Sherlock Holmes NEVER 'Deduced' Anything
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The word "deduction" is often used synonymously with "reach a conclusion." But deduction is much more specific than that. Watch to learn about the three types of reasoning -- deduction, induction, and abduction -- and find out which method Sherlock Holmes actually employs.
⬣ TIMESTAMPS ⬣
00:00 - Introduction
03:13 - Deduction
14:35 - Induction
20:21 - Abduction
26:03 - Conclusion
⬣ INVESTIGATORS ⬣
Slug is what Formal Alex is telling you. Don’t include spaces.
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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.
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"?
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."
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.
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
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"
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.
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 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.
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.
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
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
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.
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.
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?
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!
The "Who am I, Socrates?" ended me 😂
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
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!
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 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.
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.
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.
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
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!
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
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.
"i'm a matematician! Of course i'm pedantic" might be my favourite abduction of the video.
Distinguishing and recognising different types of reasoning is really important. For example, one can easily detect biases in arguments!
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.
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?
This ALWAYS bothered me!!!! Thank you for making this video to validate me
Always glad to see my pedantry is shared by others 😅
My mom after hearing me explain this: "I gave birth to you therefore-"
I detect an unsound argument (but only abductively, not deductively)...
11:48 "Who am I? Socrates?" made me laugh
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!
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 😅
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.
I love these videos. Another Roof is my favorite new(ish) math channel.
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!
This was fascinating! Not surprised that you’re a teacher/tutor, this was really skillfully taught. Many thanks!
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)
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.
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.
you're really good at explaining things! I hate this kind of stuff but you made it sound fun and easy to understand, so thank you for taking your time!
Awesome video! I love learning the actual correct terms, mostly using definitions as well.
I think the general problem here is more about Sherlock Holmes as a concept rather than the adaptation. Of course, "fixing" the issues can make for a better movie. But the point is, Sherlock is an ideal person so "clever" he's supposed to be capable of detecting every possibility in each case he's given.
So he starts inside a "possibility" group (like the wet road group) and is able to rule out everything but the truth based on new information, therefore arriving at the correct subgroup (the rain subgroup). This is why despite being a classic to many, Sherlock's also commonly considered to be entry-level detective stuff. He's always right, so the reader doesn't need to think other than to try and keep up with him.
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!
"I'm a mathematician, of course I'm pedantic" haha that sounds about right
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.
24:41 - The best clip insertion in TH-cam history. 🤣🤣🤣
Very well done!!!
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)
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)
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 just started real analysis 4 weeks ago and its my first proof writing/logic class. You're such a Legend!
Watching this video I induced this channel is going to have very great videos! Thanks for the clear information
hi! i clicked on the video knowing about abduction (and sorry if i saw it 1 month later, i'm not subscribed but youtube remembered i watched your first video (but not all the other ones until today that it recommended the indepence day towers destrucion problem) )
i'm now writing this part of the comment after watching the full explanation of the deduction part, so without knowing what you'll say about the other two, i wanted to say i used abduction after reading a tumblr post about sherlock holmes tv show series abduction process, i went to wikipedia to read more about it and i started using it in many things as the people around me never really helped me in educating me, even with things that you would assume are common knowledge, but that i never discovered because not even my parents talked to me about, most probably not even now.
and the first time i used it worked. i was so surprised!
p1. last weekend there was a cat festival (i know it because i saw a billboard about it) p2. a person asked me "guess where i went last sunday!" with certain happiness p3. that person likes cats
c. that person went to the cat festival last sunday
i never realised dr. house was using abduction, but it makes very much sense and why i liked that series.
unfortunately i never went too deep in matchematics, even if i really want to, but it would never matter to me, so i never noticed me using abduction on university hard problems.
well, you didn't really said much more that i already knew, but at the end you quickly said that many people use abduction, but think they are using deduction...i could guess it's true, but in the same way you said you need to become more logical to use deduction arguments instead of abduction arguments, i feel like the same could be said for abduction ("you need to become more logical to use abduction arguments instead of illogical abduction arguments")
thank you for the lecture!
Reminds me of the first chapter of Jaynes's Probability Theory. He goes through a series of weakening syllogisms that people use for reasoning:
First, the deductive: "If A is true, then B is true; A is true; therefore, B is true."
Then, weaker, "If A is true, then B is true; B is true; therefore, A is more plausible."
Then, yet weaker, "If A is true, then B is true; A is false; therefore, B is less plausible."
And finally, even weaker, "If A is true, then B is more plausible; B is true; therefore, A is more plausible."
Then he goes on to derive the laws of probability theory (in a Bayesian way) from these kinds of principles.
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.
Clear and entertaining as usual. I love the little asides.
I can't believe that I sat down to watch a nice video about Sherlock and now I've got reminded that William Lane Craig exists and says things.
Excellent and informative video! Keep 'em coming!
Very nice video that teaches the basics of formal logic. Its also good to use symbols or letter when evaluating arguments for their validity or their soundness. For example, all man are mortal can be presented as all A's are B's S is an A. Therefore, S is a B. Its always easier to evaluate arduments when we summarize things. But its important to understand quantifiers, qualifiers.. and other parts of premises when we create their symbolic representations. Anyway, as a big fan of a formal logic i will sub to this channel its great, and these kind of videos inspire me to review my knowledge on formal logic that i studdied as a hoddy a few years ago. It helped me a lot in my programming career. Very useful skill to have in any area of work and study.
I'm self-studying formal logic and proofs using Velleman's book, so this video is convenient and much appreciated!!
I'm glad to see that at least the mess of a show series that is Sherlock, prompted the creation of this great video. Massive thanks for this 💞
I love how you explained the difference between maths and science at the same time!
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 was a great video. I always suspected that Holmes was not using strict deduction. Thanks for clarifying.
I believe that the value from people being more apt at distinguishing different types of arguments is related to valuing clarity in communication.
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.
mycroft : "balance of probability, my dear".
It's somehow curious that I never heard of abduction until now. I guess I've heard of the same concept under the disguise of Ockham's razor or the parsimony principle.
But definitely, the Venn diagrams that Alex showed brought me back to the Bayesian analysis, where one may calculate the probability of an antecedent event given that the consequent has happened, but coming from the inverse one.
Usually, this is notated as P("Streets are wet"|"It has rained").
Great video Alex! (but I guess my taste on movies is more canonical and I don't know your directors).
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 😢
Logic spoiled me for Sherlock Holmes years ago, and now it drives me up the wall when I hear Holmes' methods called "deductive reasoning" or "deduction."
@@DMW4 Yes I do agree. I think it is accurate to say that Holmes dipped into several types of logic and reasoning. While it would be incorrect to say that Holmes never used deductive reasoning, it would also be incorrect to say that deductive reasoning was a novel innovation that Holmes brought to his investigative techniques (which is how Holmes is sometimes characterized).
what an uncanny video to make considering my comment from the community post. :)
The funniest thing is that I was thinking of Holms among other things.
Great video!
Time travel confirmed?
One of my favorite House MD premises: "It's never lupus"...
Until he uses inductive reasoning to change the premise to "it's never lupus, unless it is".
I absolutely love these videos on logic!
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"
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 really enjoyed the video. Good work.
I'm the same way about the overuse of the phrase 'begs the question' and the complete failure to use the usually correct phrase 'raises the question.' The question is rarely being begged when people say it it.
Don't they essentially mean the same thing though? What's a case where it'd actually be correct to say “begs the question”?
To raise the question is simply to notice a thing and query it. To beg the question is to assume the answer within the question, e.g. 'When did you start beating your wife?' when the person has not yet admitted that they, in fact, do beat their wife @@hedgehog3180
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.
Thumbs up for the sole reason that you took the time to put on a tux for a 5 second bit. That's dedication. 😁
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.
Thanks for this amazingly good video, so clear and necessary that I'll watch it with my 7 year old daughter, certainly not a small compliment.
Not quite my target audience but if it helps her grow into a logically astute and rational individual then glad I could help 😄
Wow
Thx for this wideo
It it one of the greatest lesons in long time (highscholl) that is intreasting and opens eyes
Your the Best
Ps:
One of the Best ads that i seen
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!
This is such a great video on logic, my hat is off
I had no idea I would have found all this fascinating!
As an applied mathematician who relies on inference most of the time... I have to admit that I had not heard of "abductive reasoning", I Holmes's arguments weren't deductive, but I thought they were inductive. So thank you for showing me the difference!
P1: Nothing is better than eternal happiness.
P2: A ham sandwich is better than nothing.
C: A ham sandwich is better than eternal happiness.
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.
wait a minute... this isn't about sherlock holmes... you've tricked me into learning logic!
That wedding ring scene from Sherlock isn't sound reasoning, which is what annoyed me about it. Anyone married who never takes their ring off will find it looks clean on the inside from shifting about just a little bit all the time, and rough on the outside from being scraped and bumped into things on a regular basis. Yup: the ring in Sherlock is what a ring that is worn all the time and never taken off looks like. Especially since it was so easy for Sherlock to remove it, meaning it is loose enough to move about constantly and get polished against the skin. If it were nice and clean and smooth on the outside, that might be a sign it isn't worn much, which can also be due to a large number of valid reasons.
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).
Induction is also important for mathematical research: through observation we form conjectures which attempt to explain the observations of results that we see proven. Over time we find counterexamples to these conjectures and revise our conjectures until eventually we arrive at a conjecture which is true and is proven deductively (or forever remains a conjecture because the deductive arguments that can prove the statement escape our limited comprehension and creativity).
"Therefore, she was having an affair with the air fryer."
"Astonishing, Holmes!"
I found you through your Countdown video. and this one is another cracker! thank you.
Lol I wouldn't have noticed the "clutter" in the background unless you pointed it out. Now I can't unsee it! I appreciate the apology regardless though.
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 :)
I love it. So generally you could say you use induction to generate theories and models of the world, deduction to expand on those models and predictive power, and abduction to apply them to a specific circumstance?