constrain the suitable models of that theory, what we conclude from mathematical induction is not that the conclusion applies to *all* numerals, but just the ones are successors of our base case. Or what this is really saying is that you cannot write the conclusion of mathematical induction in first-order logic, as otherwise you need infinite terms in the single statement of your conclusion. When we make a computer evaluate the statement we are already making assumptions about the model in order to even run the program.
So there is some meaning to discarding mathematical induction in some deductive scenarios.
Obviously this only about first-order logic, higher order logic is its own can of worms that I can't say much about.
@MagicGonads the first-order induction schema is still true in nonstandard models of arithmetic, since of course that's what it means to be a model of PA. "For all x, P(x)" really does follow from P(0) and P(x) => P(Sx) (where P is a first-order formula with one free variable).
The reason this works is that nonstandard naturals have infinitely many predecessors. Hence around nonstandard x there is a copy of *Z* akin to {..., x-3, x-2, x-1, x, x+1, x+2, ...}. The model, however, is forced to assert that it's turtles all the way down for that segment, meaning P(x) really is true.
Of course, second-order induction ends up failing in such a nonstandard model, precisely because second-order logic -- basically, a logic that can see subsets of the model -- can "observe" the gap that is created.
Summing things up, though, we have that mathematical induction is a deduction purely because we assume it as a premise for every first-order formula.
Lastly, as for making induction constructive, there are no issues of consistency compared to PA. First-order classical PA is strictly stronger syntactically than first-order Heyting arithmetic (PA without excluded middle).
Another group of frequent ring removers are medical professionals like nurses. The ring can protect any pathogens and filth trapped under it from being washed off.
So while my mother was a frequent wedding ring remover, she is not an adulterer
You also can't wear metal objects while getting an x-ray or being near an MRI machine. So that's another reason why medical professionals or just any scientists might remove their jewlery.
Good point, however the coloration difference would come (usually) from exposure to sunlight, outdoors. Therefore a nurse who presumably only takes her ring off indoors might not have a discernible untanned region.
Also industrial workers and shop hobbyists. Reason being: Degloving injuries are quite unpleasant.
She "may" not be an adulterer. And she "may" not be a frequent adulterer.
On the other hand she could have been schtupping a couple of the neighbors and the milkman and the postman and various repairman while wearing her ring. As she could have also done in a one-night fling before you were born.
Also, though I have no hard data, I believe that married men remove the rings to hide their marital status in order to have illicit sex more often.
my first thought is she could be a chef
I'm very pedantic myself, but I'm a language teacher so I'm personally pretty okay with a word having a general public meaning different from its academic meaning.
I do understand what you mean though, for as incredible as it sounds, I once had to explain (or tried to explain anyway) to a creationist that "theory" in "theory of evolution" doesn't mean "hypothesis".
Hmm, "hypothesis" is not far off, since scientific theories are never proven. Newtonian dynamics are useful and taught in physics class, but that theory is nevertheless wrong. Similarly, the theory of evolution is at least likely to be incomplete.
But the term "theory" is indeed not intended as "speculation".
@@landsgevaer Newtonian mechanics isn't wrong, it's incomplete. It breaks down at high speeds, but within it's boundaries it's close enough. Newton himself knew his theory was incomplete.
The same applies to General Relativity, it breaks down at really small scales.
To be fair though, the term "theory" has become somewhat muddied in academia. I blame string "theory" for that (more like string conjecture).
Theories are hypotheses that have been tested and validated so often, it would take an enormous amount of evidence to refute them.
So all theories are hypotheses, but not every hypothesis is a theory.
And that's a simplification, most theories are a set of hypotheses.
@@ayumikuro3768 I would argue that Newtonian mechanics is fundamentally wrong still. It treats space and time wrong (fibre bundle vs. Minkovski space). You can't repair that by simply adding something while retaining its foundations, so I cannot call that "incomplete".
I agree it is a very decent approximation, and as a framework it is very useful, but it is fundamentally wrong nevertheless.
But setting all that aside, since you agree that theories are not unlike hypotheses, for the purpose of this thread we agree. Thanks. 🤝
Evolution doesn't mean evolution. Almost no one means evolution by evolution
@@landsgevaer In the debates what is usually referenced is "Darwinian evolution" as a particular theory which is straight up wrong on a number of points. What matters in science is predictive validity, and no scientific theory can be "complete" even for a small domain not least of all because things can be re-conceptualized
This calls for a new Sherlock Holmes series, where the guy is just like Saul in Better Call Saul, a faker detective, who always comes up with supposedly brilliant deductions which frequently end up being wrong, but the guy conspires creatively to make himself look good every time, in ways that one could call "amazing", achieving some level of success.
That’s basically Psych… lol
There is an old movie called without a clue.... In which Sherlock is an actor and Watson is the one who solves the crime with Sherlock being the face and voice of Watson
@DanteYewToob thanks for already making this comment for me.
I would argue Sherlock Holmes does a lot of Inductive reasoning as well - depending on which interpretation of the character you are watching, I guess. In many versions of Sherlock, he spends a lot of off-camera time, and just a tiny bit of on-camera time, exhaustively studying various obscure events to form inductive conclusions about the results, unrelated to any particular case. Then later when he encounters a similar event during a case, he is already equipped to pull out a pre-considered inductive rule and apply it to the observations made.
I suppose you could reasonably argue for either "induction" or "abduction" as a label for that final step, but it's the previous inductive step that occupies the character's time even though it's the last step that is shown on camera, due to being more exciting.
If I remember correctly, in the first story he is working on blood splatter and clotting.
The ring deduction always bothered me, because I fidget with my ring constantly, switching the finger it's on. So glad I found this video!
The problem I have with the wedding ring debunking argument, specifically in regards to how just because it's cleaner on the inside and is removed frequently, doesn't mean she's a cheater, is that it doesn't take into account the state of the rest of the jewelry she wears, nor the rest of her appearance as a whole. Sherlock explains that while she cares a lot for her appearance and the rest of her jewelry is clean, the wedding ring remains the only dirty piece of jewelry on her, implying that it's cared for less than the rest of her stuff. Why would someone of that nature care so little about her wedding ring of all things? This is what he couples with the fact she removes it frequently to ultimately come to the conclusion that she's unhappy in her marriage and cheats.
@matthewscorner2990 the answer is it's bad writing
@@Sammysapphira The only aspect of it I might consider bad writing is the jumping straight to cheating angle and having a series of partners. I would probably have stopped at her being generally unhappy in her marriage as there wouldn't really be much evidence to suggest she was actively doing anything about it. But her being unhappy in her marriage is clearly illustrated in the state of the rest of her jewelry compared to the wedding ring, but people ignore that to just say Sherlock said "taking your ring off means you're cheating"
Good video, that was interesting.
I'd say it's not misappropriation to call what Sherlock does "deduction" or "logical" because these words were used by people way before philosophers logicians and mathematicians formalized them to mean more specific things.
I'm a physicist, and I can't really complain when crystal healers talk about "negative energies", because people used energy to mean liveliness-stuff, and generally vibe, along with 'the ability to do stuff'.
It is fair to ask people nicely in your case, to say "hey, here's a better word for what you mean, now we can tell these things apart", I think most people, if you had their attention, would say sure, sounds good to me.
Others will probably call you a nerd and ignore it lol
Indeed, for example "allergy" has gotten today a stricter medical meaning than originally stated or in common use
@@2adamast huh. What did it mean in the olden days?
Intolerance.
@@mawillix2018 I guess that would make me allergic to the manosphere. Makes sense, that terrible community irritates me just as much as almonds or birch pollen
20:13 "What if Sherlock isn't doing any of the three types of reasoning?"
I've always seen the "whatever remains" part to actually mean "whatever remains", not just what is known to you. That would make this statement actually true, and if Sherlock isn't using any of the three types, then he must be using something else. That something else is still part of "whatever remains" in my interpretation.
Though I can definitely see how it could be interpreted differently.
Well, "if I have correctly eliminated X, Y and Z, then the truth must be contained in the set of possibilities excluding X, Y and Z" is pretty solid (mostly because it gets around the possibility that one of X, Y or Z should not have been eliminated, and doesn't say anything about how broad or narrow the remaining field of possibilities is)
To me. This is simply indicating that the writer doesn't know how to write detective stories.
So I look it up and... yeah. The directior doesn't like detective stories
Off the top of my head, I’d say the problem with trying to eliminate possibilities in an environment where the possibilities aren’t outset for you, is that you never know if you have in fact eliminated all other possibilities, meaning you’re still at the mercy of your own biases and/or limitations.
@@Silkie_Dragon Hence why almost all good detective stories are set in some sort of location where things can't change like a moving vehicle or a remote mansion. And in a lot of other cases there's some other key limiting factor that narrows down the possibility space.
@@Silkie_Dragonbut our limited understanding of the world does not erase the general truth of the statement itself. “If you eliminate all impossibilities, whatever is left is true” does not say anything about a human’s ability to correctly ascertain that truth.
I could even break it down into a deductive argument.
P1: Something happened
P2: Anything that did not happen could not have possibly happened
Conclusion: when you eliminate the impossible, whatever remains (…) must be the truth.
I completely agree with the conclusion, its also why a "theory" has come to mean a hypothesis instead of something that has overwhelming evidence. (I don't like to say proof outside of deductive math reasoning as it's only guaranteed to always work and be true in hypothetical math land)
@@DMW4 might wanna also mention the "previous answer" that chatgpt gave.
@@DMW4 how? do I come over to your house and check what you asked chatgpt before asking that question? the answer chatgpt gave you says, "and there are numerous examples in the stories where he uses deductive reasoning to solve cases, as I mentioned in my previous answer."
Which means this wasn't the first question. I do understand that he does employ deduction many times as it is very hard not too, but sometimes an example outside "as I mentioned in my previous answer" is quite useful...
@@DMW4 Chill dude, he just wanted to know the previous answer. Your making drama over it. To be fair I also want to know the previous message so I can understand him.
@@DMW4 ChatGPT won't always give the exact same answer, also ChatGPT is a hilariously bad source to use.
One of the things I’ve always loved about the novels is Watson admitting that a lot of the time Sherlock is actually wrong, & the instances in which he actually pulls something remarkable with his strange method he selectively presents those stories to the public. This follows logically; making huge categorical assumptions & coming to wild conclusions about mundane phenomena would make you a bit foolish more often than not.
Agreed. And it stands in contrast to the BBC show which seems to present Holmes as a super genius who's never wrong!
Well, they always try to make film/TV adaptations entertaining, which sadly means turning Sherlock Holmes into a magician. But after reading the original stories by ACD I get a feeling that Holmes does use deduction, alongside the other methods. Firstly, he is introduced as a consulting detective, which means he mostly applies already solved cases to fresh ones. This gives us the idea that his reasoning must be pretty solid. Secondly, many of his conclusions are: 'you have a tattoo that could only have been made in China, therefore you have visited China'. Unlike on the silver screen, he often seeks more evidence before jumping to conclusions; but of course he also theorises a lot.
That is to say, SH stories have a ridiculous amount of mistakes for a detective series, so I wouldn't be surprised if ACD didn't really know what deduction is, or wanted to give an impression that Holmes simply cannot make a mistake, by choosing the most foolproof way of reasoning.
The video itself is great, and it explains the difference between the three very well, and with visual representation. Many thanks!
The video does not prove that Sherlock never used deduction. The video explained instances in which Sherlock misused the term 'deduction', but since it did not examine *all* of Sherlock's arguments or conclusions, it did not prove that Sherlock 'never' used deduction. Nor did the video prove that all unexamined instances fit into the same category as the examined instances. Therefore, ultimately, the title was clickbait.
I whooped and hollered alone in my apartment when you cited House as the best modern Holmes adaptation. Yes. Absolutely. I couldn't agree more.
Only narrowly beaten out by Jeremy Brett's Holmes for all-time greatest IMO.
Just because you're not the doctor in the room
@@KSignalEingang I agree with you. AnotherRoof's ranking is based on the degree of sensibility and reasoning used, but if you are talking about who the best "Holmes" is, then Jeremy Brett is, in my opinion too, the best of them all. He is the Sherlock Holmes of the books.
@@2adamasthow do you know?
@@beanorama Watched the show a few times with a doctor in the room.
The term deduction can be used by bad faith actors just like a lot of logical fallacies so it's important to be able to dissect the elements. Thank you very much for this!
19:32 In the books Sherlock Holmes actually researches a lot of what he uses to reason when investigating. I remember faintly he testing different types of tabaco for something. Maybe that was on that UK tv show, I don't remember. I think in the books it makes clear he studies and examines a lot of behavior of things and people in his 'spare time', outside of investigations.
24:50 this is exactly what I was thinking as I was watching this section, glad you touched on it. Though I will say, the closer I get to the end of my phd the more I think its not necessarily true that abductive reasoning is *not* the approach taken by science. It is probably the one we'd like to avoid using if we could but as you say right after, its often all we have, and thats true in science as well and is often the motivator for further research, typically once the technology or theory (or funding...) becomes available.
But I love this one, always up for a good math+popculture merger.
Good to hear from you again! Yeah totally agree! Abduction to me is nearly always the first step -- find the patterns and plausible explanations, then seek to investigate to prove or support later.
I believe one of the problems with Sherlock's "deductions" is everything that's not shown in the movies/episodes because it would make them 10x longer, for instance, he's constantly ruling out possibilities (with whatever reasoning, be it deduction, induction, abduction or just logic) before simplifying the results for easy "understanding" by the lesser gifted. So, the inside of the ring being clean and adulturer premise and conclusion is the last remaining possibility after he has removed the other possible possibilities (for instance frequently removed due to work reasons etc), ie the premise would actually be several pages long but simplified to a short sentance.
I guess it still might not be pure deduction but it atleast explains a bit more about the process and premise.
Oh man, when you were doing the "wet road" and "rained last night" diagrams I wanted to reach through the screen to yell "Noooo! The size of those circles are misrepresentative of what would most likely happen in the real-world!" and then you went ahead and adjusted the sizes of the circles. Waves of relief washed through the ether and natural order was restored to the universe.
Liked the yellow Alex easter egg. Also the old-timey reel of RDJ Sherlock to get around copyright. And the quick "formal" suit side gag. And the Denis, Fincher, and Ritchie references to incorporate your love of film into the vid. Great way of teaching deductive, inductive and abductive reasoning. The whole video was bloody excellent.
RE: part 2 puzzle video I suggest you do it separately to your next planned video. For the simple reason that we get more videos. The yt algorithm is a fickle beast sometimes, with a large element of luck, so if you can do two quality videos instead of one, you're effectively doubling your chances of an algo-boost. More opportunities of engagement without impacting quality, and you're keeping the content recent + frequent with viewers.
Thanks for your comments! I've said it before elsewhere but my original channel idea was film review / analysis, and I think my desire to chat film creeped in here!
Yeah still mulling over the Countdown idea. Lots to discuss. The algorithm shined on the last one, maybe I'll earn its favour again!
@@AnotherRoof I would watch that film analysis! Name suggestion: Another (box office) Booth
"i'm a matematician! Of course i'm pedantic" might be my favourite abduction of the video.
This is leading me to the headcanon that Sherlock doesn't actually know what the difference is between forms of reasoning - he has a great track record of pulling it off, but he's actually really bad at explaining how he arrived at his conclusions. It's already canon that Sherlock doesn't bother to learn about things that he deems irrelevant to him - like the movements of celestial bodies - maybe he doesn't care to know how his own mind works. I feel like that would fit in with his existing character flaws
I think that's just a BBC thing. In other versions that I've seen, Sherlock is pretty well-versed in general knowledge and current events. Not knowing how celestial bodies work makes him look like an uneducated pleb.
@@One.Zero.One101I mean, then if he ever had a case relating to astronomical stuff in the slightest he’d be screwed to hell and back. Hahaha…
@@One.Zero.One101 In the original books he also doesn't know about astronomy (and literateratue) in the slightest, being astounded by the idea of the solar system, and there are a few other things like gardening and politics that be barely knows.
@@EthSephCW17 For anyone interested, Watson himself wrote about Sherlock's knowledge. Which goes like this:
Sherlock Holmes-his limits.
1. Knowledge of Literature.-Nil.
2. Philosophy.-Nil.
3. Astronomy.-Nil.
4. Politics.-Feeble.
5. Botany.-Variable. Well up in belladonna,
opium, and poisons generally. Knows nothing of practical gardening.
6. Geology.-Practical, but limited. Tells at a
glance different soils from each other. After walks has shown me splashes upon his
trousers, and told me by their colour and
consistence in what part of London he had
received them.
7. Chemistry.-Profound.
8. Anatomy.-Accurate, but unsystematic.
9. Sensational Literature.-Immense. He appears to know every detail of every horror perpetrated in the century.
10. Plays the violin well.
11. Is an expert singlestick player, boxer, and
swordsman.
12. Has a good practical knowledge of British
law.
Excellent video, thank you! Very well worded conclusions in last 4 mins. Even deductions can be tricky. All bachelors are unmarried men. Sarah is a bachelor of science. Therefore Sarah is an umarried man of science. Meanings are slippery and can alter from premiss to the next, sometimes subtly.
The "Who am I, Socrates?" ended me 😂
So he doesn't deduce, he just does fancy assuming.
He has superpowers essentially
and he's pretty lucky to be right
Which makes him look super pretentious and unlikable.
As a Sherlock Holmes fan myself (I consider Doyle's stories to be my favorite literature), I've always kind of thought this was funny. Sherlock is pretty much always just making assumptions not logically deducing facts. It doesn't hurt my enjoyment of the story or the character, though. This was an interesting dive into what each term specifically means.
@@DMW4 , ChatGPT is not an authority on anything. To illustrate this, I just went to ChatGPT and told it Sherlock Holmes doesn't use actual deductive reasoning. As you can see from the following response, it agreed.
You are correct. Pure deductive reasoning is only applicable in certain contexts, such as formal logic and mathematics, where the rules of logic are well-defined and the premises and conclusions are absolute. In that sense, it is true that the deductive reasoning used by Sherlock Holmes is not the same as the pure form of deductive reasoning found in formal logic. However, it is still common to refer to Sherlock Holmes' use of logical inference as "deductive reasoning" in a broader sense. Sherlock Holmes uses deductive reasoning as a shorthand to refer to his process of elimination and logical inference, even if it does not fit the strict definition of deductive reasoning. This is likely due to the fact that deductive reasoning is a commonly understood term that conveys the idea of logical inference, even in situations that do not fit the definition of deductive reasoning. Overall, while the terminology used to describe Sherlock Holmes' methods may be imprecise, it is clear that his approach to investigation involves a combination of induction, abduction, observation, and intuition, all of which contribute to his highly effective and influential methods.
I haven't learned about what abduction is while I was in school/university. And I think we should teach about this and give it some attention not just put spotlight only on deduction and induction. Even in math when I read some math proof, it feel like proof writer already know the answer and they use deduction to proof it later. (And I always left with an unanswer question "what lead them to this answer in the first place?" and I often can't find it becuase spotlight was put on the finished product, the deductive proof itself)
First, you are the best, I really understand how set theory defines numbers now. I read Godel, Etcher, Bach, but I really didn't get the proof until you explained it. Your reference to "Pigs On The Wing", that is golden! Please keep making these!
I am so glad you explained the unsoundness of the wedding ring argument in this video, because the moment I heard it I was questioning it’s soundness but without realizing that’s what I was doing, I just figured I must not know something about how removing wedding rings effects the rings.
This confusion happens a lot for me and when the argument comes from a figure of intellectual authority I will remain skeptical of it but assume I must’ve simply missed something that they know and I don’t. Now when I get that feeling I’ll do more than simply remain skeptical since they might be intentionally glossing over information to support their argument, and I’ll see if there is any reasonable explanation for the steps that I have not been shown.
The problem I have with the wedding ring debunking argument, specifically in regards to how just because it's cleaner on the inside and is removed frequently, doesn't mean she's a cheater, is that it doesn't take into account the state of the rest of the jewelry she wears, nor the rest of her appearance as a whole. Sherlock explains that while she cares a lot for her appearance and the rest of her jewelry is clean, the wedding ring remains the only dirty piece of jewelry on her, implying that it's cared for less than the rest of her stuff. Why would someone of that nature care so little about her wedding ring of all things? This is what he couples with the fact she removes it frequently to ultimately come to the conclusion that she's unhappy in her marriage and cheats.
24:50 i would argue that the abductive approach is often used in archaeology wherein there is scarce information to base conclusions on. While induction isnt foreign to this science, cases in which it can effectively be used are not common.
Archaeology also often borrows methods from the humanities.
It was (probably, maybe) used for religious purposes.
In linguistics, especially when it comes to genealogy of languages, abduction is often done in the form of pure speculation.
The problem with the :
- some of b is is a
- some of c is in b
- therefore some of c is in a
Is that the initial example would have constructed a triple nested Venn diagram, where a is entirely with b, and b entirely within c.
The language kind of implied it, but not explicitly, and that's where the issue first artist. Your analysis of the Venn diagram you drew is also perfect, alongside your counter example, but I believe we may need to change how we word things to disambiguate
This channel is a golden mine, love it! Last week I was explaining formal logic at class and Sherlock Holmes came instantly as an example of deduction, that's if you take the crime scene as a closed system with relations of literary necessity. Seeing this video I think I will restrain myself to syllogisms next time to not cause any confusion hehe 😅
Oh, wow. Such a source of frustration to me. Thanks for explaining that the reason I never really understood what “deductive” means is because people almost always misuse it.
I think the true meanings do matter because (in the US)… well, if people use these words at all, it’s usually some sort of power play. Like, they don’t remember anything except that deduction is supposedly the “best” type of reasoning, so they say something is deductive to imply that it’s unassailable, not that it’s sound. Whether or not I say it out loud, it’s going to be a huge help for me to be able to say, “Aha, but what you’re talking about isn’t actually deduction!”
Wow. You do have a knack for producing hugely thought-provoking videos and making the abstruse absurdly approachable! Yet another of yours I thoroughly enjoyed ...though I feel bad at having never grasped the formal differences between the types of reasoning before. But hey, my degrees are in the liberal arts, so ...par for the course, I guess😅
Thanks so much for watching! I hope you make videos spanning the liberal arts some day because I'd love to fill gaps I have in my knowledge there...
@@DMW4 Well, the obvious first response is, "citation required". If there are many instances of Holmes actually deducing something, let's have at least one specific instance, rather than mere assertion. ChatGPT should be better than that!
Second thing to say: I don't think it matters. The significance of this video, for me, is that it lays bare the existence of three distinct types of logical reasoning and then goes on to explain how you tell one from another. In and of itself, it is sufficient to its purpose and needs no reliance on Conan Doyle specifics to make it's point.
@@DMW4 Your main point is simply wrong then. The video's title is a mere assertion, not a logical deduction, induction or abduction. The best you can say is, "it's wrong", therefore. It's not an example of a logical fallacy at all.
@@DMW4 The rather obvious point I was making is that since the title is a mere assertion and not a logical deduction, it cannot be a logical fallacy. It is merely correct or incorrect. Like your assertion that it is a logical fallacy.
There's nothing logical about asserting something. Therefore mere assertions cannot be logically fallacious.
As you put it, a "logical fallacy is flawed, deceptive false **argument**". If I say "the sky is polka dot pink and purple", that isn't an argument. It's a statement. It's an incorrect statement, of course. But it's not a reasoned argument.
@@DMW4 If you had confined yourself to saying it was incorrect, I wouldn't have argued with you on the point. Your claim of 'logical fallacy' was what I took issue with.
I would (and did!) ask you, however, to back up *your* assertion with a citation. Which you failed to do. If Holmes frequently resorted to the use of deduction, cite me one example of him doing so. You were the one making that claim. Regardless of your source, you need to back it up.
The entire video has made a good fist of explaining why your assertion is incorrect, after all. A simple citation can refute that claim.
This ALWAYS bothered me!!!! Thank you for making this video to validate me
Always glad to see my pedantry is shared by others 😅
New viewer here. I loved that you used the blackboard as a visual aid as you explained each type of reasoning. It has helped me to very clearly discern the differences between each. The examples you provided through text and speech were also very helpful. I think I have a sort of mixed learning style; I cannot solely rely on visuals, speech, text, or personal experience by themselves. Some combination of these must all come together so that I can truly understand a topic. You've done well by combining the 3 of 4 of them. Hopefully one day, I can experience these reasonings myself so I may understand fully. I hope that in the more videos I watch from you, you continue this mixed style of instruction. It fully encompasses all different learning styles at once, leaving no one unaided.
Again, thanks so much. I wish you the best. I hope you do your best. So far, so good! 😁
Thanks for watching, and welcome!
I actually think this video is my least diverse in terms of props and visual aids. My earlier videos are very tactile with lots of physical props.
Also while "learning styles" are a bit of a myth, I think having a range of models / diagrams / aids is good so I'm glad you found it helpful!
11:48 "Who am I? Socrates?" made me laugh
It's a brilliant comment because it flips over the expectation of usually people wouldn't mind being compared to Socrates.
The elusive fourth reasoning type is “seduction”
Personally I'm a fan of Reductive Reasoning
This was fascinating! Not surprised that you’re a teacher/tutor, this was really skillfully taught. Many thanks!
wait a minute... this isn't about sherlock holmes... you've tricked me into learning logic!
We've been bamboozled!
I love these videos. Another Roof is my favorite new(ish) math channel.
Anything that produces toast is a toaster,
your air fryer produced toast
therefore your air fryer is a toaster
You know what they say. All toasters toast toast. - Mario
Toasters cook things into toast
I cooked chicken nuggets in my air fryer
My chicken nuggets are toast
In the video, Alex talks.
In the video, Alex talks about how he toasted.
Conclusion: Alex is a talkie toaster.
So glad I'm not the only one who thought of this! :)
I have a story of how someone got totally wrong conclusions because they were a Sherlock fan. Someone came up to me on a bus, said they liked Sherlock, and asked if they could check their powers of observation by drawing conclusions about me based on my appearance. I liked Sherlock too so I agreed. He said I have a cat and a dog because I had two types of pet hair on my skirt. I had two cats. He made a correct observation but drew the wrong conclusion. He then said my boots were new because they were clean. They weren’t new (or particularly clean) but I do take care of my clothes. He again drew the wrong conclusion. Unfortunately I can’t remember if he said anything else but I do remember he didn’t get anything about me right.
Honestly, before the self-promotion segment, I didn't even notice your subscriber count. The only thing that made me a little "suspicious" was that camera placement looks a little odd, but never really payed that much attention to it. Anyways, I find your videos very educational, I hope you will reach a wider audience soon!
Such an excellent breakdown and explanation of the different types of reasoning! I once used, in one of my Intro to Comp. Classes, how the BBC Sherlock is an example of deductive reasoning vs. The RDJ Sherlock being one for inductive reasoning (since that's somewhat how the films try to portray them). But yours is much better. Also -- the entire trope of the snooty smarter-than-mortals Mr. Holmes is an example of literary ratiocination if you ask me.
When I lose my keys, I always find them in the last place I look.
(Of course, this is because I stop looking when I find them)
Thank you for caring and being pedantic! I really liked your explanation and overall approach. I'm on the "we-should-always-use-the-correct-term" side myself.
The line about "once you eliminate the impossible yada yada, whatever is left no matter how improbable is the obvious conclusion" leads me to believe that Sherlock is using the process of elimination and I'm gonna try and show that with the wedding ring example.
We have a dead woman in the middle of an abandoned house looking like a suicide amidst a string of suspicious suicides, Sherlock finds her ring is polished on the inside and she is wearing a fancy coat. I think in the episode itself someone says she's far from home, Sherlock uses this to eliminate the chance that she's local so now she's a traveller.
she's pretty young looking, her outfit is matching and fashionable which means she's either going for a meeting or something else within the city. Sherlock uses the added fact that the ring is polished on the inside due to frequent removal. A traveller with a fashionable matching outfit that frequently removes her ring- Therefore she's an adulterer.
How he decided she's a serial adulterer is a whole other thing, but basically my point is that he takes all the things he sees and one by one eliminates them based on the facts given until it lands on the most logical reasoning.
Edit: If I'm wrong I'm wrong, but I think this makes the most sense to me
@@DMW4 Maybe he does use deduction, but the answer to your question is still no. It would not be a logical fallacy. Someone being wrong rarely constitute a logical fallacy, nor is their claim necessarily a logical fallacy (which I assume is what you really meant). They may have simply got the facts wrong. This would also be the case here. To be logically fallacious, he would have to contradict himself, but he does not. You are bringing in new information to claim that he is wrong.
@@DMW4 ChatGPT is a very unreliable source. There are not "many instances of Holmes using deduction." Process of elimination is not deduction.
@@moth5799it is, if you have actually eliminated everything else and can show that
@alexh8754 Yeah, except its not possible in the real world to eliminate all but one possibility. So Sherlock Holmes' process of elimination cannot be deduction.
@@moth5799
john had enough money to buy 1 of 3 things from the store. he bought one of them. it was definitely not 2 or 3. therefore item one was the item john purchased.
item one was the only item capable of doing such an action at a crime scene! it was a very particular antique keypad unlocker. one of one. the inventor passed away as soon as he made it and it was unseen until john bought it. good work holmes!
I wish your videos had existed when I was trying to study formal logic at uni with the world's most boring lecturer. You managed to explain this far more clearly in 30 mins than he did in an entire semester.
Let me just start by saying I absolutely loved your Pink Floyd reference!
Nice video! I really liked your dicussion in the end of the viedo. I want to add that: yes, it might be problematic to use words with a spesific meaning in science to mean something else colloqially. Generally it's not a problem though. This is how language works. If words didn't evolve and change meaning we wouldn't have all these amazing and useful languages. It's not a problem when we in every day converation use the word "theory" to mean what scientists would call an hypothesis. But it IS a problem when people don't understand that theory does not mean hypothesis in scientific terms as "the theory of evolution" or "the theory of gravity". ("But that is just a theory!")
That's why I always get more interested in a debate when the debattants start by making some definitions. You might not even agree on how different words SHOULD be defined, but it doesn't really matter if you just can agree on something "for now". If my opponent define atheist as someone who "hates God", that is very, very silly, but I can technically live with my opponents stupid definition, as long as I can define my self as a PNCOTEOAG (person not convinced of the existence of any gods) and use that in our debate. (Of course you never get any way if you go completely Jordan Peterson though, and ask people to define every single well defined word when people disagrees with you)
19:05: I am so glad you brought this up. SO many people just seem to not remember that what is considered "scientific fact" can change based on new evidence.
Not to be overly pedantic, but words have specific meanings, especially when discussing science.
In science, a "fact" is generally understood as an observation or a measured value that has been repeatedly confirmed and accepted as true by the scientific community.
For example, the statement "Water boils at 100°C at sea level" is a fact, based on repeated observation and measurement. The theory of thermodynamics helps explain why this fact holds true under specific conditions.
When you use the phrase "scientific fact", it would seem you actually mean hypothesis or theory. These are open to change over time as new facts are discovered, and logical reasoning identifies incorrect assumptions and conclusions. The theory is modified, leading to correction over time. The facts themselves don't change.
We could discover an entirely new interpretation of gravity that fundamentally changes the way we understand the universe, yet the scientific facts we currently have would necessarily comport with this new gravitational theory for it to be considered true.
In other words, in science, a fact (accepted by repeated measurement and validation) is a form of evidence, and evidence isn't open to change.
@@icycooldrink6085 This is a great explanation. That is what I meant. I find that a lot of people forget the different between scientific theory and scientific fact. This has caused trouble in the past; the house arrest of Galileo for instance.
@@lukeleslie9648 A theory can be as fleshed out as the theory of evolution, or the theory of gravity, but they can still be classed as "theories" in science, due to their ever-expanding index of new discoveries.
This becomes particularly annoying when people (usually theists) use it as a way to strong arm debates, "its a theory, therefore not real", something along the lines of that.
@@derpy9452actually the term theory in science simply refers to the total body of knowledge of a given subject. It has no relationship to whether or not there's still new things to learn. Even if provably everything to know about a subject were known, it would still be called theory, there's nothing to move beyond to.
By “deduction” Holmes really means “massive quantities of cocaine”
4:10 I've never seen a Non-arabic person reflecting with this level on a term especially with a language such as English (I'm Arabic and we have such a pride with the poetry/ versatility of Arabic language) and it's amazing to observe.
It makes sense that they used the word deduction, rather than abduction.
It's better to say he's amazing at deduction rather than say he amazing at abduction. Might get stares for that.
Fun fact, in German mathematical induction is called "complete induction" (vollständige Induktion) because it is induction, it just happens to be valid because you're not showing something for many numbers and conclude it must be true for the rest of them, you're showing something for _all_ the numbers.
"Once you're eliminated the impossible, whatever remains, no matter how improbably, must be the truth. So far we ruled out the possibility that the suspect walked to the crime scene, for he has no legs. Now we just need to rule out the possibility that he drove, cycled, teleported, garnered the assistance of aliens or remotely commit the crime using telekinetic powers."
"Do you really think all of that is likely?"
"Likely, no, but possible, yes!".
Greetings Dr McGraw, The curse of being a Mathmematician among Innumerates. Just discovered your channel. I'm a Some-College 72 year old avid reader who always had some math facility. Without Pedantry we'd all be Footless and falling on our.... Again thanks, I'm looking forward to more. All the Best, Jacques Mexico retired but no tired
"I'm a mathematician, of course I'm pedantic" haha that sounds about right
I think the distinction in definitions is immensely important. I've gotten so sick of getting into arguments with people, only to realize later that the issue was actually incorrect definitions, and not a genuine disagreement. Language is important.
Regarding the last point you made that deduction in common parlance is not the same as deduction in more rigorous settings I think is trying to fight the tide. It's like how "theory" in common parlance just means "idea" while in more scientific settings a theory is much more rigorously defined and is pretty much what we'd call a done deal in day to day conversation. I understand and agree it's frustrating that jargon is used in ways directly counter to what they mean, but I don't think it's something worth expending the time or calories being bothered by.
Broadly speaking, I agree -- it's hard to fight the tide and maybe not worth the effort. My point was more that the common parlence version has seeped into arenas (like debate) in which the rigorous version should be demanded. And many people don't know the difference which is what I hope to remedy with this video.
@@AnotherRoof that's a fair point I didn't catch the first time around. I agree.
FWIW, when explaining the more rigorous definition of "theory", I often find people get it when I bring up the notion of "music theory" - it's not the bare supposition that "music exists" or anything like that, it's a framework that allows us to talk about music in a way that's helpful to understanding and discussing the underlying "facts" of tone, rhythm, harmony, etc., and how they relate to one another.
@@KSignalEingang that's a really good shorthand. I'm going to use that going forward!
I think efforts to educate people about the proper meaning of theory have been pretty successful though, like you don't even see creationists saying “it's just a theory” anymore so that has to be a sign of progress.
Abductive reasoning is used all the time in medicine when making a diagnosis. The patient’s symptoms rarely line up perfectly with the textbook definition of one diagnosis, but rather fall in between a few “likely” diagnoses that are arranged in order of likelihood
so what you are saying is: sherlock uses "the science of abduction" to solve his cases. Very fitting, very fitting indeed.
I didn't know what you meant until I watched your video, and now I realize I use real deductive logic in programming! Thank you for breaking down this topic!
My mom after hearing me explain this: "I gave birth to you therefore-"
I detect an unsound argument (but only abductively, not deductively)...
Very nice, very clear, very instructive !
I didnt know "abduction", but maybe it's because it has a completely different name in french whereas induction and deduction are basically the same word in both
i took a course in logic, and am currently talking one in mathematical proofs, but neither of them really explained anything here past the deduction section. i also find it interesting that mathematical induction is still a form of deduction. it took me quite a while to understand why mathematical induction worked as an actual proof
Didn’t he say in the video that mathematics only uses formal deduction?
@@qy9MC look up mathematical induction. it's a form of proof that uses recursion and it is actually deductive based on what he said, but it's called induction. it's quite a fun type of proof
@@azrael_hypo Ohh induction proofs yes. You’re right it’s odd we call it induction in English. In french they call it récurrence (recursion).
The key distinction of a mathematical and scientific conclusion is verifiability. For a challenging math problem like finding the prime factors of a large integer, someone claiming to know the correct answer can have their answer verified with 100% confidence whether or not it was accurate. For a challenging scientific problem, the best we can do is test it and assert that we were unable to disprove it based on our current understanding.
Be careful making toast in an air fryer. Depending on the design the air can push the bread up to contact the coil and you can imagine the rest 😢
I think it's in the Red Headed League short story where Holmes tells the client he's a clerk because the cuffs of his jacket are shiny. He could have bought the jacket at a thrift store, or borrowed it from someone. That's the example that I've always pointed to as proof that Holmes' "deductions" aren't logical.
True story: when I was six years old, my brother began teaching me how to multiply. The first thing he taught me was that 3 x 3 = 9. I asked him why, because I wanted to know. He shot back with "it doesn't matter why, 3 x 3 = 9." After watching the entire video, I'm not sure where that falls in the category of logic. All I know is, he was right, because when I got to the 3rd grade a couple of years later, they told me the same thing, also without explanation. This may have to do more with indoctrination than with logic, but even today, 47 years later, 3 x 3 is still 9. Good stuff, this math...
Really they haven't explained that if you add 3 times 3 - 3+3+3 then you get 9? Why?
A lot of simple maths is the way it is because that's how we define it. Not sure about that, though.
Sherlock in the books, it is said that he has methods to know what has more chance to implies something, when observing someone and that he has already used these methods so much that it makes him have a magical intuition, but it is never revealed what these methods are, so...
My god I love the fact that you say "I'm a mathematician... of course I'm pedantic!"
As a chemist, probably my favourite part of this video.
Thank you for your amazing educational work by the way :)
Correction: when the ground is wet it is often isn't from the day before because it is also wet when it is raining, and you often notice it then. That said you're quite justified still as it breaks some of Grice's Maxims when we mention such options too much. A pedantic curse of being completist in our structures. An other form of trivials for communication
Where can I get 4 Socrates pies around here?
You don't even need to remove the ring frequently for it to be polished!
Try moving your ring nervously back and forth or pensively spinning the ring around your finger. Do that 10,000 times and you've buffed the ring smooth with your skin and hairs.
Even as a boy I slightly mistrusted the postulate from Conan Doyle via Holmes that "When you have eliminated the impossible, whatever remains, however improbable, must be the truth."
I became increasingly unconvinced, as I was forced to gradually surrender the simplistic and convenient notions of youth, that it would ever be feasible to marshal ALL the alternative hypotheses to account for *known* facts (and that's setting aside their usual scarcity, in comparison to unknown and in some cases unknowable facts), let alone strictly and reliably split those hypotheses across the nebulous and hypothetical boundary between impossible and highly improbable.
But even if this were possible, it seemed particularly unlikely that there would ever be only one hypothesis left on the "highly improbable" side of that boundary (unless, as often seemed the case in the Holmes stories, a woefully inadequate number of alternative hypotheses had been adduced in the first place, often only two or three)
Finally the methology seems to me blatantly fallacious now you have laid out with a simple Venn diagram, in a specific instance, how Holmes' truth claim about wedding rings violates the formal definition of deduction.
There is a good reason that the Holmes canon is shelved in the "fiction" section of libraries. It does make great reading, I have to admit, to pretend that the affairs and contexts of social interaction are necessarily susceptible to logical dissection with reliable prognoses. But if my happiness is ever hostage to the findings of a detective or judge, I can only hope they will not have learned their "logic" at Sherlock's knee.
The methodological flaw with this reasoning is unknown unknowns. Holmes can never ever be certain that he has removed all other possibilities because he cannot ever know that he knows everything pertaining to the case. Like maybe that ring actually had a special coating on the inside that kept it clean that Holmes has never heard about and since he isn't particularly up to date on nanoscience he doesn't even know such a thing could exist.
@@hedgehog3180 It's a compelling and plausible example of an unknown unknown. The pedant in me does nevertheless feel compelled to consider a faint plea in mitigation for Conan Doyle: Holmes did observe that the ring was dirty on the outside, and it seems rather unlikely (although of course not impossible) that the ring would lose its external protection, or never have been externally protected, and yet retain its internal coating.
However, an infinite number of very unlikely things are happening every instant.
There is a huge distance between "very unlikely" and "impossible", a key consideration which Holmes completely and chronically overlooks.
Which is why your example transcends my pedantic quibble, and perhaps hints at one reason why such quibbles, even though they may be worth dissecting, are usually immaterial.
You’re right, of course, but the idea is that when Sherlock Holmes says, “The state of this ring indicates serial infidelity,” he has eliminated other possibilities through obscure expertise (e.g., BBC Sherlock canonically authored an article about the “The X Different Kinds of Cigarette Ash,” so when he later makes a claim about an ashtray indicating something, the viewer is to understand that he has the requisite expertise to prove that claim by necessity.). It’s a superpower that works better when it’s not explained (which is good because it can’t be explained because it doesn’t actually work irl).
Let’s be honest though, the BBC show makes sherlock’s reasoning especially silly
I believe that the value from people being more apt at distinguishing different types of arguments is related to valuing clarity in communication.
Tysm for this lol! Since I was younger, Holmes & these types of male characters in general often irked me with their type of reasoning, making premises that don't necessarily follow to then, at best, guess a conclusion & look like smug genies when correct. Especially when it came to assumptions about women's sex lives. I just couldn't put my finger on why, but it felt like it wasn't deduction.
The best I could formulate was "At least say it's *likely* that this is the case, or make it clear we're talking about probability." Funny that that's basically what abduction is, which is what they were doing most of time. It also explains why I liked RDJ's version of Holmes better, bc the story shows he can be off sometimes.
There's an issue in general with romanticising people's conditions as them being God, like that show about a man who can ALWAYS tell when someone lies, or the one about a woman who remembers everything & never forgets, or hell even The Good Doctor. Autism and sociopathy don't make you a well of truth. Despite these conditions, you're still human.
he's always right because thats how the author wrote it
i'm so happy to have found your channel! i took some classes in propositional logic in college way back then, you're helping me take out the rust from my brain.
video start at 11:00
should have seen this sooner
The following may be better as separate comments, but I've decided to make it one comment:
I remember finding that “deduce” doesn't necessarily mean deduction. I used “abduce” (invented by me) instead. (Now, I've realised that that probably was induction, so I was also wrong in that way.) I wrote about how I could end up with an incorrect definition of a word. One of the ways was by mishearing something. Someone suggested that I may have misheard “deduce” as “abduce”. I explained how I actually got this. (I couldn't remember why I thought “deduce” meant deduction)
Here's an example of another one to illistrate how I used “abduce”: I saw a video where a streamer played a game. (I'll use some terms that I think are common for many games, but if you don't know, just treat them like people treat made-up words such as “gostak”.) There, they made a bingo card with various possible things they could find in the level. One of them was “elevator button”. I didn't know what it was. At some point, the streamer jumped and that had effect. They called it an elevator button. I abduced (or induced) that it meant detecting jumps. Later, it turned out that it actually meant a useless trigger
I think deduction and induction are special cases of abduction. Deduction is when the method guarantees it with absolute certainty (assuming the premises are true), which is a case of high likelihood, and induction is when it's by generalising examples. In both cases, the result is likely true
Here's a copypasta I've found recently:
> # Smart characters written stupidly
>
> Why does nobody like Sherlock? Because it has smart characters written stupidly.
>
> Anton Chigurh from No Country for Old Men is a smartly written smart character. When Chigurh kills a hotel room full of three people he books to room next door so he can examine it, finding which walls he can shoot through, where the light switch is, what sort of cover is there etc. This is a smart thing to do because Chigurh is a smart person who is written by another smart person who understands how smart people think.
>
> Were Sherlock Holmes to kill a hotel room full of three people. He'd enter using a secret door in the hotel that he read about in a book ten years ago. He'd throw peanuts at one guy causing him to go into anaphylactic shock, as he had deduced from a dartboard with a picture of George Washington carver [sic] on it pinned to the wall that the man had a severe peanut allergy. The second man would then kill himself just according to plan as Sherlock had earlier deduced that him and the first man were homosexual lovers who couldn't live without eachother due to a faint scent of penis on each man's breath and a slight dilation of their pupils whenever they looked at each other. As for the third man, why Sherlock doesn't kill him at all. The third man removes his sunglasses and wig to reveal he actually WAS Sherlock the entire time. But Sherlock just entered through the Secret door and killed two people, how can there be two of him? The first Sherlock removes his mask to reveal he's actually Moriarty attempting to frame Sherlock for two murders. Sherlock however anticipated this, the two dead men stand up, they're undercover police officers, it was all a ruse. "But Sherlock!" Moriarty cries "That police officer blew his own head off, look at it, there's skull fragments on the wall, how is he fine now? How did you fake that?". Sherlock just winks at the screen, the end.
>
> This is retarded because Sherlock is a smart person written by a stupid person to whom smart people are indistinguishable from wizards.
Induction as discussed here is also used in mathematics, although its results aren't called theorems until proven with deduction. They're usually called conjectures. It is commonly used in the study of L-objects
I think a kind of deduction is similar to induction. The difference is that all the cases are considered. In Russian, it's called перебор (homonym for overkill). There are also two kinds of deduction known as induction. One is for sets defined by operations on them. One way of defining them formally is as the intersection of all sets closed under these operations. (It's possible to prove that they are themselves closed. Here's a fully formalised definition of one such set: x:∀N(∀n(∀ee∉n∨∃m(m∈N∧∀k(k∈n⇔k∈m∨∀e(e∈k⇔e∈m)))⇒n∈N)⇒x∈N). Here, I've used logical operators in a way I think makes it most clear and didn't use what I regard as shortcuts: quantors restricted to sets and identity. The latter means that I'm using a system when it isn't an elementary predicate; in such a system, the axiom of extensionality should be what is otherwise the substitution property imported from the identity package.) This meaning of induction is that every closed subset is the whole set. To me, the video mentioning that many people misunderstand it didn't explain it; I only realised what it actually is this month. There is also transfinite induction, which is basically the well-orderedness of a set formulated in a slightly different way
I probably planned (very short-term) to write another point; if I remember (recall) it, I'll put it below
I think Holmes uses deduction all the time, the premises simply aren't stated in the text because he's a detective, not a maths professor.
For example-
Gregory (Scotland Yard detective, to Holmes): “Is there any other point to which you would wish to draw my attention?”
Holmes: “To the curious incident of the dog in the night-time.”
Gregory: “(But) The dog did nothing in the night-time.”
Holmes: “That was the curious incident.”
Here's the implied deduction-
P1: Dogs don't do nothing when there's a nighttime disturbance, unless there's something curious occurring.
P2: A dog did nothing during a nighttime disturbance.
C: Something curious occurred.
He then uses abduction to determine the nature of the occurrence, but the foundation of all of that is the initial deduction.
That's the actual problem I've always had with Holmes cases, brought to the point. I always saw at least one other possibility (usually a myriad) and never understood why the accidental cummulation of his lucky guesses made him such an ingenious detective, while usually single wrong guesses could have lead him to completely wrong paths.
The problem I have with the wedding ring debunking argument, specifically in regards to how just because it's cleaner on the inside and is removed frequently, doesn't mean she's a cheater, is that it doesn't take into account the state of the rest of the jewelry she wears, nor the rest of her appearance as a whole. Sherlock explains that while she cares a lot for her appearance and the rest of her jewelry is clean, the wedding ring remains the only dirty piece of jewelry on her, implying that it's cared for less than the rest of her stuff. Why would someone of that nature care so little about her wedding ring of all things? This is what he couples with the fact she removes it frequently to ultimately come to the conclusion that she's unhappy in her marriage and cheats.
The silent film adaptation was brilliant. I’m glad you couldn’t show the original clip.
i just started real analysis 4 weeks ago and its my first proof writing/logic class. You're such a Legend!
One of the extrinsic reasons for there to be maths: "HOWTO Think". (Or howto think about one's thinking - and so be aware of the weight of current thoughts?)
My terminological bugbear is the way "refuted" seems to be shifting in journalistic parlance (speakage, I mean, but Frenchified) from what it means to something like "denied emphatically" or "loudly and confidently asserted", depending on what its being used to verbally beef up with stronger sounding words.
It's fine for ordinary people to be careless like that, but someone whose training is meant to start with a training in very solid language use, and knowledge of current usage (as well as clever tricks like how to notice you don't know what something means, and then look it up in a dictionary) I think we're entitled to complain. Yes, language will change, partly by slop, but that doesn't mean it's up to the journalists of our time to provide as much of that slop as possible. A journalist is meant to be left out of the language slop game. It's for the less educated rest of us, not for them. They're meant to be playing something like the pedantry game.