The Liar Paradox - an explanation of the paradox from 400 BCE

  Рет қаралды 952,809

Jeffrey Kaplan

Jeffrey Kaplan

Жыл бұрын

I am writing a book! If you want to know when it is ready (and maybe win a free copy), submit your email on my website: www.jeffreykaplan.org/
I won’t spam you or share your email address with anyone.
The liar paradox goes back at least to Eubulides, the Ancient Greek philosopher and student of Euclid in the 4th century BCE. That’s the year negative 400. In this lecture video I explain what the liar paradox is and why it just won't go away. I also try to make some jokes about Captain Kirk of Star Trek.

Пікірлер: 3 700
@talonthehand
@talonthehand Жыл бұрын
In the book Thief of Time by Terry Pratchett, the auditors of the universe, beings of pure order and logic, eventually overcame this paradox by classifying three types of sentences: True, False, or Bloody Nonsense.
@stevehorne5536
@stevehorne5536 Жыл бұрын
Para = beyond/aside from - let's say separated from. Dox = opinion/idea/belief - let's say sense. So a paradox is separated from sense - i.e. in the modern vernacular of Ankh-Morpork, bloody nonsense.
@stevep2448
@stevep2448 Жыл бұрын
And this demonstrates clearly the genius of Pratchett.
@stephengibbs8342
@stephengibbs8342 Жыл бұрын
he was a genius
@damiaomedeiros8873
@damiaomedeiros8873 Жыл бұрын
Thief of Time, one of the most delicious books ever writen!
@mrtonod
@mrtonod Жыл бұрын
Reminds me of the caption in my Statistics 101 textbook which proudly stated that there are , "Three kinds of lies, lies, damned lies and statistics."
@davidantonson9003
@davidantonson9003 Жыл бұрын
This paradox is instantly relatable to anyone who takes an exam from a professor who isn't careful with their grammar and sentence structure. I am often stuck between wondering if the question is a "trick" or just not thoroughly thought out.
@domomitsune5920
@domomitsune5920 Жыл бұрын
This kind of reminds me of how my teachers used to teach the lessons, and told us to write everything down because it was going to be on the exam. But when you took the exam, they worded the questions so unintentionally, that you had a does not compute situation, and your brain started to fry itself trying to figure out what the hell the answer supposed to be, even though you knew the answer. Because the teacher said this was going to be on the test.
@ENFPerspectives
@ENFPerspectives Жыл бұрын
Ha. Exactly.
@carlhartwell7978
@carlhartwell7978 11 ай бұрын
Definitely relate, grammar can be a bitch, but so can philosophy. Combine them and even the most experienced and knowledgeable tutor can be 'strung up'!
@VKEvilution
@VKEvilution 11 ай бұрын
"Choose the answer that's least wrong"
@robertcowan7610
@robertcowan7610 11 ай бұрын
Been there. It sucks.
@sslavi
@sslavi 9 ай бұрын
This is possibly the longest and the most convoluted presentation of arguments against the figure of Captain Kirk the world has ever seen.
@iluxa-4000
@iluxa-4000 11 ай бұрын
With situations like this, I always propose the thought of "it has no meaning". In this case - some sentences are true, some are false, and some have no meaning behind them, thus not worthy of a thought. The pair of sentences that reference each other and create a paradox don't posses any meaning, so they should be treated as just that - a jumble of words
@philcorrigan5641
@philcorrigan5641 11 ай бұрын
Yes, similar to how the correct answer to dividing by zero is that it is ‘undefined’. Or to put it another way: garbage in, garbage out.
@Charles.Martin
@Charles.Martin 10 ай бұрын
@@philcorrigan5641 I just had this same thought when watching the video!
@Squant
@Squant 8 ай бұрын
That's just a less eloquent, and potentially incorrect way of saying "neither true nor false".
@iluxa-4000
@iluxa-4000 8 ай бұрын
@@Squant em, no. You just refuse to play the game because it makes no sense, that's all
@dragonslair951167
@dragonslair951167 8 ай бұрын
@@Squant Take a sentence that doesn't contain a claim, like a command: "Go fetch me some milk." Or a question: "Who are you?". You could technically say that the sentence is "neither true nor false" and therefore "not true", but in doing so you're stretching the definition of "untrue" to the point where it simply makes no sense to use it linguistically. "That command is untrue" or "That question is untrue" is wordplay at best and gibberish at worst. The logic you're using operates under the false dichotomy that something can either be true or untrue and there's nothing in between or outside that. But sometimes something IS in between, half true, or (Most importantly) simply irrelevant or meaningless.
@donwanna3906
@donwanna3906 Жыл бұрын
I feel like making it into two sentences instead of one doesn’t eliminate self-reference, just elongates it from one sentence to two. The set of two sentences is self-referential in the same way the set of one sentence was self-referential.
@lozzamoore
@lozzamoore Жыл бұрын
Really enjoying these videos. Yes so to my mind (with no formal philosophy training) the paradox arises due to the existence of a circular reference. Remove these from any set of sentences. Problem solved! I'm sure I'm missing something here....
@jeffwells641
@jeffwells641 Жыл бұрын
It's more recursive than self reference. You could say a recursive system can't make reliable statements about itself.
@TheSwiftCreek2
@TheSwiftCreek2 Жыл бұрын
I was also kind of thinking of dual self-reference, but I wasn't convinced I was right.
@TheSwiftCreek2
@TheSwiftCreek2 Жыл бұрын
@@jeffwells641 Good point.
@Fuckyoubloodymoron
@Fuckyoubloodymoron Жыл бұрын
Circular logic be circular.
@drzonbrone3346
@drzonbrone3346 Жыл бұрын
Yes, the splitting into 2 sentences might remove self-reference, but it introduces it's own referential problem. You can replace the "The sentence below" with the actual sentence below. Similarly with the sentence above. You get into a similar infinite regression.
@anxez
@anxez Жыл бұрын
That's where I was at. Which means you can ban all logic based on any loop of truth, and we already do that by calling out circular logic.
@vincentc9072
@vincentc9072 Жыл бұрын
It's like an indirect self-reference
@lorefox201
@lorefox201 Жыл бұрын
in short, the two sentences don't exist in a vacuum by definition they are linked by referencing one another,so saying that you can do liar paradoxes by making liar PERIODS instead of liar SENTENCES is just... more recursion.
@nilespierson
@nilespierson Жыл бұрын
That's exactly right. Splitting into two sentences doesn't remove the self-reference, it's just a higher order of self-reference.
@benheideveld4617
@benheideveld4617 Жыл бұрын
Indeed! The problem lies with referencing. According to Aristotle in his essay “On Interpretation” the requirement of a proposition is that it needs both a subject and a predicate. Kaplan erroneously uses the word sentence, but a sentence does not need to be true or false, a proposition in ordinary logic must be either true or false, but that doesn’t mean you can know if it is true or false. There are other tricks too, like “The final digit of π in decimal representation in unknown.” In order for this sentence to be a proposition, “The final digit of π in decimal representation” pretends to be the subject. But we all know that π has no final digit, because it’s decimal expansion is unending. Therefore the phrase purporting to describe the subject is describing an impossibility, therefore the purported subject is invalid as a subject. Therefore the sentence lacks a subject. Therefore according to Aristotle the sentence isn’t a proposition. Therefore the sentence cannot have a truth value. A subject containing a reference that does not completely materialize, here meaning lose all reference elements after a finite number of substitutions, just isn’t a valid subject and without subject we don’t have a proposition and a sentence that isn’t a proposition cannot have a truth value and hence cannot yield a paradox.
@NeedsContent
@NeedsContent 8 ай бұрын
I'm just impressed he's able to write everything backwards so well.
@GlutenEruption
@GlutenEruption 8 ай бұрын
Can’t tell if this is a joke or not but in case anyone doesn’t know, you just write normally and then mirror the video in the edit.
@NeedsContent
@NeedsContent 8 ай бұрын
@@GlutenEruption Well that would make a lot more sense!
@BOOGY110011
@BOOGY110011 8 ай бұрын
You my friend should watch some "shapes and colors" type of video. Might to early for paradoxes for you hehe
@rebelsclipsntricks
@rebelsclipsntricks 8 ай бұрын
When he wrote the sentence "fribble is not true." But wrote the sentence in backwards order from true to fribble, to much lol
@User24x
@User24x 5 ай бұрын
@@GlutenEruption I didn't know either
@jeffreytackett3922
@jeffreytackett3922 8 ай бұрын
I've always felt that this kind of thing isn't a limitation of math or human understanding, it's a limitation of language. In an odd but simple example, there are an infinite number of decimal steps between the number 0 and 1, but there are no (or very few) widely-accepted steps between false and true.
@DemiImp
@DemiImp 8 ай бұрын
It isn't a limitation of language. It is an intentional choice that "true" means "completely true". An equivalent is true means 1 and false means 0. If the value is 0.5, then it is either true (1), not true (not 1), false (0), or not false (not 0). In the 0.5 example, it is both "not 0" and "not 1", so it it satisfies both "not true" and "not false". Typically when people say something is false, they mean "not true". Or rather that the statement is not completely true. An example of this is "Hobbits are small humans". It is true that Hobbits are small, but it is false that they are humans. People will say that the statement is "false" as a shorthand for "not completely true".
@wingstrongwingstrong
@wingstrongwingstrong 8 ай бұрын
a sentence as such is not binary maths and can be not only "true" or "false", it can also be "an incorrect set of words", so there is a third option: "the sentence is rubbish"
@hicri9739
@hicri9739 5 ай бұрын
That's one of the (not so great) options but you can formally express the paradox too. Language is what conveys you the paradox but not the paradox itself
@peterskove3476
@peterskove3476 Ай бұрын
I very much a novice in this area but I was wondering about that very thing as I listened. Then I wondered if this problem arises in the real world , or just a puzzle…and if that’s a measure of it being a language thing…
@ericpheymannicie5044
@ericpheymannicie5044 Жыл бұрын
The 1986 film *Labyrinth* has a very well-hidden reference to this paradox in the 2 Doormen Riddle scene. Sarah is tasked with the riddle "You can only ask one of us [which door leads to the castle]," "[but] one of us always tells the truth and one of us always lies." Sarah thinks she figures this out by asking one doorman "would [the other doorman] tell me that this door leads to the castle?" She receives the reply "yes" and concludes that the other door must lead to the castle based on a similar self-reference liar quasi-paradox. Sadly she fails the riddle, and to the audience, it seems to be written off as just one more example of how the Labyrinth is "not fair." Except there's a beauty to *why* she failed. Her logic seems sound and very well could be, except for the fact that the rules were recited to her by the very doormen who claim to be a lying/truthful pair. So trying to break down the logic of whether the rules themselves could be true or not true reveals the true paradox: Can the person who says "one of us always lies" be telling the lie? A simpler breakdown is based on the fact that the two rules, "One of us always tells the truth/always lies," and "you can only ask one of us," are each recited by a different doorman. Assuming that the one who recites the truth/lie rule is lying breaks the riddle entirely and leaves no assurance that either doorman is bound or even willing to tell the truth; while assuming that the one who recites the truth/lie rule is telling the truth breaks the solving process entirely, and concludes that the 'you can only ask one of us' rule must be a lie so you have plenty of opportunities to interrogate both doormen. In fact, in assuming that the truth/lie rule is truthful, you lock yourself into assuming that the doorman who recited that rule is the only one you should ask anything. Underlying truth be damned, if you believe that rule, you *MUST* logically believe that you have already solved the riddle (though if the riddle is real, you may not have and can never really know). Sure, it really is just another example of how the Labyrinth is "not fair"; but isn't it so much more sinister knowing why? Also, everything I just said is a lie! =P
@ridestreet20
@ridestreet20 Жыл бұрын
Fuck.
@georgemaragos2378
@georgemaragos2378 Жыл бұрын
Hi, this was done earlier in Dr Who with Tom Baker - Pyramids of Mars It was well explained If he asked the "truth" guardian where would the other guardian point to as correct exit the truth guardian would point to the false door - death If he asked the "lying/false" guardian which door would the other one point to he would lie and also point to the death door The analysis was that both answers would highlight the lie every time so the other exit was the correct one
@Frankie726
@Frankie726 Жыл бұрын
​@@georgemaragos2378 i think the original comment takes it one step further by stating: if these rules are told by the brothers, (of which one is lying) that must mean that the rules are a lie. Which creates a new set of problems like: maybe they are both always lying. But you will never know for sure, and that makes it unsolvable
@Dunnimc1
@Dunnimc1 11 ай бұрын
Right, just like a picture that looks “real”, the structure of language seems like “truth” because it’s the structured symbols that we base all learning and communication. Those brothers were both correct in what they said. It wasn’t until she put meaning to it that she was wrong. Like Schrödinger’s cat.
@cyrosgold7
@cyrosgold7 11 ай бұрын
I like how they handled this riddle in episode 5 of Journey Quest. Where the guy presented with the riddle kills one of the door keepers(the one that speaks truth) the asks the other which way is correct. Then tells him that if he is lying he would kill him and asks if he understands. The door keepers says no, so the guy asks if he wants to die so the door keepers says yes, and the guy throws him through the door that is thought to lead to doom and when the door keepers doesn't die the guy seduces that that is the safe pass. The lying doorkeeper eventually becomes the guy's squire by always flattering him and being his "yes" man.
@BellCube
@BellCube Жыл бұрын
I propose that we introduce alongside "true" and "false" a new term by the name of "repeatitively recursive." As a computer scientist, I'm most use to such a concept. If a program with inputs X calls somewhere in its executions itself with inputs X, it will therefore repeat until halted hy some external factor (such as the power being yanked). Remember, things like time and user clicks can be considered inputs. In such a case, you will never get an output of any kind; all you'll see is a loading spinner. I feel that formal logic should have a term for this.
@AllanHytowitz
@AllanHytowitz Жыл бұрын
The essential duality of the Universe is how Edwin Schrodinger came up with his classic theory where he named his two cats Anny and Sheila after his wife and mistress.
@ellenmarch3095
@ellenmarch3095 Жыл бұрын
We do, it's called "endless loop".
@nilsbabcock7686
@nilsbabcock7686 Жыл бұрын
We should call it Schrodinger's Sentence.
@ccoder4953
@ccoder4953 Жыл бұрын
In logic circuits, we often allow such things, in fact we even design them. The most basic example is the ring oscillator - just an odd number of inverters (n>1) connected in a loop. Many oscillator designs have some form of that at their core - self contradictory logic. They might have a bunch of analog trickery to get better timing, but at their heart, they are just some form of logic that can't make up it's mind which state it should be in.
@SeanJMay
@SeanJMay Жыл бұрын
​@@ccoder4953 always saw that more akin to a pendulum. The potential is transferred and thus gone, but it comes back around again. Not necessarily paradoxical because you can trace it through time, even if we’re talking about speeds akin to the speed of sound through nanometers of copper. It becomes a ridiculously fast NASCAR race, full of nothing but left-hand turns. In the same way, languages that aren't based on stack frames are generally more amenable to running recursively in perpetuity, whether singularly recursive, or mutually recursive. Most Lisp languages (that aren't built on top of Java) for instance could happily oscillate back and forth to the heat death of the universe (or random traces on the motherboard, whichever comes first).
@glenmassey3746
@glenmassey3746 7 ай бұрын
That was one of the best episodes in sci-fi that shows how to defeat an advanced AI. If that AI, has to answer the question that uses a paradox before doing another question or action and it might stop the AI or slow it down till it can answer that question.
@starroger
@starroger 4 ай бұрын
Computer, compute to the last digit the square root of 2.
@zeekfromthecreek
@zeekfromthecreek 3 ай бұрын
Unfortunately, I don't think the AIs we're about to replace ourselves with will fall for it.
@abergdahl
@abergdahl 4 ай бұрын
I think the solution is quite simpe actually. "is true" and "is false" are used to evaluate propositions, claims of some kind. Like "it rains" so to use the phrase " is true " or "is false" is only meaningful in order to evaluate a claim or proposition. A way to think is that we reduce away all "is true" or "is false" and see if there is a freestanding claim,. "it rains is true" is reduced to "it rains" which is a claim "it rains is false" reduces to another claim. However if we take "this sentence is false" and reduce it to "this sentence" we do not have a proper claim or proposition. The same evaluation comes into claim with "fetch me some water" is not a claim it is not true or false Searle discuss such sentences in depth and state that they have "conditions of satisfaction" by stating "fetch some water" it becomes satisfied if someone brings me water but it is not true or false. So the conclusion becomes that "is true" and "is false" are operations on propositions i propose that "it rains" and there fore it can be true or false. If i write out "It rains is true" it says no more that the original sentence "it rains" . "it rains" i true if, and only if it rains. "it rains is true" is true if, and only if it rains. "this sentence" is neither true or false and if we reduce "this sentence is false" to "this sentence" we see that adding "is false" is simple a mistake because it is not added to a proper proposition. The answer then is "this sentence" is not a P and only a P can be true or false"🤓
@Adyen11234
@Adyen11234 Жыл бұрын
I think the most amazing thing about humans is the ability to stop thinking about things like paradoxes.
@ChipsMcClive
@ChipsMcClive Жыл бұрын
That’s because language was made to save energy instead of spending more of it.
@contrawise
@contrawise Жыл бұрын
Seems I don't have that ability. Like it.or not, I keep seeing them.
@jeremyashford2115
@jeremyashford2115 Жыл бұрын
I see dead theories.
@NashvillePastaman
@NashvillePastaman Жыл бұрын
I see “Mostly” dead theories!!!
@DePhoegonIsle
@DePhoegonIsle Жыл бұрын
Eh, because alot of people instantly see this as invalid. Regardless true or false, it is invalid as it violates the given ruleset it proposes. More paradoxes than you might think end up being invalid because humans are just masters at breaking things. With some being closer to untested Exploitive things and lack the deeper knowledge to either resolve the truth of it or make it clear it isn't possible outside imagination & fiction. Paradoxes often happen because of a VERY simplistic take on a system with much deeper understandings required, and past that are invalidated because it was crafted to be that way. Just like we view those who think flying is proof of either a paradox or conspiracy as idiots... in time we will view those who honestly believe such paradoxes in earnest as fools as well. The issue is 'we do not fully understand what we need to' for alot of these paradoxes, and some are just people being douches and breaking a system because they can.
@janschwart4060
@janschwart4060 Жыл бұрын
I've watched a lot of his videos now and I must say I'm just absolutely flabbergasted by how well he's able to write backwards on that glass pane
@tomboyd7109
@tomboyd7109 Жыл бұрын
He is writing normally and the camera is inverting it. Look at his wedding ring. Some new U-Tubers have not figured out how to fix that camera glitch. He is simply using it.
@omnipop4936
@omnipop4936 Жыл бұрын
@@tomboyd7109 Yup, the ring, and his watch, and his shirt buttons...
@goldmirado3
@goldmirado3 Жыл бұрын
Ahh new here?
@what6306
@what6306 Жыл бұрын
lol they just flip the video so its readable lady
@mutasimaldory
@mutasimaldory Жыл бұрын
Interesting..I simply assumed he was writing on a mirror, not a glass window, and the black background was to mask the camera; I never imagined anyone would see it any other way! 😂
@zambo6453
@zambo6453 8 ай бұрын
my personal favourite application of this is from portal 2. giving as few spoliers as possible, an AI is displaced from running a facility by another AI which is specifically designed to be an imbecile (there is a sensible in-universe reason to design such a thing...kind of) so the first AI plots to retake the facility by destorying the second with this paradox (while turning off its mic so it can't hear what it is saying, and therefore destroy itself). The AI hears the paradox, thinks for a second and says "hmmmm. I'm gonna go with.... false. Did I get it right?"
@Downhuman74
@Downhuman74 7 ай бұрын
I always loved this part of the game. GlaDos doesn't seem to know that even her knowing about the liar's paradox is, itself, a paradox. Just merely knowing and understanding the paradox and what it apparently does to a being of pure logic should destroy her as well based on her understanding of it (which means it shouldn't matter if she hears it or not.) But it doesn't destroy Wheatley, just like it doesn't destroy her. Man, there are just layers upon layers to that whole exchange.
@flecko5
@flecko5 2 ай бұрын
It's not necessarily a paradox for her to know that she shouldn't use it on herself. All she really needs to know is that it'll break her circuits if she thinks about it.
@prischm5462
@prischm5462 8 ай бұрын
The book "Gödel, Escher, Bach: An Eternal Golden Braid" by Douglas R. Hofstadter also explores this in great detail. It can also be expressed by the Quine sentence: "'Yields falsehood when preceded by its quotation', yields falsehood when preceded by its quotation."
@Rot8erConeX
@Rot8erConeX 8 ай бұрын
GEB:EGB mention nice
@Paulsinke
@Paulsinke Жыл бұрын
Why can't we just let the word "paradox" be the solution to this? It is true or false? No, it's a paradox. Thanks for all your work making these videos, I'm really enjoying them
@Exception1
@Exception1 Жыл бұрын
Probably because they always try to force the sentence into a classical logic-ish interpretation. Like he did with the "this sentence is not true" example. Then used axioms and inference rules of classical logic on it to generate a contradiction. But in classical logic... a sentence that is true and false or neither is not a sentence at all. (well not a "proposition").
@njsmeets66
@njsmeets66 Жыл бұрын
I concur. Our universe should contain, must contain, needs to contain mysteries.
@thaddeuspawlicki4707
@thaddeuspawlicki4707 Жыл бұрын
Because you would have to consider the statement ; "This sentence is not a paradox"? In essence "paradox" == "Neither True nor False". Introducing a new term doesn't solve the problem.
@stepheneickhoff4953
@stepheneickhoff4953 Жыл бұрын
Like the definition of x/0?
@keystothebox
@keystothebox Жыл бұрын
False, paradoxes do not exist
@mihaichira2888
@mihaichira2888 Жыл бұрын
In my youth I discovered this paradox, by myself, without knowing about its existence, but in a simpler form: "I lie all the time". I follow your lessons with great pleasure and interest. I applaud you.
@kennarajora6532
@kennarajora6532 Жыл бұрын
hey me too.
@mihaichira2888
@mihaichira2888 Жыл бұрын
@@kennarajora6532 Nice. :)
@WWLinkMasterX
@WWLinkMasterX Жыл бұрын
For me it was the episode of SpongeBob where he proposes a "no rules" rule.
@mihaichira2888
@mihaichira2888 Жыл бұрын
@@WWLinkMasterX Oh, that's so cool and funny. :)
@p.kay_____
@p.kay_____ Жыл бұрын
Yep me too 😁
@marcdraco2189
@marcdraco2189 8 ай бұрын
That self-reference to your bald spot knocked me off my stool Dr. Kaplan. Salute sir!
@jeffdavies2824
@jeffdavies2824 Жыл бұрын
Software engineers call this self referential property "recursion", and in some cases, is hugely powerful (ie calculating numbers to a power, navigating graphs, etc). A for statements that refer to each other, this is "head recursion" or "tail recursion".
@melkiorwiseman5234
@melkiorwiseman5234 11 ай бұрын
Welcome to "deadlock"; a known potential problem with recursion. Ye olde GW-BASIC had a "deadlock" error message built into it, but I've never seen it come up. I assume it would only occur when using shared files which have locked records and GW-BASIC is the only version of BASIC I've seen which had the ability to use shared files and locked records, and I've never seen a program which needed to use them (although I did write a prototype "chat" program which used them, just for fun.)
@xpusostomos
@xpusostomos 11 ай бұрын
Any computer programmer knows to be careful with recursion that you exit the loop. This seems like a case of recursive sentences that don't exit their loop. As soon as you refer to yourself, even indirectly via another function, you have to have a plan for when that loop ends
@Mk101T
@Mk101T 11 ай бұрын
Speaking of computers/software .... which I am only vaguely familiar through game modding software , so pardon my ignorance. But is that why "AND / OR / NOT" are used ? ( logic gates I guess you call them ) Giving 3 options instead of 2 ... and pretty much the idea of truth is somewhat singular in that it is the journeys destination . So false is in a sense taking no journey ? IDK ... but maybe that is how the liar paradox can be solved ... embrace the journey ?
@nekomikumata
@nekomikumata 11 ай бұрын
@@Mk101T it can be solved by a simple inversion truth table. Just take the sentence at face value then invert it. 0 = 1 1 = 0
@SarthorS
@SarthorS 8 ай бұрын
@@Mk101T AND / OR/ NOT, and others, are used because computers operate on pure logic. Computers cannot perform mathematical calculations directly. They simulate them using logic operations on true and false values. I would give a better explanation, but it's been decades since I studied how CPU's work. Here is an image from Wikipedia that shows the logic gates within a certain CPU used to perform basic arithmetic. upload.wikimedia.org/wikipedia/commons/thumb/c/c0/74181aluschematic.png/600px-74181aluschematic.png
@llywyllngryffyn8053
@llywyllngryffyn8053 Жыл бұрын
The Two sentence paradox or really any multiple sentence version of the paradox suffers from the same Self-Reference issue. It is an issue of recursion. You have to ban all recursive references and a final evaluation of truth must be reserved for a sentence whose references have been replaced with their target representations. The reference "The Sentence Blow" is true must be replaced with the actual sentence blow. So when you do this, that sentence contains another reference which must be resolved before a final sentence can be established. in your example, that would make the reference Null since it points to something that no longer exists. You cannot form this paradox without depedent references.
@korbyd236
@korbyd236 Жыл бұрын
I hate how he said the sentence "this sentence is not true" can't be neither true not false because it can like this sentence isn't true ok then it's false no then it's true no ok so it's neither true not false
@korbyd236
@korbyd236 Жыл бұрын
And then bro pulled the if it's Accurate it's true and I was like that's an ass pull it pissed me off cuz like yes technically you could do that but when the "this sentence is false" it doesn't apply then it wouldn't with not true as well or it would apply to both the same way
@kalanivernon7273
@kalanivernon7273 Жыл бұрын
The fundamental problem isn’t recursion. Recursion is a symptom. The fundamental problem is the inability to resolve any kind of mutual exclusivity when both options are EQUAL. And this goes back to a fundamental and flawed assumption in logic itself: That there is always a better/more accurate/superior option. And baked into that assumption is a second assumption: That logic itself is always the superior option to resolve X. Without even realizing it, every one of us who relies on logic has a secret belief we may not be aware of: Logic is always the superior option to resolve X. If X cannot be resolved by [current understanding of logic], [current understanding of logic] is flawed. Ergo: A perfect, pure form of logic must exist that can resolve all variables of X. At no point is the first premise ever countered. Deep down in our souls, we believe there is a pure, omega logic that perfectly resolves everything. Every possible paradox; Every possible scenario; takes into account every possible variable; and with perfect results every time. This is an unfalsifiable assumption, and for reasons that baffle me - completely rejects the Null Hypothesis without even attempting to prove the premise is true. My premise: Logic may not always be the superior option to resolve ALL instances of X, and by extension - no perfect, pure, omega logic exists. For example - to the best of my understanding, logic cannot be used to solve the following: A has a value of 2 B has a value of 2 Choose the option with greater numerical value. A or B. (And the question provides a radio button with which to select your response). Since you cannot enter both/neither, or an another answer of your choosing (and are limited to choosing A or B as your only answers), this question cannot be resolved without relying on something other than logic (personal bias, random selection, etc).
@dougaltolan3017
@dougaltolan3017 Жыл бұрын
​@@kalanivernon7273 The problem is not (and cannot be) logic, since logic is rigourosly defined to be correct. The problem is the presumption that language must be logically correct. This and other so called paradoxes merely show that language lacks rigid (logically correct) semantic rules.
@dougaltolan3017
@dougaltolan3017 Жыл бұрын
​@@kalanivernon7273 Ohh, and to answer your question: B in virtually all cases... While A and B might have the same value, B has a greater name. In fact, B is the correct answer regardless of the values of A and B since your question only asks for the greater option, not the greater value of the option.
@tonyduff-forbes5748
@tonyduff-forbes5748 8 ай бұрын
My father was a senior university lecturer in philosophy, his area was logic, and mathematical philosophy, great video!
@daniellehallihan6015
@daniellehallihan6015 10 ай бұрын
You're a really great teacher. You go through each point slowly and clearly and give us plebes the time to process what you're saying. I've watched Russell's Paradox and this one, the Liar Paradox, and I'm just blown away by your ability to break things down and explain complicated, mind-bending ideas. Also, you're funny 🤭 and have the hot professor thing going on. Soooo... I'm definitely subscribing. 😂🔥
@ingvaraberge7037
@ingvaraberge7037 Жыл бұрын
The liar paradox reminds me of the rule in mathematics that says that one can not divide by 0. One can write for example 5/0, but it gives no mathematical meaning. Any answer you come up with will be wrong. In a similar way, if a sentence has as a consequence the denial of the sentence itself, that sentence is logically impossible.
@irgendwieanders2121
@irgendwieanders2121 Жыл бұрын
Chuck Norris can divide by 0!
@nicomoreno5028
@nicomoreno5028 Жыл бұрын
​@@irgendwieanders2121 lol Chuck Norris's beard can divide by zero.
@irgendwieanders2121
@irgendwieanders2121 Жыл бұрын
@@randomrandomizer You can also define 0/0=1 Depends on your choice of axioms...
@ingvaraberge7037
@ingvaraberge7037 Жыл бұрын
@@randomrandomizer That doesn't sound too wrong. Until you try it the other way around and multiply infinity with zero. How long you continue the row 0+0+0+0+...., you'll never make it to 5. Or to put it the other order: Zero infinities is not 5. So your answer doesn't work, even though your suggestion is a tempting conclusion.
@gm2407
@gm2407 Жыл бұрын
If Zero Mostel had a high school diploma than he understood basic maths. At one point he must have proved he understood division. Therefore at one point something was successfully divided by 'Zero'.
@carlcramer9269
@carlcramer9269 Жыл бұрын
This seems like Gödel's incompleteness theorem - Inside a system you can state a question that the system cannot include (quoted from memory, so go check it up if you are bothered).
@wcsxwcsx
@wcsxwcsx Жыл бұрын
First thing I thought of.
@HowardS185
@HowardS185 Жыл бұрын
Me too - I thought that Dr. Kaplan would mention, or explain more, linking this to Godels Theory
@HowardS185
@HowardS185 Жыл бұрын
The last work should be theory (damn spelling correction!).
@ItsJustJessOkay
@ItsJustJessOkay 8 ай бұрын
Your paradox videos tickle my brain in a most pleasurable way.
@trishoconnor2169
@trishoconnor2169 8 ай бұрын
There must be something in the way my neurons are wired that makes me simply reject most "logical paradoxes." For this particular one, my intuitive response has always been something along the lines of "Irresolvable loops (no matter how many steps you try to put in them) have no meaning." It's kind of like the error message a spreadsheet will give you if you try to divide by zero, just a simple, "Nope, that can't be done, so do something else instead." It just seems so obvious to me that this is the answer that I don't understand the effort expended on it over the centuries. Intellectually, I realize that brilliant thinkers have been fascinated by it since at least 400 AD, so I know it's not actually stupid, but this awareness does not keep my personal reaction from being, "That is just stupid." Same with Zeno's Paradox: No, it's not paradoxical to try to walk from Point A to Point B because you have to walk half the distance, then half of that distance, ad infinitum, so you never get to B. I don't intuitively "get" the paradox because we DON'T walk by halves. Period. That's just not how it works. This has left me feeling quite free to move on with my life, and clearly would have made it impossible for me to make a living as an academic logician.
@CodeguruX
@CodeguruX 8 ай бұрын
Language is a man made construct. Assuming there is no fault in a manmade construct is false.
@trishoconnor2169
@trishoconnor2169 8 ай бұрын
@@CodeguruX That statement is true.
@tanjirouzumaki444
@tanjirouzumaki444 7 ай бұрын
Actually, we could potentially “walk by halves” depending on your definition. The only reason the paradox is false is because infinite sums don’t produce infinite values.
@goldenkurlz
@goldenkurlz Жыл бұрын
I like to think that, while our language (and I mean all language, human language) is incredibly sophisticated, developed, and nuanced, it is only a tool. It is only a way to communicate what is, it does not define what is. It's basically a verbal model that, while well equipped to do what it needs to, is as limited as any model is at describing anything.
@Joe-nh8eq
@Joe-nh8eq 11 ай бұрын
That’s the whole point of the paradox. Our language is just how we communicate reality, its not reality itself. And because of that fact there are inherent quirks and ambiguities in our language which create logical paradoxes. “This sentence is false” isn’t actually a paradox. It’s neither true or false. It’s not real… Which is kind of the whole point of the paradox…
@ilovepavement1
@ilovepavement1 10 ай бұрын
For Chomsky it wasnt that thinking was a result of language, but that language taught us how to think.
@michaelw7115
@michaelw7115 9 ай бұрын
I think it's both, and anyone who knows 2 or more languages pretty well will testify to that. The better your grasp of language the deeper you can develop thought but deep thought can also reveal a lack of words in a language (which can end up affecting whole societies and cultures unaware of the existence of such words known in other languages. @@ilovepavement1
@petermcminn9508
@petermcminn9508 5 ай бұрын
Exactly. Our shared understanding of the "sentence", a construct in itself, presents a mobius strip of a kind, a flawed vehicle we use to navigate our universe: if-this-then-this in perpetuity. @@Joe-nh8eq
@santaclaus0815
@santaclaus0815 Жыл бұрын
Hats off to Ethan! He kept Jeffrey from telling us things about the liar's paradox that aren't true - or worse - neither true nor false.
@michaelglendinning1738
@michaelglendinning1738 8 ай бұрын
Your videos are fun. Sometimes you jump from scenario to scenario so fast that my brain kind of explodes.
@magicofreality
@magicofreality 3 ай бұрын
What about Gödel’s incompletness theorem? Does it concern this problem?
@paulpease8254
@paulpease8254 Жыл бұрын
Thank you Professor Kaplan! Watching your videos has rekindled my love of philosophy and academia. Cheers!
@bradr3541
@bradr3541 Жыл бұрын
“This sentence is partially true.”
@flygawnebardoflight
@flygawnebardoflight 11 ай бұрын
My favorite thing about "this sentence is false" is that if you declare that it is paradoxical then it becomes true as it isn't false, breaking that paradox and creating a new one.
@benjaminshropshire2900
@benjaminshropshire2900 8 ай бұрын
To me, the resolution to the paradox is simple; the world is under no obligation to make every possible statement self consistent or even meaningful. The fact that a statement is neither true nor false is interesting (mostly in what it says about the language the statement is made in), but not at all surprising. In fact, the non-existence of such statements would be the surprising thing.
@Real_Lion_of_Judah
@Real_Lion_of_Judah 8 ай бұрын
@@benjaminshropshire2900 Agreed, and I would go even further. A statement can NEVER equate to absolute truth or absolute falsehood, since words have no precise meaning, being sounds or markings that trigger memories of experiences, not having any fixed meaning. This even includes mathematical statements such as 1+1=2, because numbers have no actual meaning until assigned to represent something (e.g. 1 apple + 1 apple = 2 apples).
@benjaminshropshire2900
@benjaminshropshire2900 8 ай бұрын
@@Real_Lion_of_Judah I wouldn't go that far. Words have precise meaning, at least to the extent the people using them agree on what they mean. And societal discourse depends on having wide agreement on that. Where things get strange is when one side of a debate tries to win by trying to choose the meaning of terms the other side already used and then say that is what the other side meant. The problem there is that changing the meaning of words doesn't change the meanings people are expressing. At best it just pisses off the people trying to talk about something. At worst it tricks the other side into thinking they succeeded making it impossible to resolve anything in a civil way.
@Real_Lion_of_Judah
@Real_Lion_of_Judah 8 ай бұрын
​@@benjaminshropshire2900 What I meant is words never have *absolutely* precise meaning (to speak of relative precision in this context doesn't make sense). A statement can never be absolutely true or absolutely false. One could argue a mathematical statement can, but I would again point out that math has no actual meaning when the numbers are isolated (i.e. when they aren't representing anything "real"), and that always includes concepts with no absolutely precise meaning. What is the average airspeed of an unladen swallow? What do you mean? African or European swallow?
@benjaminshropshire2900
@benjaminshropshire2900 8 ай бұрын
@@Real_Lion_of_Judah your clarification is saying what I already understood your original statement to say. I still disagree with both.
@florianp4627
@florianp4627 9 ай бұрын
Instead of the third 'neither true nor false' option, there should be an option on a higher level 'computable' or 'not computable'. Because ultimately an infinite recursive loop is not computable because no turing machine could compute the result
@DemiImp
@DemiImp 8 ай бұрын
I would prefer "indeterminate". Self referential statements and the like can be indeterminate. You can't give it a label of either true nor false as it cannot be evaluated.
@Brand64730
@Brand64730 11 ай бұрын
It's interesting applying programming logic to a paradox like this. Take a function in Excel for example; you can't create a SUM function that includes itself, it becomes circular logic. So programming just goes ahead and says you can't use self reference, and that's good enough for me, lol.
@seijirou302
@seijirou302 Жыл бұрын
A thought that came to me while watching this is that it sounds a lot like Gödel's Incompleteness Theorems. It seems to me that language can be replaced with mathematics, as Gödel did for symbols. In the same way that Gödel used this system to prove that mathematics can not be complete and consistent, it proves also that language can not be complete and consistent. As language is a fundamental constituent of formal logic (I know, I'm probably recklessly asserting here) it follows that formal logic can not be complete and consistent. Or perhaps a way out is to say that logic may be complete and consistent but the expression of logic can not be.
@johnyork5121
@johnyork5121 Жыл бұрын
I feel like a sentence cannot be self aware and a pair of sentences cannot be self aware or aware of each other. Love the star trek references
@SilverBullet93GT
@SilverBullet93GT 11 ай бұрын
This video does not exist
@DG123z
@DG123z Ай бұрын
This comment does not exist
@youinfosucker8887
@youinfosucker8887 Ай бұрын
This comment is false
@SilverCN
@SilverCN Ай бұрын
Your comment is false Meaning my comment is true
@trucid2
@trucid2 29 күн бұрын
That's not a paradox. That's just a false statement.
@butter5144
@butter5144 12 күн бұрын
True/false
@nickmarras249
@nickmarras249 8 ай бұрын
A classic case of overthinking. And THIS sentence….is TRUE!!!
@w3rkh0f67
@w3rkh0f67 Жыл бұрын
'I am my own oxymoron', or 'Every rule has its exception, even this one..' are some of my favorit quotes. What comes to mind is the Schrödingers Paradox (with the cat in the box) and entanglement in quantum physics. Cool thought provoking video, thanks!
@N.i.c.k.H
@N.i.c.k.H Жыл бұрын
The Shrodinger's cat thought experiment is not a paradox. The cat really is neither alive nor dead until it is "observed".
@w3rkh0f67
@w3rkh0f67 Жыл бұрын
@@N.i.c.k.H Thanks for correcting the terminology. I'm no mathematician, so: as the rules in creation seem valid, until 'observed' (investigated) and then revealing the paradox,- it still strongly reminds me of the Schrödingers two simultaneously valid states.
@miriam-english
@miriam-english Жыл бұрын
My favorite is "All sweeping statements are wrong." It's not directly self referential, which I like.
@w3rkh0f67
@w3rkh0f67 Жыл бұрын
@@miriam-english Haha, yes! Or similar: 47.5% of all statistics are made up on the spot.
@N.i.c.k.H
@N.i.c.k.H Жыл бұрын
@@miriam-english This is not a paradox, it is wrong. It is not a paradox because being wrong does NOT imply that "All sweeping statements are right" only that "SOME sweeping statements are right" and there is no reason to assume that this is one of those. If you believed it was true THEN you would have a paradox.
@alonzomuncy6871
@alonzomuncy6871 Жыл бұрын
I'm just a programmer buy to me the problem to me seems to be Circular Reference rather than Self-Reference per-se. It would seem to me that if you have some method of terminating a circular reference in your logical system then you can avoid this. I'm pretty sure some smart philosophers have already considered that option, but I have no idea what they came up with or how they managed to restate the problem again.
@lendrick
@lendrick Жыл бұрын
I was going to comment on this as well. It seems obvious enough to me that I'm certain it's already been brought up. I'd be curious how logicians respond to it.
@jaysoncowan5763
@jaysoncowan5763 Жыл бұрын
A programmer has self reference, its called recursion. Recursion that has no action is disposed of by the compiler, because it is indeed nothing.
@timhaldane7588
@timhaldane7588 Жыл бұрын
The beauty of being a programmer when it comes to philosophy is that you work with logic on a regular basis. Programming is applied logic in the same sense that engineering is applied physics.
@ajb667
@ajb667 Жыл бұрын
The usual way to deal with circular references is to either ban or ignore them. Given the references are really numbers (i.e. memory pointers or database index ids) you could also wilfully misinterpret the circular references as numbers (change the context) for the sake of something like a serialisation task. I wonder if there's anything from all that we can transfer to this philosophical debate?
@sandornyemcsok4168
@sandornyemcsok4168 Жыл бұрын
I am an amateur programmer thus probably I can understand what you try to say. But I can tell you that the problem is not Circular Reference or Self-Reference (i.e. recursive reference). If you read my separate comment I think you will understand where the "cheating" is. 😀
@spirosxania3745
@spirosxania3745 14 күн бұрын
Hello! I've recently discovered your channel and i loved it! I have a question about this video which could be kinda silly but i couldn't answer it and would like some help. Just before this video i watched your video on Plato's Euthyphro in which you mentioned the example with the greenness of the grass and the trueness of the sentence (the grass is green) and how the first explains the second and not the other way around. In 1:10 in this video you stated that "if the sentence is true then the ship is on fire". So my question is: shouldn't the fact (sentence) that the ship was on fire explain the trueness of the sentence "this sentence is true" and not the other way around? If its the other way around (being parallel to god saying that murder is virtuous in your Euthyphro video) that would mean that if the sentence was for example that murder was virtuous that would mean that it would actually be virtuous because the sentence above said that the sentence (below) is correct. I hope you read this and keep up the good job!
@Dungeon47
@Dungeon47 11 ай бұрын
Both math and philosophy are imperfect fields. Paradoxes like this combine the most broken parts of both to create something truly wild. I suspect that the only real resolution must come from improved models of both math and philosophy. Once we can see these two in better context, we will realize that the unanswerable questions make, themselves, no sense.
@Surefire99
@Surefire99 Жыл бұрын
The thing that this and Russel's Paradox leaves out of the equations is the time factor. We live in a world that involves time, so the way we describe things should as well. This problem is evident in programming. It manifests itself in circular logic and infinite loops. That can happen with multiple variables or self-references. But essentially, in order to test something, you need to solve the preceding statement first... which can never happen as you showed at 7:30 in the video. So in programming you could say the solution is "undefined." Another possibility in programming is to pause the loop and test the current state. When you do that, you can't just say "this IS the answer", you'd have to say, "this is the answer at a certain point in time".
@kennarajora6532
@kennarajora6532 Жыл бұрын
It's interesting, because your explanation actually bears a lot of similarities to an explanation for the liar paradox made all the way back in the 5th Century AD, by a linguist/philosopher called Bhartrhari.
@jgunther3398
@jgunther3398 Жыл бұрын
a computer is sequential tests and operations, but the"this sentence is false" problem implies at the current point in time. like division by zero; always meaningless. or if a result is demanded for some reason, then "undefined"
@Surefire99
@Surefire99 Жыл бұрын
@@jgunther3398 the brain is just sequential tests. Things don't make sense if you don't process one word at a time. It might seem instantaneous, but it's not.
@Surefire99
@Surefire99 Жыл бұрын
@Kenna Rajora just looked into him. Yeah it does seem very similar to what I was thinking.
@MandoMacDonald
@MandoMacDonald Жыл бұрын
Right! It’s like “GNU is not Unix”!
@devonadler5835
@devonadler5835 Жыл бұрын
a fantastic book on self reference and metamathematics comes to mind- "Godel Escher Bach, the eternal golden braid" where the author talks about some of the similarities and paradoxes involving metamathematics, the impossible architectures of escher, and the melodies of back
@nosuchthing8
@nosuchthing8 Жыл бұрын
That book rules
@lorefox201
@lorefox201 Жыл бұрын
it rules so much
@Akari-br7ci
@Akari-br7ci 5 ай бұрын
I've heard of this paradox before, I think most of us have, but I've never really thought about it that much. I just went "that's kind of cute" and move on. I never realized how many variations there were and all the implications they have. Really great video.
@robertashton8942
@robertashton8942 7 ай бұрын
Hi Jeff. Your paradox explanations and analysis are the best of all the paradox videos on KZfaq. Thank you so very much for this great work. I have become your fan instantly.
@cardinalhamneggs5253
@cardinalhamneggs5253 11 ай бұрын
Wheatley famously lacked the processing power and intelligence necessary to overload his processors on this paradox in _Portal 2._
@seniukas
@seniukas Жыл бұрын
Thanks for keeping us sane, professor. You are the paradox guy, always fascinating to watch.
@Stroheim333
@Stroheim333 Жыл бұрын
The Liar's Paradox, and all of it's variations in the video, is dependent on pure semantics, and the only thing the paradox prove is that pure semantics is not, and cannot be, perfect or consistent. Semantics is NOT reality, it is just a tool for us to communicate reality (or fantasies, or nonsense, if we want to).
@MacWiedijk
@MacWiedijk 8 ай бұрын
The point is that there are two things that don't necessarily match. The first is the content of a statement and the second is the status of the content of the statement. In “this sentence” the content is referred to as the statement, but not the status of that content. The statement is false because that is the content of the statement. But if the content of the statement is false, that makes the status of the statement true. “This sentence is false.” is therefore true.
@binbots
@binbots 9 ай бұрын
By responding true or false to the statement “this statement is false” is to imply that it is a question. But a question needs at least two variables. The reason you can’t answer the question “is this statement false?” is because it only contains one variable (false). This is why it is a paradox. This is equivalent to asking is 2+3 true or false? The response to this question (true or false) is not the answer to the question. It is the second variable in the equation. You can’t get the final answer to this question until you multiply both variables (question and response) together. This becomes a lot more obvious when we compare this statement to its opposite “is this statement true?” True=(+) False=(-) This statement is true (+) x true (+) = true (+). This statement is true (+) x false (-) = false (-). This statement is false (-) x true (+) = false (-). This statement is false (-) x false (-) = true (+). When multiplying you need to know what both variables are (negative or positive) before you can know if the answer is negative or positive. Therefore you cannot know if the answer is true or false until you know if the question is asking if it is true or false and if the response to that statement is true or false and then combine them together. This statement is false has no answer. It’s equivalent to asking what colour is something without knowing what that something is. But saying “this false statement is false” does have an answer and it is true. The two statements “the next sentence is false” and “the previous sentence is true” are not two separate equations. Both contain one variable each and must be combined to form one equation that can be answered. ((The next sentence is true) x (the previous sentence true)) = true ((The next sentence is true) x (the previous sentence is false)) = false ((The next sentence is false) x (the previous sentence is false)) = true.
@matteritchie
@matteritchie Жыл бұрын
Just started watching some of the Jurisprudence lectures because I wanted to become more conversant in the field, and - wow - I really love these lectures...just about all of them I've sampled. Thanks for sharing them!
@impyre2513
@impyre2513 Жыл бұрын
Seems to me that the problem is the combination of implication and circular reference... I mean, if you ever dig into how implication works it seems obvious that circular references using them would be inherently problematic (since they are *not* bidirectional)
@danyael777
@danyael777 8 ай бұрын
"I am a liar and i'll keep lying i promise" -Eubulides- Sir Henry Rollins
@DonkeyPunchAllstars
@DonkeyPunchAllstars 7 ай бұрын
I stumbled on your videos for the subject matter, I stayed for your suburb analysis of Star Trek captains.
@starroger
@starroger 4 ай бұрын
Seems to me, comparing Star Trek captains just within the context of their particular shows without also considering the popular culture of the time these shows were produced is an offshoot of the 'self-reference' problem. There is a 30 year lag between TOS and TNG. Cultural attitudes regarding women changed somewhat over that time.
@marcvanleeuwen5986
@marcvanleeuwen5986 Жыл бұрын
While it is true that the Russell paradox arises from self-reference, it does not arise simply because a set can be an element of itself: there are consistent set theories where this is allowed. The contradiction comes from allowing a set to be defined by selecting (by a predicate) items from a universe to which the to-be-defined set itself belongs. Similarly the liar paradox arises from allowing the meaning of a sentence to depend on the assignment of truth values to collection of sentences to which the sentence itself is supposed to belong.
@vorpal22
@vorpal22 Жыл бұрын
@@CorwinSTP No, we just learned what constitutes a logically consistent entity, and we refined our definitions to call those sets. Clearly, derivations of properties of inconsistent entities that are set-like fall apart, so it is important to make the distinction. There's no cherry picking involved.
@njsmeets66
@njsmeets66 Жыл бұрын
This is why we created or invented the "paradox."
@Bronco541
@Bronco541 Жыл бұрын
@@CorwinSTP it seems to me like most people are unwilling to accept that this whole thing represents a limitation of our present brain power; or our modus operandi to which we perceive/create the universe.
@marcvanleeuwen5986
@marcvanleeuwen5986 Жыл бұрын
​@@CorwinSTP The Russell paradox arises in a _formalization_ of naïve set theory. As an informal theory, naïve set theory only informally describes what sets are, how they behave, and what one can do with them (like take intersections of them, form sets of sets). For instance, while Georg Cantor definitely meant to study infinite (as well as finite) sets, I doubt whether he actually stated a clear rule that some infinite set exists (and without such a rule, one cannot _prove_ that any infinite sets exist; indeed Greek philosophers held that nothing can possess actual infinity, as an infinite set would, and this is a logically consistent point of view). So if one wants to do rigorous mathematical reasoning about sets, one needs to fix the rules, i.e., formulate axioms of set theory. Gottlob Frege undertook such a formalization (maybe not exactly of Cantor's set theory, but something essentially equivalent). The set of rules must be proposed; there is no (cherry-)picking from a pre-existent set of rules involved. The main things that formalized naive set theory proposes about sets involves equality of sets (two sets are equal if anything is member of the first if and only it is member of the second) and an axiom about sets that (must) exist; for the latter it states that any well formed predicate (in the language of set theory) defines a set (of everything that satisfies the predicate). This is elegant and economical (for instance one does not need to state explicitly, as starting point, that an empty set exists, since the predicate that is always false "creates" the empty set; similarly, the predicate that is always true creates a universal set, as set of which everything is member. Unfortunately this elegant axiom also make the theory inconsistent, as Bertrand Russell pointed out to Frege. (Incidentally, the inconsistency arises by applying Cantor's theorem, stating that every set has strictly smaller cardinal than the set of all its subsets, to the universal set; no great originality on the part of Russell was required.) So nowadays we use a formalization of set theory (usually the ZFC axioms), in which the naive rule for "creating" sets is replaced by several axioms that state that certain sets exist. One for instance states explicitly that an empty set exists, another that some infinite set exists, and ZFC has some other existence axioms. Most relevant here is that instead of "naïve comprehension" mentioned above it has "restricted comprehension", stating that for any set X and predicate P one can form the set (subset of X) of all x in X for which P(x) holds. The fact that an explicit (already existing, in a sense) set X must be supplied, instead of implicitly selecting from the universal set as in the naïve theory, avoids Russell's paradox in ZFC. This is what I meant by "The contradiction comes from allowing a set to be defined by selecting (by a predicate) items from a universe to which the to-be-defined set itself belongs".
@njsmeets66
@njsmeets66 Жыл бұрын
Excellent! Much appreciated, thanks!
@explodingpotato6448
@explodingpotato6448 Жыл бұрын
The way I always thought of this sentence is for a sentence to be true or false there has to be a way to evaluate it, in this case there is isn't, so you have to first assume that it is true or false for the paradox to begin.
@irrelevant_noob
@irrelevant_noob Жыл бұрын
Precisely. There are sentences for which no truth value can be assigned. 👌
@stevehaire6324
@stevehaire6324 8 ай бұрын
I have never before learnt so much about a subject but ended up knowing the exact same amount about it as I did prior to learning it. How's that for a paradox.
@aaronanytime8897
@aaronanytime8897 4 ай бұрын
There seems to be a missing variable here which I'd call the "unknown". If someone were to ask me "is it true that Tommy went to the park yesterday?", I'd reply "I don't know if it is true or false so it is unknown."
@va3ngc
@va3ngc 11 ай бұрын
I think the solution is still about self reference ending up being a form of recursion. In the two sentence version, when you have one sentence pointing to the other, you end up with the recursion problem again.
@georgelionon9050
@georgelionon9050 8 ай бұрын
Exactly, but "there will be a surprise test tomorrow" has absolutely no reference and still gets a similar self contradicationary cycle (there cannot be an announced surprise, but once the sentence is considered absurd it is true because it will be a surprise)
@0x7f16
@0x7f16 Жыл бұрын
A thought on the circular reference problem in the video: If we formalize the sentences (a) The sentence below is false (b) The sentence above is true as follows X := ~Y Y := X (where := means “is defined as”) then substitute the second sentence, which is the definition of Y, into the first sentence, and we have X := ~X which is the same as the liar’s paradox: X occurs in the definition of X itself. Therefore it will be an infinite loop if we substitute X’s definition for X in X’s definition. I think it’s a problem with circular definition - a name that contains itself in its definition. Thus when we try to expand it, it will end up in an infinite loop. So can we just ban circular definition to avoid the problem?
@0x7f16
@0x7f16 Жыл бұрын
I’m thinking of a macro-language compiler that substitutes every name in a sentence with its definition (except for the primitives). In order for the compiler to finish in finite time, at any point of expansion, it should not be the case that a name occurs in its own definition (which is a thing we can test for, say, write a program for it).
@NemisCassander
@NemisCassander Жыл бұрын
Banning circular definition is, essentially, removing self-reference. Kaplan sort of says you can avoid self-reference, but it's really just hiding it. The issue is with series of statements whose _entire_ definition relies on other terms. Statistically, you can say that the system of circular definitions you give have zero degrees of freedom, which means the error cannot be measured. Ergo, the truth cannot be determined in such a system.
@lasarila1629
@lasarila1629 Жыл бұрын
Interesting idea. ChatGPT could probably help you expand on it if you wanted to test it quickly. Good luck!
@camelCased
@camelCased Жыл бұрын
Well, the problem is that you cannot ban something from existence if it exists :) So we cannot ban circular definitions "just because". Also, there are practical real-life situations when we have to deal with circular references - it's when serializing a parent-child data model where they both reference each other. The developers of serializers implemented different tricks to deal with this, but they could not "ban" it.
@hihoktf
@hihoktf Жыл бұрын
I don't think circular definition in and of itself is the problem i.e. X:=~Y Y:=~X is circular, but is always true and without paradox. I think it's self-referential denial (whether immediate or mediated), which is what you presented, that is the failure mode of the liar's paradox.
@happymountainproductions
@happymountainproductions 5 ай бұрын
One can still self reference across multiple sentences. Plus the assumption that a double negative is the same as a postive, yet thus creates one is a distinction that splays this into 4 options.
@jtm1283
@jtm1283 8 ай бұрын
Where this video crashes and burns is at 4:50 where it's argued that if something is false, then you can just "reverse it" but the whole point of the preceding four minutes was to establish that there's a third option so reversing in no longer valid.
@norawheeler2555
@norawheeler2555 Ай бұрын
He is not stating that the statement has to be true or false and there's no third option he's expressing the law of the excluded middle, which states that either A or Not A must be True, which is not the same thing as true or false
@inujosha
@inujosha 11 ай бұрын
I got a hard case of semantic satiation on the word true in this video. Fascinating topics. Love it. 😊
@richardmeyer3214
@richardmeyer3214 Жыл бұрын
Responsibility is not the only trait needed to be a captain! Kirk was bold and that's important. Solid video tho
@bernardoohigginsvevo2974
@bernardoohigginsvevo2974 Жыл бұрын
William Shatner the bed.
@fisyr
@fisyr Жыл бұрын
Frankly I think Kirk should have been the chief of security and Spock the captain. Since Starfleet always insists on not being a military organization, it'd make much more sense to have a more diplomacy/science oriented leader in that position. But I don't know why I'm discussing that in a video about logic. ^^
@TheSwiftCreek2
@TheSwiftCreek2 Жыл бұрын
He was also more likely to sacrifice himself than Jean-Luc.
@ruprecht9997
@ruprecht9997 Жыл бұрын
Jean Luc was bald too.
@ruprecht9997
@ruprecht9997 Жыл бұрын
@@TheSwiftCreek2 It was quite hard for Kirk to sacrifice Jean-Luc given that they lived in different eras! ;-) I know they overlapped a few times, but still I had to make this important point. Heh heh.
@mmmk6322
@mmmk6322 8 ай бұрын
Question in the dismissal of the self refence using two sentences. Is it not that the two sentences would lose meaning if they were written without being underneath/above the other sentence? Doesn't that just make it back to a case of self-reference with that addition that the refence entails that both sentences reference each other, making them a self-reference paragraph/unit.
@staceynainlab888
@staceynainlab888 8 ай бұрын
fripple is a word for a fictitious creature. There is an educational computer game I played as a kid called Thinking Things. one of the games within it was about running a fripple shop, full of creatures of varying colours, some with spots, some with stripes, some plain, some with hair, some with no hair, some with glasses, some without glasses, etc... and the task was to select which one met the customer's criteria in each round
@ravinraven6913
@ravinraven6913 8 ай бұрын
Thinkin' Things? Never forget to go to fripple town
@jeremypnet
@jeremypnet Жыл бұрын
The two sentence version is still self referential. I prefer the Quine version (which is where I thought you were going with the infinite fribbles). This goes something like this: “Is false when preceded by its quotation” is false when preceded by its quotation. This is a sentence that tells you how to construct a new sentence from a sentence fragment. It also gives you a property of the newly constructed sentence I.e. that it is false. If you follow the instructions, you happen to get the same sentence back. It’s self referential without referring to itself.
@benheideveld4617
@benheideveld4617 Жыл бұрын
The problem lies with referencing. According to Aristotle in his essay “On Interpretation” the requirement of a proposition is that it needs both a subject and a predicate. Kaplan erroneously uses the word sentence, but a sentence does not need to be true or false, a proposition in ordinary logic must be either true or false, but that doesn’t mean you can know if it is true or false. There are other tricks too, like “The final digit of π in decimal representation is unknown.” In order for this sentence to be a proposition, “The final digit of π in decimal representation” pretends to be the subject. But we all know that π has no final digit, because its decimal expansion is unending. Therefore the phrase purporting to describe the subject is describing an impossibility, therefore the purported subject is invalid as a subject. Therefore the sentence lacks a subject. Therefore according to Aristotle the sentence isn’t a proposition. Therefore the sentence cannot have a truth value. A subject containing a reference that does not completely materialize, here meaning lose all referencing elements after a finite number of substitutions, just isn’t a valid subject and without subject we don’t have a proposition and a sentence that isn’t a proposition cannot have a truth value and hence cannot yield a paradox.
@markoates9057
@markoates9057 8 ай бұрын
I agree here. Processing the statement "This sentence is false" also requires a parser of sorts. I don't see a paradox in the statement, rather a misinterpretation (and perhaps blind trust) that the parser of the sentence behaves in a way that it does not. A trivial example: a 5 year old kid is running around the room saying "This statement is false lol". Obviously a "language parser" for this context would be a little wiser than simply being flung into an infinite recursion and deadlock. It would discard the sentence as nonsense and invalid.
@11jackinthebox
@11jackinthebox 10 ай бұрын
These videos are so great! I have a thought: At 4:55, you say “if a sentence is false, then you just have to reverse whatever the sentence says”. Is that even accurate anymore? We’ve just introduced a third option other than just true and false, so can we still think of false as just “the opposite of true”? That still feels like bivalent thinking.
@shannonlawhorn1674
@shannonlawhorn1674 8 ай бұрын
This is a macroscale example of the standard models superposition. At the quantum scale answers that are in superposition are accepted as such, but bring them up to the macro world and suddenly they are paradoxes.
@a.hardin620
@a.hardin620 Жыл бұрын
Shatner is definitely suing you. Be prepared! 😃
@rickboucher5419
@rickboucher5419 Жыл бұрын
Except that Shatner is objectively a worse actor than Stewart.
@kakyoin3856
@kakyoin3856 Жыл бұрын
The paradox reminds me instantly of XOR logic gates. It negates the output after both inputs aren't equal. It is funny how the paradox works with its "logic".
@plazmica0323
@plazmica0323 11 ай бұрын
that makes it a valid third option
@marth._.
@marth._. 8 ай бұрын
You by happenstance also just explained regression to me without mathematical terms. If I had had just one such example during highschool math, so much would have made sense
@paulividergamer7727
@paulividergamer7727 11 ай бұрын
Game Theory helps to understand things of this nature. One of things not go into obviously for focus and brevity is the notion of assuming. If we can assume one or the other of the two sentences is correct then we can follow through on idea that the other is a lie. It is not meant to be definitive but progress well progress itself. By assuming one or the other is correct we can then formulate outcomes. Still a very fun video well done.
@Clumbob
@Clumbob Жыл бұрын
The paradox results from infinite recursion, not self reference, right? "This sentence is 30 characters long" is self referential but not paradoxical. Changing from one to two sentences that reference each other still results in infinitely long sentences when you replace "the sentence above/below" with the sentence that phrase is a stand-in for.
@kennarajora6532
@kennarajora6532 Жыл бұрын
It actually reminds me a bit of Thomson's lamp.
@irrelevant_noob
@irrelevant_noob Жыл бұрын
*35. Spaces are characters. ;-) But even if we grant you that it's not "any kind of" self-reference that is the issue, only infinitely recursing ones; how can we decide whether some given self-ref is infinitely recursing or not? The halting problem isn't solvable... :-| PS You're correct that the 2-sentence alternative goes into the same infinitely-recursive box, but it was presented as a way to bypass the SELF-referential nature of the paradox, not the infinitely-circular nature.
@headhunter1945
@headhunter1945 Жыл бұрын
The liar's paradox seems something like expecting to be able to say what color the animal was from the sentence "An animal swam in a lake." Maybe there is a correct answer, but it does not yet arise from the given premise. Or perhaps a better simile would be "How does the food of an empty bowl taste," "What is the sound of one hand clapping," etc.
@irrelevant_noob
@irrelevant_noob Жыл бұрын
But what's the premise which is insufficient to get to that "correct answer"?! Also, in your "how does non-existent food taste" example, i think any answer would be valid, since in logic, false premises can imply anything.
@marcdraco2189
@marcdraco2189 8 ай бұрын
In programing we call these recursion and double recursion. It's often a short way to do something complex and it is also a great way to crash a computer.
@TheSourKraut
@TheSourKraut 11 ай бұрын
I'm gonna have Schrödinger level nightmares for weeks after trying to make sense of this.
@leslieviljoen
@leslieviljoen Жыл бұрын
These videos are fantastic. Thanks so much for putting them up!
@psifiusc
@psifiusc Жыл бұрын
Like Zeno’s paradoxes and the end consequence of much in philosophy, the value of the Liar’s Paradox seems to be the lesson we don’t want to accept: even at its best the human capacity for reason and comprehension hits a limit pretty early on. The actual point seems to me to recognize that we’re a much less clever species than we pat ourselves on the back deluding ourselves to imagine. Logic is likely as good as we can do but as we designed it, it’s still embarrassingly flimsy.
@Zebulization
@Zebulization Жыл бұрын
Or the liars paradox is a collection of words that have been arranged according to grammatical rules, but which actually have no meaning. Such as: The invisible pink unicorn. Just because concepts can be shoved together doesn't mean that they will have meaning once they are put into the same arbitrary container.
@fluffysheap
@fluffysheap Жыл бұрын
On the contrary - the problem is inherent to logic, and it's only human cleverness that lets us see outside the logic box and actually solve the problem (Godel's Incompleteness Theorem).
@indrapolak5042
@indrapolak5042 3 ай бұрын
May I point to a relevant classical text on this subject "Classical Recursion Theory" by P. Odifreddi. Its about how you define functions in such a way that they still have some meaning. An example of a function losing its meaning is by defining it in terms of itself, as you demonstrated by the need to "unfold" a placeholder indefinitely. As mentioned by others, recursion is a way of defining functions very elegantly in mathematics and in computer science, but you have to be careful to make sure the function you are defining "in terms of itself" has only one possible meaning. For instance, the function defined by f(0) = 0 and f(x) = f(x-1) + 1 for all x>0. This is a well defined recursive function (say f(2) = f(1)+1 = f(0)+1+1 = 0 + 1 + 1 = 2.) The text describes various ways to define various classes of functions which are capable of computing various things, and naturally we come across halting problems and godels famous incompleteness theorem that also is the main star of Godel, Escher Bach. Then you learn that sets and more importantly the recursive enumerable ones are in fact the same thing so we reach full circle with your video's on the liar paradox and rephrasing set theory as predicates. Its all in the book :P In computer science we are mostly interested in recursive functions that do terminate and not result in an infinite loop, although sometimes infinite loops are used but can be exited by user intervention and that is fine, but in such loops recursion is never used since that would lead to so called "stack overflow", unless optimized away by a good compiler.
@-messagefromthestars5471
@-messagefromthestars5471 4 ай бұрын
Reflecting on the Liar's Paradox through the lens of the ideas that existence is one homogeneous entity without a true notion of self or consciousness, and that the notion of self arises only as an illusion of separation, provides a profound and non-traditional perspective on this ancient paradox. In this view, the core statement of the Liar's Paradox, "I am lying," or any assertion that presupposes a distinct 'I' engaging in an action, becomes deeply problematic, not merely for its logical inconsistency but for its fundamental misunderstanding of the nature of existence and self. The Illusion of Separation and the Unified Self The assertion within the Liar's Paradox presupposes a separation between the 'I' (the subject) and the act of lying (the object/action). However, if we embrace the idea that existence is a singular, unbroken whole, and the notion of self or individual consciousness is merely an illusion, then the distinction between the liar and the lie collapses. In a reality where everything is interconnected and undivided, the act of lying and the entity that lies cannot be separated; they are part of the same undifferentiated fabric of existence. The Nonsensical Nature of "I am something" In a framework where there is no true self, the statement "I am something" (with "lying" being a specific instance of "something") is rendered nonsensical or at least deeply misleading. It suggests a distinction and a dualism (the self and its actions or characteristics) that does not exist at the most fundamental level of reality. The paradox, then, isn't just a logical puzzle about truth and falsehood but a reflection of the deeper misconception about the nature of self and existence. The Liar's Paradox as an Artifact of Illusion From this perspective, the Liar's Paradox can be seen as an artifact of the illusory perception of separation and individuality. It is a construct that arises within the dualistic framework of language and thought, which presupposes and reinforces the illusion of distinct selves engaging in specific actions. The paradox highlights the limitations and distortions introduced by this dualistic thinking, pointing back to the underlying unity of existence. Implications for Understanding Truth and Reality Reflecting on the Liar's Paradox in this context invites a reconsideration of concepts like truth, falsehood, and identity. If the notion of self is an illusion and existence is a singular, homogeneous entity, then truth and falsehood are not properties of statements made by separate individuals but qualities of a more holistic understanding of reality. The paradox challenges us to look beyond the surface of logical inconsistencies and question the deeper assumptions about separation, identity, and the nature of existence itself. Conclusion In essence, viewing the Liar's Paradox through the idea that existence is one unbroken whole without true selfhood transforms the paradox from a logical dilemma into a profound philosophical inquiry. It urges us to question the very foundations of our understanding of self, other, and the nature of reality, revealing that the paradox is not just about the truth or falsehood of a statement but about the illusion of separation that underpins our conventional thinking. This approach does not resolve the paradox in the traditional sense but dissolves it by challenging the assumptions that give rise to it in the first place.
@satyestru
@satyestru Жыл бұрын
A fellow student in my philosophy program recommended you to me, and your 2-3 videos I've seen (in their entirety) so far have been great. Thanks! I'm curious: are you really writing on glass when the video is sped up? :P
@rasoolmohammady3442
@rasoolmohammady3442 11 ай бұрын
Yeah. My question too. How is written on the glass
@love-wisdom
@love-wisdom Жыл бұрын
Will you ever do a whole video dedicated on how to use logic and logic tables?
@morgoth5460
@morgoth5460 Жыл бұрын
you might want to try out the following playlists if your interested in logic and logic tables: kzfaq.info/sun/PLqEJ_rxb3Xf1l1KbR33vNyjAqwg8Adq8K kzfaq.info/sun/PLKI1h_nAkaQq5MDWlKXu0jeZmLDt-51on The first one is more philosophy oriented and is taught by David Agler (a phil assistant professor) and the second playlist is more general and taught by William spaniel, an assistant professor from a political science department (doesn't use standard philosophy of logic syntax, which can make it a bit easier for beginners, but this is not so useful later on at an advanced level)
@im1066
@im1066 8 ай бұрын
This and the Russell paradox are essentially similar in my mind. The part I missed in both videos is where you resolved it?
@trishoconnor2169
@trishoconnor2169 8 ай бұрын
If they were resolved, they wouldn't be paradoxes, would they?
@horrid8024
@horrid8024 8 ай бұрын
I am having a problem with the 2-sentence example, which I am going to pick up, since it is presented here. Maybe there might be a pair of expressions/sentences that work and probably someone can clarify where I am wrong or expand on it to clarify why the example still works. So, I can accept the premise that 2 sentences might remove the self-reference problem, but in the given example and explanation I still see self-reference and I cannot see how to remove it. First, the word "below" is too unspecific. It could mean any sentence below the sentence that says it. There could be 15 other sentences. So it would need to be more specific. So what could you do? You could say "the sentence immediately below this sentence" => self-reference, doesn't work. Maybe give them numbers/names/symbols and say "sentence number 2 of this sequence". But that would be self-reference, as well, because the whole sequence would contain sentence number 1 as well. Basically what I want to say is that this example of two sentences only works, because it is a self-defined, self-contained closed system of two sentences in which you can go around the problem, that you have to relatively refer to the second sentence within the first sentence. And that, I think only works without self-reference within the fist sentence, if the system is closed like this. But a closed system, where there is only one option of relative reference to avoid self-reference can firstly not be generalized and secondly it shows characteristics of a self-reference, that is just one level above the two sentences and takes that burden for them. Just like my sequence example above, this closed system makes both sentences connected by definition, but it is not as obvious. So ultimately the upper sentence can only refer to the lower sentence without self-reference, because they are stuck together by a self-referencing system. Without self-reference you could not define that system, and thus self-reference is not eliminated. Or can you? If someone can logically explain how to make a set of expressions refer to each other without self-reference by defining itself as part of the set, that'd be nice. :)
@MichaelAnderson-ir7hz
@MichaelAnderson-ir7hz Жыл бұрын
Kirk is a(n amazing) soldier. Picard is a(n amazing) diplomat.
@philwaters9751
@philwaters9751 Жыл бұрын
At last a decent answer to the only real debate in this debate... xxx ;-)
@johnmartin5671
@johnmartin5671 Жыл бұрын
"I always lie" is an alternative way of expressing the liar paradox.
@ShredPile
@ShredPile Жыл бұрын
And a better one I think. It feels like the other examples could be argued from a grammatical stand point.
@johnmartin5671
@johnmartin5671 Жыл бұрын
@@ShredPile Thank you!
@buycraft911miner2
@buycraft911miner2 Жыл бұрын
Its not really. The sentence is false -> I always lie is false This doesnt mean "I never lie", it means "I dont always lie" so you can still sometimes lie, you just dont do it always
@irrelevant_noob
@irrelevant_noob Жыл бұрын
@@ShredPile how is it better if it's incorrect? :-)
@MatthewCampbell765
@MatthewCampbell765 8 ай бұрын
I have a few solutions to this, I might post a few of them in different comments, but: One possibility is that there's a finite speed to the cause-and-effect of sentences here. Let's say we go with the dual-sentence variation: The sentence below is false The sentence above is true There might be a finite speed at which the two sentences affect each other. Think of it less as a conventional statement and more as a set of infinitely repeating instructions, like: If switch A is set to 'on', set switch B to 'off' (and do the reverse if not). If switch B is set to 'off', set switch 'A' to 'off' (and do the reverse if not). You follow these sets of instructions as long as you like. So, the sentence pair above rapidly switches between being true and false as rapidly as the reader is willing to imagine them.
@jurgenmeyer7602
@jurgenmeyer7602 6 ай бұрын
Truth is a thought construct, also please make more videos.
@Aim54Delta
@Aim54Delta Жыл бұрын
As I always found amusing in elementary school: "Today is opposite day." And, thus, the universe imploded. There is an interesting experiment in QM that might be interesting in this context, called "The Quantum Bomb Detector." Effectively, by doing some clever things with splitters and wave functions, you can build a detector that tells you about something that didn't happen. It could point to our mathematical sense of logic being partially flawed or incomplete. There again... using QM to try and answer philosophical questions is about like using philosophy to answer QM questions and we are left with an existential crisis as we can't answer whether or not the moon is there when we aren't looking (to take the problem to hyperbole as Einstein did).
@camelCased
@camelCased Жыл бұрын
That led me to an amusing question - are were "here" when we are not aware of ourselves (e.g. sleeping)?
@DarkVeghetta
@DarkVeghetta Жыл бұрын
@@camelCased It's entirely possible the answer could be 'no', if we're actually a type of simulation. It would resolve many fundamental problems with reality. @OP I would argue that, similarly to QM, there are more than two logically achievable states. Specifically: true, false, and recursive (which is, ultimately, just another word for 'paradox' - but it just might be the only method of addressing the issue).
@camelCased
@camelCased Жыл бұрын
@@DarkVeghetta Yeah, it feels like Schrodinger's cat - it's both true and false, until you open the box (stop recursing) and do the measurement.
@fluffysheap
@fluffysheap Жыл бұрын
There are great videos on the quantum bomb experiment by Sabine Hossenfelder and PBS Spacetime. It's a completely different weird thing than this, but they are both weird!
@Aim54Delta
@Aim54Delta Жыл бұрын
@@DarkVeghetta Is there really a third state, or is it simply our inability to perceive reality which creates the appearance of two distinct states? For example, asking whether something is a particle or a wave results in the conclusion it is somehow both... which is weird only because we are using our perception of reality and mathematical tools of prediction to describe the behaviors of something which does not necessarily have to conform to either. There is a very interesting work, a manga, called "Dead Dead Demon's Dededededestruction" - it's a sort of modern Gulliver's Travels in a sense and mostly a social critique - but there is an interesting sci-fi premise as it pertains to the perception of reality. It also falls into the "deathworld" and "humans are space orcs" category. A sort of fusion of the anthropic principle wherein we don't necessarily create reality, but our imperfect perception/grasp of what is truly occurring has a consequence for how that reality is experienced. Consider how easy it is for us to talk about a subject in the abstract. If I come up and start describing a set of directions for how to get somewhere, you can couple the use of sounds and symbols to the abstract ideas of things that are not within your perception at the moment. I can describe a building or set of landscape features that you can understand as something not currently present. Now consider the perspective of a dog. You come up to it and start saying things. It might recognize the word grass... or tree... but clearly, you're being silly, as neither such thing is present. Or maybe you're telling it you intend to go outside? The capacity of a dog to formulate abstract concepts is extremely small relative to people. They are obviously not without intelligence, but the multiple layers of reasoning to create language, that are second nature to us, are completely alien to anything a dog understands. Likewise, perhaps our inability to resolve these challenges is a similar mental block and with more capacity to process information, it would become obvious to us. I kind of suspect we are smart enough that, given enough time, we can reason through any problem - but there again, the chasm between 140 IQ children and 110 IQ children would indicate that there may be hurdles that can only be cleared through improved baseline performance. ..... of course, behavioral disorders and the like among high IQ examples kind of draw into question whether or not that would hold true..... i am rambling at this point.
@NemisCassander
@NemisCassander Жыл бұрын
I love it. I would have asked for more in the application area (bring up how it was used by Godel and Turing), but this is great. Would you consider covering the Curry-Howard Correspondence? It might be a bit more on the practical side, but it shows great application of many different areas of logic to computer science beyond the obvious.
@planetofkryk
@planetofkryk 11 ай бұрын
I have a question. Can we say that the paradox happens when the sentence refers to itself, or when in groups of sentences there is a reference that is not uni lateral? Sorry for my English, I hope I made it understandable
@ravinraven6913
@ravinraven6913 8 ай бұрын
both.....because it still ends up self referencing either way as he explains
@maxwellschmidt235
@maxwellschmidt235 9 ай бұрын
Great review of Spock's character. One theme of TOS is that logic is valuable, but that logic cannot capture the totality of experience. Logic should be our closest advisor but it should not overtake our human ability to empathize.
@nigeldepledge3790
@nigeldepledge3790 Жыл бұрын
Erm . . . but isn't it the case that we can always construct self-contradictory statements in any language-based system? We're often told that there are no stupid questions, but I find it easy to construct a stupid question by subverting the rules of language. (I use the example "What is the difference between a duck?" to illustrate how easily we can make a stupid question when we put our minds to it.)
@lazarushernandez5827
@lazarushernandez5827 Жыл бұрын
When read, the question seems incomplete because the words 'difference' and 'between' infer that 2 or more things are going to be compared. In the right context, the question can be understood as, what is the difference between 'any' duck? As in the person asking that question does not perceive any appreciable difference (to them) between one duck and the next. For example replace duck with soda. What is the difference between a soda? The person asking this question may be talking about sodas in general and lacks a preference for one particular brand.
@mattrothe149
@mattrothe149 Жыл бұрын
A duck has no between the toes because it's full of webbing. Wow, it's been a long time! Does anyone else remember this?
@Eyeballsandwich
@Eyeballsandwich Жыл бұрын
Of course, the well known answer to this is, “one of its legs is both the same”. Ask a stupid question…
@xtieburn
@xtieburn Жыл бұрын
I always get caught up in a similar issue with many of these types of examples, which is that they seem to make a huge leap between semantics and logic. We already know language isnt logical so it doesnt seem that surprising that you can form logic breaking sentences. So it seems that youd have to prove that these specific sentences are an accurate representation of something more fundamental. Its much the same with the Russells Paradox video, perhaps its just for brevity, something thatd take too long or be too boring to cover in a KZfaq video, but there always seems to be this odd jump, despite it being quite clear you cant do that, that our language is not even close to being some ideal system you can analyse in perfectly logical terms.
@MikeyDavis
@MikeyDavis Жыл бұрын
You spittin fire Bob, couldn’t have put it better myself.
@stuartzekaj1423
@stuartzekaj1423 Жыл бұрын
I wouldn't exactly know how to construct a satisfactory argument against what you just said, but my immediate thought is that the jump was always there to begin with. To create a logical system you necessarily need some form of signification, a language is at some point formed (an interconnected system of signs and signifiers) which gives rise to semantics within the very form of logic itself. It seems that there is no way (from our human perspective) to come up with a logical system without first having a language to base it on. My idea here being that you are fixated on a "leap", which perhaps can only be observed after initially ignoring an original "leap" from language that gave rise to the logical systems you are now thinking about. Although I''m genuinely interested to know what you mean exactly by "language isn't logical".
@101Mant
@101Mant Жыл бұрын
We use language for convenience but you can express the same things with the same paradox in formal logic. So it cannot be an issue with language but the underlying concepts.
@davidhoekstra4620
@davidhoekstra4620 Жыл бұрын
@@101Mant Methinks formal logic is itself a language. It seems to me language is a way to deal with reality symbolically because this simplifies life. These paradoxes might be telling us that there is no perfect way to do this. Nevertheless language is so useful that we must resort to it despite it's imperfections.
@ungrave5231
@ungrave5231 Ай бұрын
As a computer scientist its easy to just think of this as an oscillating circuit. In other words, its the same type of error as dividing by zero, or undefined.
@axiomfiremind8431
@axiomfiremind8431 11 ай бұрын
Are you saying that all statements about one's self is false? So how do I agree to contracts as I must reference myself to sign it. Is my contract neither true nor not true.
The famous Chinese Room thought experiment  - John Searle (1980)
28:30
Jeffrey Kaplan
Рет қаралды 434 М.
Gottlob Frege - On Sense and Reference
34:06
Jeffrey Kaplan
Рет қаралды 300 М.
1🥺🎉 #thankyou
00:29
はじめしゃちょー(hajime)
Рет қаралды 79 МЛН
Do you have a friend like this? 🤣#shorts
00:12
dednahype
Рет қаралды 58 МЛН
The Potato Paradox
8:02
Vsauce2
Рет қаралды 4,3 МЛН
Plato's Euthyphro - Which comes first: God or Morality?
28:41
Jeffrey Kaplan
Рет қаралды 844 М.
The ONE RULE for LIFE - Immanuel Kant's Moral Philosophy - Mark Manson
21:50
Peter Singer - ordinary people are evil
33:51
Jeffrey Kaplan
Рет қаралды 3,7 МЛН
David Hume's Argument Against Moral Realism
23:39
Jeffrey Kaplan
Рет қаралды 123 М.
Russell's Paradox - a simple explanation of a profound problem
28:28
Jeffrey Kaplan
Рет қаралды 7 МЛН
The Paradox of Time Travel Paradoxes
19:33
Tale Foundry
Рет қаралды 630 М.
Aristotle's Wheel Paradox - To Infinity and Beyond
13:14
Up and Atom
Рет қаралды 2,6 МЛН
Why Smart People Believe Stupid Things
15:39
After Skool
Рет қаралды 844 М.
Logic at its Limit: The Grelling-Nelson Paradox
13:35
Dialect
Рет қаралды 394 М.