*RYAN’S NOTES* Please keep in mind that this series is composed of short and raw videos containing many original ideas. The videos are not textbooks. Let’s use these videos as a starting point for a conversation. Whether you agree or disagree with the ideas in the videos, leave your thoughts in the comments and we’ll talk it through. I will be posting comments, corrections, and FAQs here once I get some feedback on this video.
I have been searching RUclips on this paradox and this is by far the best entry imo! I think the main point is that the logical statements inside the prisoner's head are inconsistent/contradictory. Now the question is, what the reaction to this contradiction should be. There is no right or wrong answer, as this is not in any way specified. It depends on how we model the prisoner's mind mathematically. For example, he could believe in contradictory statements, which allows him to believe to be executed on every day at the same time. Then, if we interpret "surprise" as "The prisoner does not believe he is executed on the day of the execution", the judge was technically lying.
Thanks! I think saying that the prisoner has contradictory thinking or that the judge was lying is a copout to this problem. I would argue that the solution that I proposed is entirely consistent, it just requires a new perspective more inline with our quantum intuitions of measurement and superposition.
@@keystoneperspectives I have to admit that I do not have a quantum intuition :P Anyway, it is a really interesting view on the pardox. But doesn't ln(e) measure his world all the time so that there are no quantum superpositions from his perspective?
Your question goes to the heart of Shrodinger's Cat: how can Shrodinger's Cat be in a superposition if he is measuring his world all the time? You've reached the heart of the classical assumption: that all moments are measured. There is no evidence to support this assumption. In fact, there is evidence of the contrary. Consider the Quantum Zeno Effect where a particle can only move if it is not being measured. This suggests that change only happens when we are not looking.
this Pinocchio paradox of yours is really, really clever and i have not beat it yet, but i know it has to be beatable. give me a little time to try. Full marks on this though. Be back to you soon.
@@keystoneperspectives So you say the fairy told Pinocchio that “his nose would grow instantly after his telling a lie and for no other reason. He then says, “my nose will grow as soon as I finish this sentence.” I believe I have the resolution, but I must say, this is very, very clever, far more so than the drivel we have been debating thus far. So, Pinocchio makes “the statement” that his nose will grow as soon as he completes it. Why? For what reason? The statement as it stands alone conveys no information by which it as a statement could be considered true or false and thus there is no judgment which can be assigned to it and thus no claim as to whether his nose would grow or not. In other words, why would he state that his nose would grow? Nothing precedes the claim that it would, which can be judged as to that which it referred. His nose would grow because he said….what specifically that was false? We know that he is not, in the statement, referring to a previous utterance because had he and told a lie his nose would already have grown as per the fairy’s instruction and as yet, as he makes “the statement”, it had not. So the statement is self-referencing. What is wrong with this? There is no content of “the statement to which the consequence of his nose growing refers. It is just like the liar’s paradox in which “this statement is false” contains no information which to judge true or false thus invalidating the paradox as such. “The statement” in this refers back to the fairy’s instruction for the judgment of its truth or falsity but again, there is nothing by which that referral is made/would be made. The paradox stops at “the statement” of Pinocchio. Do you see?
@@jamestagge3429 You've avoided the question: does his nose grow or not grow after uttering the statement? Once you answer this question you will see that his statement does have content. If his nose grows then the statement was true and if his nose does not grow then the statement was false.
@@keystoneperspectives havent avoided the question. still working on it. This one is really tough, the toughest yet. But it is fun to work on. Give me a little more time.
Though you might find this interestig but it deals with the hangman version..........First of all, many who consider possible solutions to the hangman’s paradox attempt to resolve it by rewriting it or second guessing the author’s intent, the latter very visible in presentation. The hangman’s paradox, as all are, was formulated as it was deliberately to create the paradoxical function. In the hangman’s paradox, that which the judge instructed must be believed as true and proper or there is no paradox, that aspect its entire purpose. That the prisoner’s understanding of his instructions might be found to be inadequate but would have to be considered as logical in the second order (perhaps arising from a false premise) though not necessarily true (because it cannot be true for there are no real paradoxes). If not then the paradox fails. Written in formal logic, its conclusion drawn in formal logic and it presented in formal logic, it must be critiqued in formal logic. “That” is logical. One cannot apply some other logical system to try to generate a remedy and consider it valid, such as the nonsense of dialethism, which would then violate or defy all of the work of Frege, Wittgenstein, et. al., on meaning. One cannot have it both ways. So, the conclusion the prisoner came to that the hangman would not come for him on Friday has a logical structure to it but, obviously is in error. One could calculate that he could be taken any day of the week, including Friday, each day included as a possibility by the judge as per the paradox and the prisoner would in fact be surprised in the context of his theory that he would not be taken. The paradox does not claim that the prisoner’s theory is necessarily correct. It is only required that it be logical and it demonstrated a proper measure of that. His theory was the conclusion drawn from, and secondary to what we are obliged to accept as the truth of the judge’s instruction. The consideration of the above is that the prisoner’s theory addresses the days of the week backwards (each day effecting the previous, not that subsequent) which is not how they progress, i.e., they progress in the other direction in time. As per the paradox, the prisoner calculated from Friday to Monday that the hangman could not take him, for once Friday was eliminated, Thursday became the new end of the week then Wednesday, etc. But he moved forward in time through that week. The key to the resolution of this paradox then is that the judge said quite specifically that he would be taken at “noon” (on whichever day) and the prisoner calculated that if he were not taken by 12:00 pm that day, he could not be taken the next day for it being the new end of the week as per his calculation, he would not be surprised. The error in his logic is simple to see. It is only by his presence in Thursday not Wednesday that Friday could be eliminated as a possible execution day and he is not yet there. Also, he could not eliminate Thursday because Friday could not be eliminated prior to Thursday’s arrival and on Wednesday he is two days away. This applies to Monday and Tuesday as well. In other words, the week would have to pass to Thursday before Friday could be eliminated, beginning the chain of eliminated days and he could be taken any time before that. What do you think?
It's like a quantum state , if you try to analyze some particular state it collapse and here if we'll observe the cat on any particular day, it might be dead or alive.?
NO! This is not a paradox. If the prisoner believes he WILL NOT be hanged on any of the 5 days then any of those 5 days will be a surprise for the prisoner.
In the original telling of the paradox he does indeed believe that he will not be surprised and so he can be executed as you say. But what if he took the reasoning to its limit. Should he believe that he'll be executed or not?
keystone it doesn’t matter what he believes. If he thinks he’s going to be executed then he thinks any day is equally likely or he doesn’t think he’s going to be poisoned and therefore is surprised that it happened at all. Kinda like how we know electrons’s orbital or spin but not both or something
You present it as if there are two options of what to think. But isn't it most reasonable for him to remain undecided? If so, surprise requires an element of defying expectations, but what if he can't even determine what to expect? Can he truly be surprised?
keystone for each day two independent situations are happening. It’s important to note they’re independent. Situation one is if he dies at noon. Situation two is does he believe he will die at noon at 11:59. What he believes doesn’t affect what actually will happen. To answer your question of should he believe if he’ll die, I’d argue that it doesn’t matter when he dies just accept that by Friday you’re dead and you should enjoy your time left.
He can only be executed if he's surprised so I disagree that the two factors are independent. This paradox is closely tied to the liar's paradox and much more time and thought has been invested in that paradox because it's clearer and doesn't have the same language complexities as this paradox (e.g. what exactly does it mean to be surprised?). I recommend that you check out my video on the liar's paradox and see whether my arguments there make more sense to you. Perhaps we could continue this discussion around that paradox on that comment thread...
Simple: his state on Thursday cannot be measured. This may seem like a copout but there are limitations to measurement in QM as well. For example, the Planck length is a fundamental limitation on our resolution of the universe, preventing measurements from being too close. In the case of the cat, measurements on Thursday and Friday would be too close.
I hope the following version of the paradox will both entertain and reveal its flaw. In the prison there's a courtyard paved with flagstones. The prisoner's told that under one of them, but nobody knows which, there's a hole leading to a tunnel he can escape through. He only has to look under each stone till he finds it. He sneaks into the courtyard at night with a crowbar and decides to start in one corner and continue with one stone after the other till he reaches the far corner. He reasons that it can't be under the last stone in his plan because by the time he gets to it he'll know that must be where the hole is, but he's been told nobody knows, so it can't be. But that means it can't be the second to last either, because by the time he gets to it he'll know that one's where the hole is, but again it can't be since no-one knows. And so on back to the very first stone. So it's not under any stone at all and he therefore decides he'll never get out that way at all. Later he learns to his mortification that a fellow prisoner escaped by a hole under a stone in the courtyard, and he could have as well.
He can look under all the stones, find out which one covers the hole, and escape. Your story has no paradox. On the other hand, if he's told that nobody can *ever* know where the hole is then it is quite the paradox as to how anyone can escape...but quantum physics has a solution to this paradox (quantum tunneling).
@@chrisg3030 Your story has no paradox because the prisoner was simply lied to...someone *could* find out where the hole is just by looking. As such your story has no connection with the paradox. You are attacking a straw man.
@@keystoneperspectives1) The prisoner in my story wasn't lied to. Nobody knew where the hole was, that's why somebody had to look. 2) The prisoner in the original story could find out when he was going to hanged just by waiting, just as the hole in my story could be found just by looking. If there was a paradox in either story, I suggest it was simply due to the prisoner's crazy reasoning. That craziness is just a bit more obvious in mine.
@@chrisg3030 Your prisoner's only barrier to escape is his lack of a brain. He's told that 'nobody knows which' so he incorrectly deduces that 'nobody *can* know which'. He has no reason to eliminate any stone from consideration so if he had any sense he would look under each stone. The prisoner in the Unexpected Hanging Paradox is not dumb and there is nothing crazy about his reasoning. He is justified to eliminate all days from consideration. His problem is that he didn't take his reasoning far enough as with further thought he would have to reconsider all days, then eliminate them, then reconsider them, and so on ad infinitum. He was trapped by infinite, not blocked by his lack of a brain.
The cleanest method of dispelling the paradox is in its imprecise language in particular "Surprise" Surprise is not the same thing as unpredictable surprise carries other connotations. No day can be ruled out of being a surprise this is because as the more confident you are in any day being excluded the more likely it is to be the day you are executed. There is no paradox because no day can be ruled out he can be executed on any day and it would be a surprise.
You're assuming that we start with 5 days ruled in and then see whether we can rule out any days (which we can't with certainty). However, if we start with 0 days ruled in and then attempt to rule in some days we find that no days can be ruled in (with certainty). Is one approach more valid than another? You may claim that the original phrasing of the paradox is in better agreement with the first approach, but, if so, consider a rephrasing of the paradox where either approach is equally valid. Then how do you get out of the paradox?
I would like your opinion on this given that it has come up in our discussions on paradoxes. You seem to have great insight on this sort of thing. So, Schroedinger’s cat…..the same box, the same emitter, the same counter, the same hammer and the same vile, but rather than be filled with poison, it is filled with acid the fumes of which would still kill the cat. Now for the only change…..the vile is mounted on a mechanism which if the cat were to fall over to the floor of the box, would cause the vile to tip over and still its contents on the floor. I guess you should also consider spikes of some sort to prevent the cat from voluntarily lying down. So, after a time, we see the acid leaking out of the box from where it ate through the bottom meaning- the vile was broken by the hammer, the cat died and fell over, the mechanism turned the vile over and the acid fell to the floor and ate through it. Here we would have a string of deterministic events which we know were completed for we see the acid leaking from the box meaning that the cat had to be dead and only dead or that would not have happened. We did not open the box or have to. No wave form of the cat being alive and dead at the same time, just dead. What do you think? Have I missed something?
It's not about literally opening the lid to the box. If the box was made of glass, you could see the dead cat without having opened the lid. It's about information of the cat's death escaping from the box by any means and reaching an observer. We can speak of a definite state of the cat only once it has been observed. The observer plays an active role in our Quantum Universe by turning the potential ("Dead or Alive" superposition) into the actual (a definite state of "Dead" or "Alive"). I like that you're thinking about Quantum Mechanics here...
@@keystoneperspectives But the information “escaping from the box” does not happen until the acid eats through the bottom which it cannot do until and unless the cat is dead and only dead. The problem (I think) arises because the cat’s death is not the last question in the line of deterministic events, i.e., the cat has to die to fall over and to tip over the vile and for the acid to have time to eat through the box. How could the cat be both alive and dead at once?
@@jamestagge3429 What you are describing is akin to the "Delayed-choice quantum eraser" where measurements in the present seem to alter events in the past. It's how our Quantum Universe works.
@@jamestagge3429 "How could the cat be both alive and dead at once?": Imagine that the cat lives in a simulated universe. For the time being let's not focus on the complexities of this universe, but instead say that all that matters is the state of the cat: alive or dead...1 or 0. Let's say the computer is going to simulate the cat's state for a week. It starts off alive (so we have a sequence of 1's) and then it dies on Wednesday around noon (so everything after that is 0's). Do you think that the computer can give the cat a definite state every instant of the week? Take note that a week is composed of *infinite* instants, so that computer would have to produce a string of 0's and 1's having *infinite* digits. For a computer to produce such a string it must necessarily be infinite in memory and computing power. In other words, this computer must be MAGICAL. I don't think we need magic to make sense of our world or of paradoxes. We can do just fine with what we know actually exists: finite computers. And a finite computer can only produce a finite string. Q: But how can a finite string describe the continuum of events spanning a week? A: By saying that the string only captures a few instants in that week and what's in between those instants (in particular, between the last 1 and first 0) is a superposition state where he is neither alive nor dead. Quantum Mechanics may violate our classical intuitions...but it's the only sensible way to describe a universe.
I may wind up with egg on my face, but I would say that this supposed paradox fails as such and seems more ridiculous than Russell’s paradox, which is not a paradox either. I will refer to it as one for the sake of expediency. So…I think that the resolution to this is the following; if they came for him on any day, before noon he would not know if they would and would be thus surprised, making the time of day as significant as the day itself in his calculations. Also, most significantly, in the paradox it is stated clearly that “IF” the man were not hanged on Thursday, he could not be on Friday for then it would not be a surprise. It is only for that reason that Friday is excluded from the possible days for the hanging. The meaning of this is clear in the definition of the paradox and carries a significant measure of weight in terms of the logic and structure. The “IF” conveys that the execution “COULD” take place on Thursday and the entire paradox collapses (this extends to each preceding day of the week). Additionally, that the paradox states that the hangman came on Wednesday, demonstrates an aspect to the logical structure which seems to be ignored by all who have contemplated the resolution. So, “IF” the man were still alive on Wednesday, the possibility of Thursday still existed for the execution as stated above. I think that the hangman coming for him on Wednesday is because he was putting a buffer zone (day) between the date of the hanging and Friday, that day of the week under which circumstance it could not take place by definition. This in effect, broke the chain used in the defining of the paradox. What do you all think? I am still working on this but I don’t see it as the big deal it is purported to be on the videos. Please comment. It’s a fun study.
Given that you think Russell's Paradox is not a paradox, I can only assume that you also think the Liar's Paradox is not a paradox. If that's the case, then there's no point talking about the Unexpected Hanging Paradox since it's just the Liar's Paradox wrapped in an entertaining story. And with more words to the story, I'm sure we'll just end up debating over the meaning of those words, like 'what exactly does it mean to be surprised?' If I were the prisoner, I wouldn't be able to settle on the possible execution dates. Part of me would think I couldn't be executed on Wednesday and part of me would think I could. By you're definition of surprise, that means that I would be entirely surprised on Wednesday, so I could be executed. But your view doesn't accurately capture the depths of my confusion. Part of me would be surprised and part of me wouldn't, so if we were precise on the matter only part of me could be executed...which is nonsensical. That's the paradox. And if you won't budge your definition of surprise, then perhaps we should scrap the word 'surprise' which contains all of your preconceived notions and create another word which aligns with my view of surprise. With this new word in place of surprise, is it then a paradox? Or as I alluded to in the beginning, perhaps we should be forget about all of this complexity and go to the heart of it all: why do you think the Liar's Paradox is not a paradox?
@@keystoneperspectives First, thanks very much for your response. I do love these kinds of discussions……anyway….The liars paradox I have heard expressed two ways; “I am a liar” and “this statement is false”. The former - this is purported to be a paradox because if whatever I say is a lie, then telling you I am a liar cannot be the truth, but if I am a liar and want to convey that I am…etc. This is childishly simple in the resolution. IF there are things I can say which cannot be lies such as, “I am” or “I am speaking” the paradox fails. The conundrum no longer exists. The latter - “this statement is a false” being supposedly paradoxical because if the statement is false it is because it is true, but cannot be true because it is false…etc. But as a statement, it is meaningless. The supposed paradox depends upon the fact that this statement does NOT reference some other utterance but rather itself. But the term “statement” in this statement has no meaning to which to refer. There is no value judgment which can be made about it. It can be neither true nor false. The claim that it is false cannot be made. In that there is no value to judge, there is no apparent contradiction. Sophomoric. A quickie on Russell’s paradox to be clear - the paradox depends upon the barber having to be a member of the only two set of men, i.e., the set of men who shave themselves or the set of men who are shaved. His sign states that he shaves only those men who do not shave themselves, so he cannot shave himself but he must…etc. The revelation of the fraud which this is, is seen in the following; the barber cannot be a member of either the set of men who shave themselves or those who don’t so there is no paradox. Note, if there were no barber, there could be no set of men who are shaved, as per Russell’s outline of the scheme. The paradox would then fail. The two sets of men defined by Russell are members of their respective sets by the same three criteria, but one. Each is a man, each lives in town and each must be shaved. The defining characteristic in the one is that the men shave themselves and in the other, that they are shaved. Absent that one characteristic, there would be just one set of men and again, the paradox fails. So, what of the barber? He too is a man, he too lives in town and he too must be shaved. But the defining characteristic and only by which he would be a member of a set is that “he shaves others”. He is thus a member of a third set of men and the paradox fails. Now you might wish to deny this but in doing so you would deny the logic and means by which the first two sets of men were defined by Russell to begin with and the paradox fails. You would also be denying the very means of the set of men who are shaved to be so and the paradox fails. If then you accept my notion of the third set of men, the paradox fails. The point being that you cannot formulate such a conceptual contradiction, ever. Reality does not allow it. As for the hanging paradox, which is also not a paradox, I based my reasoning on that which the author himself stated…”IF the man were not hanged by noon on Thursday, he could not be on Friday. What does this mean to you? To me, the statement means clearly that he could be hanged on Thursday and that Friday could only be taken out of the list of possible days IF the man were NOT hanged on Thursday. When the hangman came for him on Wednesday noon, the prisoner was surprised in any sense of the meaning of the word you might give it because he knew that he could be hung on that day or Thursday. The term IF and its application in the outline of the paradox is the only significant aspect which leaves an open door, as far as I can see thus far. It means what it means and cannot be ignored in the analysis. The author clearly wanted to convey that Friday was only eliminated as a day if the man were not taken by Thursday, a clearly stated condition. Going all around the houses trying to invent some subtle meanings to the terms used to change the thrust of the paradox or the context in which the terms are considered is silly. The author of this piffle meant what he wrote and expected the context of the scheme to be sufficient to convey the apparent contradictions. What do you think?
I’ve been notified a couple of times that you responded to my comment but I don’t see anything here. Perhaps you deleted your message but if not please try reposting.
@@keystoneperspectives First, thanks very much for your response. I do love these kinds of discussions……anyway….The liars paradox I have heard expressed two ways; “I am a liar” and “this statement is false”. The former - this is purported to be a paradox because if whatever I say is a lie, then telling you I am a liar cannot be the truth, but if I am a liar and want to convey that I am…etc. This is childishly simple in the resolution. IF there are things I can say which cannot be lies such as, “I am” or “I am speaking” the paradox fails. The conundrum no longer exists. The latter - “this statement is a false” being supposedly paradoxical because if the statement is false it is because it is true, but cannot be true because it is false…etc. But as a statement, it is meaningless. The supposed paradox depends upon the fact that this statement does NOT reference some other utterance but rather itself. But the term “statement” in this statement has no meaning to which to refer. There is no value judgment which can be made about it. It can be neither true nor false. The claim that it is false cannot be made. In that there is no value to judge, there is no apparent contradiction. Sophomoric. A quickie on Russell’s paradox to be clear - the paradox depends upon the barber having to be a member of the only two set of men, i.e., the set of men who shave themselves or the set of men who are shaved. His sign states that he shaves only those men who do not shave themselves, so he cannot shave himself but he must…etc. The revelation of the fraud which this is, is seen in the following; the barber cannot be a member of either the set of men who shave themselves or those who don’t so there is no paradox. Note, if there were no barber, there could be no set of men who are shaved, as per Russell’s outline of the scheme. The paradox would then fail. The two sets of men defined by Russell are members of their respective sets by the same three criteria, but one. Each is a man, each lives in town and each must be shaved. The defining characteristic in the one is that the men shave themselves and in the other, that they are shaved. Absent that one characteristic, there would be just one set of men and again, the paradox fails. So, what of the barber? He too is a man, he too lives in town and he too must be shaved. But the defining characteristic and only by which he would be a member of a set is that “he shaves others”. He is thus a member of a third set of men and the paradox fails. Now you might wish to deny this but in doing so you would deny the logic and means by which the first two sets of men were defined by Russell to begin with and the paradox fails. You would also be denying the very means of the set of men who are shaved to be so and the paradox fails. If then you accept my notion of the third set of men, the paradox fails. The point being that you cannot formulate such a conceptual contradiction, ever. Reality does not allow it. As for the hanging paradox, which is also not a paradox, I based my reasoning on that which the author himself stated…”IF the man were not hanged by noon on Thursday, he could not be on Friday. What does this mean to you? To me, the statement means clearly that he could be hanged on Thursday and that Friday could only be taken out of the list of possible days IF the man were NOT hanged on Thursday. When the hangman came for him on Wednesday noon, the prisoner was surprised in any sense of the meaning of the word you might give it because he knew that he could be hung on that day or Thursday. The term IF and its application in the outline of the paradox is the only significant aspect which leaves an open door, as far as I can see thus far. It means what it means and cannot be ignored in the analysis. The author clearly wanted to convey that Friday was only eliminated as a day if the man were not taken by Thursday, a clearly stated condition. Going all around the houses trying to invent some subtle meanings to the terms used to change the thrust of the paradox or the context in which the terms are considered is silly. The author of this piffle meant what he wrote and expected the context of the scheme to be sufficient to convey the apparent contradictions. What do you think?
God once said to human, you will die within a hundred year, but I will not let you know which date to come, otherwise you will become eternity. So all human live happily
Ah, I think I'm starting to get this, I was leaning to the same conclusions but needed someone to explain it clearly. If it's currently Sunday, the only day we can exclude with certainty is Friday, because we know with 100% certainy it's not going to be Sat/Sun. That's facts. But do we know for sure if it's going to be Monday? No. The entire idea is that we can't make certain 100% future predictions based on POTENTIAL events that didn't happen yet. Thus simply we can't exclude Thursday the same way we did with Friday. And if it's Wednesday night and we are still alive only and only then we have to assume it's Thursday and in that case Judge lied to us, because there wasn't any surprise. If we make it alive to Thursday night, the judge still lied to us, since we know it's Friday for sure. Uhh, am I getting confused again?
@@keystoneperspectives How can one thing be two things at the same time? This contradicts logic :( It's either either. If we can rule them out, we can't rule them back in, since it's contradictory.
@@Gen_66 I agree that one thing can't *actually* be alive *AND* dead. I argue that it is *potentially* alive *OR* dead. In other words, until it's state is measured it is in an OR state. I believe that this is what happens in reality with superpositions in quantum mechanics (with Schrodinger's cat).
keystone Ok from a point of view on Sunday, the entire week is full of potential cases. But if the cat actually makes it alive until Wed night then the days Mon to Wed become a fact and reality no longer a possible or potential. Thus on Wed night we can judge bases on facts that Thu is the day when the cat dies. In that case Judge lied. If cat don’t die on Thu then it’s Fri in which case the judge lied as well, since the new cat beforehand the exact day of execution.
@@Gen_66 If we measure the cat to be alive on Wednesday then we can deduce that the cat was alive on all preceding days. As for Thursday it must remain unmeasured so it is 'alive or dead' and as for Friday we know that it will be 'dead' as promised. So all anybody can determine is that the cat was killed either Thursday or Friday. Surprise is maintained. You mentioned that on Wed night that 'we can judge based on facts that Thu is the day' but we can't because right when we rule it in we must rule it out, and right when we rule it out we must rule it in.
This argument cannot be correct. In your construction you claim there is a 1/5 chance of being alive after noon on Thursday. That contradicts the premise which is that the execution will come as a surprise, because in those 1/5 of cases the execution on Friday would not be a surprise. That is the heart of the issue and cannot be sidestepped by thinking probabilistically or drawing quantum mechanical analogies. The same mistake occurs even earlier when you are talking about "ruling in" the cases again. The case of living on Thursday afternoon cannot ever be ruled in.
In my construction I do claim that there is a 1/5 chance of being alive on Thursday evening. But I also claim that there must be a potential state between alive and dead. As such, we cannot measure his state on Thursday because that measurement might result in an inconsistency. His state on Thursday must either be "dead" or "dead or alive". "Alive" is not a valid option.
I think of this more of Sunday night judge picks a random day between Monday and Friday and just doesn’t tell the prisoner. As of Monday morning the cat has no idea.
The judge cannot pick ANY day between Monday and Friday because he cannot pick Friday. If Friday morning comes around the cat will not be surprised to be executed.
keystone yes he can. He picks a day on Sunday, each day has a 1/5 chance of being chosen. And the prisoner just isn’t told when even though the day is already selected. Even if we simplify it and look at Friday only, if he’s sure he’s going to be executed Friday then he believes that he’s not going to be hung at all thus being a surprise. If he’s unsure he’s going to be hung on Friday then he’s still surprised. Either way he’s surprised.
*RYAN’S NOTES*
Please keep in mind that this series is composed of short and raw videos containing many original ideas. The videos are not textbooks. Let’s use these videos as a starting point for a conversation. Whether you agree or disagree with the ideas in the videos, leave your thoughts in the comments and we’ll talk it through.
I will be posting comments, corrections, and FAQs here once I get some feedback on this video.
If the prisoner is alive on Thursday night, he knows he will be executed on Friday and thus realizes he has been lied to.
Good explanation man, thank you for the video.
You deserve more subscribers ❤
Thanks for these kind words :)
I have been searching RUclips on this paradox and this is by far the best entry imo!
I think the main point is that the logical statements inside the prisoner's head are inconsistent/contradictory. Now the question is, what the reaction to this contradiction should be. There is no right or wrong answer, as this is not in any way specified. It depends on how we model the prisoner's mind mathematically. For example, he could believe in contradictory statements, which allows him to believe to be executed on every day at the same time. Then, if we interpret "surprise" as "The prisoner does not believe he is executed on the day of the execution", the judge was technically lying.
Thanks!
I think saying that the prisoner has contradictory thinking or that the judge was lying is a copout to this problem. I would argue that the solution that I proposed is entirely consistent, it just requires a new perspective more inline with our quantum intuitions of measurement and superposition.
@@keystoneperspectives I have to admit that I do not have a quantum intuition :P Anyway, it is a really interesting view on the pardox. But doesn't ln(e) measure his world all the time so that there are no quantum superpositions from his perspective?
Your question goes to the heart of Shrodinger's Cat: how can Shrodinger's Cat be in a superposition if he is measuring his world all the time?
You've reached the heart of the classical assumption: that all moments are measured. There is no evidence to support this assumption. In fact, there is evidence of the contrary. Consider the Quantum Zeno Effect where a particle can only move if it is not being measured. This suggests that change only happens when we are not looking.
this Pinocchio paradox of yours is really, really clever and i have not beat it yet, but i know it has to be beatable. give me a little time to try. Full marks on this though. Be back to you soon.
Good luck :) I believe it is 'beatable' as I think I've got a solution but let's see what you come up with.
Oh, and the Pinocchio Paradox is not mine...it's a famous one...but I did do a video on it.
@@keystoneperspectives So you say the fairy told Pinocchio that “his nose would grow instantly after his telling a lie and for no other reason. He then says, “my nose will grow as soon as I finish this sentence.” I believe I have the resolution, but I must say, this is very, very clever, far more so than the drivel we have been debating thus far.
So, Pinocchio makes “the statement” that his nose will grow as soon as he completes it. Why? For what reason? The statement as it stands alone conveys no information by which it as a statement could be considered true or false and thus there is no judgment which can be assigned to it and thus no claim as to whether his nose would grow or not. In other words, why would he state that his nose would grow? Nothing precedes the claim that it would, which can be judged as to that which it referred. His nose would grow because he said….what specifically that was false?
We know that he is not, in the statement, referring to a previous utterance because had he and told a lie his nose would already have grown as per the fairy’s instruction and as yet, as he makes “the statement”, it had not. So the statement is self-referencing.
What is wrong with this? There is no content of “the statement to which the consequence of his nose growing refers. It is just like the liar’s paradox in which “this statement is false” contains no information which to judge true or false thus invalidating the paradox as such. “The statement” in this refers back to the fairy’s instruction for the judgment of its truth or falsity but again, there is nothing by which that referral is made/would be made. The paradox stops at “the statement” of Pinocchio.
Do you see?
@@jamestagge3429 You've avoided the question: does his nose grow or not grow after uttering the statement? Once you answer this question you will see that his statement does have content. If his nose grows then the statement was true and if his nose does not grow then the statement was false.
@@keystoneperspectives havent avoided the question. still working on it. This one is really tough, the toughest yet. But it is fun to work on. Give me a little more time.
Though you might find this interestig but it deals with the hangman version..........First of all, many who consider possible solutions to the hangman’s paradox attempt to resolve it by rewriting it or second guessing the author’s intent, the latter very visible in presentation. The hangman’s paradox, as all are, was formulated as it was deliberately to create the paradoxical function. In the hangman’s paradox, that which the judge instructed must be believed as true and proper or there is no paradox, that aspect its entire purpose. That the prisoner’s understanding of his instructions might be found to be inadequate but would have to be considered as logical in the second order (perhaps arising from a false premise) though not necessarily true (because it cannot be true for there are no real paradoxes). If not then the paradox fails. Written in formal logic, its conclusion drawn in formal logic and it presented in formal logic, it must be critiqued in formal logic. “That” is logical. One cannot apply some other logical system to try to generate a remedy and consider it valid, such as the nonsense of dialethism, which would then violate or defy all of the work of Frege, Wittgenstein, et. al., on meaning. One cannot have it both ways.
So, the conclusion the prisoner came to that the hangman would not come for him on Friday has a logical structure to it but, obviously is in error. One could calculate that he could be taken any day of the week, including Friday, each day included as a possibility by the judge as per the paradox and the prisoner would in fact be surprised in the context of his theory that he would not be taken. The paradox does not claim that the prisoner’s theory is necessarily correct. It is only required that it be logical and it demonstrated a proper measure of that. His theory was the conclusion drawn from, and secondary to what we are obliged to accept as the truth of the judge’s instruction.
The consideration of the above is that the prisoner’s theory addresses the days of the week backwards (each day effecting the previous, not that subsequent) which is not how they progress, i.e., they progress in the other direction in time. As per the paradox, the prisoner calculated from Friday to Monday that the hangman could not take him, for once Friday was eliminated, Thursday became the new end of the week then Wednesday, etc. But he moved forward in time through that week. The key to the resolution of this paradox then is that the judge said quite specifically that he would be taken at “noon” (on whichever day) and the prisoner calculated that if he were not taken by 12:00 pm that day, he could not be taken the next day for it being the new end of the week as per his calculation, he would not be surprised. The error in his logic is simple to see. It is only by his presence in Thursday not Wednesday that Friday could be eliminated as a possible execution day and he is not yet there. Also, he could not eliminate Thursday because Friday could not be eliminated prior to Thursday’s arrival and on Wednesday he is two days away. This applies to Monday and Tuesday as well.
In other words, the week would have to pass to Thursday before Friday could be eliminated, beginning the chain of eliminated days and he could be taken any time before that.
What do you think?
pfff still don't get it, it just feels like the assumption are wrong from the beginning
It's like a quantum state , if you try to analyze some particular state it collapse and here if we'll observe the cat on any particular day, it might be dead or alive.?
NO! This is not a paradox. If the prisoner believes he WILL NOT be hanged on any of the 5 days then any of those 5 days will be a surprise for the prisoner.
In the original telling of the paradox he does indeed believe that he will not be surprised and so he can be executed as you say. But what if he took the reasoning to its limit. Should he believe that he'll be executed or not?
keystone it doesn’t matter what he believes. If he thinks he’s going to be executed then he thinks any day is equally likely or he doesn’t think he’s going to be poisoned and therefore is surprised that it happened at all. Kinda like how we know electrons’s orbital or spin but not both or something
You present it as if there are two options of what to think. But isn't it most reasonable for him to remain undecided? If so, surprise requires an element of defying expectations, but what if he can't even determine what to expect? Can he truly be surprised?
keystone for each day two independent situations are happening. It’s important to note they’re independent. Situation one is if he dies at noon. Situation two is does he believe he will die at noon at 11:59. What he believes doesn’t affect what actually will happen. To answer your question of should he believe if he’ll die, I’d argue that it doesn’t matter when he dies just accept that by Friday you’re dead and you should enjoy your time left.
He can only be executed if he's surprised so I disagree that the two factors are independent. This paradox is closely tied to the liar's paradox and much more time and thought has been invested in that paradox because it's clearer and doesn't have the same language complexities as this paradox (e.g. what exactly does it mean to be surprised?). I recommend that you check out my video on the liar's paradox and see whether my arguments there make more sense to you. Perhaps we could continue this discussion around that paradox on that comment thread...
So what happens in the quantum model if on Thursday hes still alive?
Simple: his state on Thursday cannot be measured. This may seem like a copout but there are limitations to measurement in QM as well. For example, the Planck length is a fundamental limitation on our resolution of the universe, preventing measurements from being too close. In the case of the cat, measurements on Thursday and Friday would be too close.
I hope the following version of the paradox will both entertain and reveal its flaw.
In the prison there's a courtyard paved with flagstones. The prisoner's told that under one of them, but nobody knows which, there's a hole leading to a tunnel he can escape through. He only has to look under each stone till he finds it. He sneaks into the courtyard at night with a crowbar and decides to start in one corner and continue with one stone after the other till he reaches the far corner. He reasons that it can't be under the last stone in his plan because by the time he gets to it he'll know that must be where the hole is, but he's been told nobody knows, so it can't be. But that means it can't be the second to last either, because by the time he gets to it he'll know that one's where the hole is, but again it can't be since no-one knows. And so on back to the very first stone. So it's not under any stone at all and he therefore decides he'll never get out that way at all. Later he learns to his mortification that a fellow prisoner escaped by a hole under a stone in the courtyard, and he could have as well.
He can look under all the stones, find out which one covers the hole, and escape. Your story has no paradox.
On the other hand, if he's told that nobody can *ever* know where the hole is then it is quite the paradox as to how anyone can escape...but quantum physics has a solution to this paradox (quantum tunneling).
@@keystoneperspectives I guess that's my point, that my story has no paradox.
@@chrisg3030 Your story has no paradox because the prisoner was simply lied to...someone *could* find out where the hole is just by looking. As such your story has no connection with the paradox. You are attacking a straw man.
@@keystoneperspectives1) The prisoner in my story wasn't lied to. Nobody knew where the hole was, that's why somebody had to look.
2) The prisoner in the original story could find out when he was going to hanged just by waiting, just as the hole in my story could be found just by looking.
If there was a paradox in either story, I suggest it was simply due to the prisoner's crazy reasoning. That craziness is just a bit more obvious in mine.
@@chrisg3030 Your prisoner's only barrier to escape is his lack of a brain. He's told that 'nobody knows which' so he incorrectly deduces that 'nobody *can* know which'. He has no reason to eliminate any stone from consideration so if he had any sense he would look under each stone.
The prisoner in the Unexpected Hanging Paradox is not dumb and there is nothing crazy about his reasoning. He is justified to eliminate all days from consideration. His problem is that he didn't take his reasoning far enough as with further thought he would have to reconsider all days, then eliminate them, then reconsider them, and so on ad infinitum. He was trapped by infinite, not blocked by his lack of a brain.
The cleanest method of dispelling the paradox is in its imprecise language in particular "Surprise" Surprise is not the same thing as unpredictable surprise carries other connotations. No day can be ruled out of being a surprise this is because as the more confident you are in any day being excluded the more likely it is to be the day you are executed. There is no paradox because no day can be ruled out he can be executed on any day and it would be a surprise.
You're assuming that we start with 5 days ruled in and then see whether we can rule out any days (which we can't with certainty). However, if we start with 0 days ruled in and then attempt to rule in some days we find that no days can be ruled in (with certainty). Is one approach more valid than another? You may claim that the original phrasing of the paradox is in better agreement with the first approach, but, if so, consider a rephrasing of the paradox where either approach is equally valid. Then how do you get out of the paradox?
I would like your opinion on this given that it has come up in our discussions on paradoxes. You seem to have great insight on this sort of thing.
So, Schroedinger’s cat…..the same box, the same emitter, the same counter, the same hammer and the same vile, but rather than be filled with poison, it is filled with acid the fumes of which would still kill the cat. Now for the only change…..the vile is mounted on a mechanism which if the cat were to fall over to the floor of the box, would cause the vile to tip over and still its contents on the floor. I guess you should also consider spikes of some sort to prevent the cat from voluntarily lying down.
So, after a time, we see the acid leaking out of the box from where it ate through the bottom meaning- the vile was broken by the hammer, the cat died and fell over, the mechanism turned the vile over and the acid fell to the floor and ate through it. Here we would have a string of deterministic events which we know were completed for we see the acid leaking from the box meaning that the cat had to be dead and only dead or that would not have happened. We did not open the box or have to. No wave form of the cat being alive and dead at the same time, just dead. What do you think? Have I missed something?
It's not about literally opening the lid to the box. If the box was made of glass, you could see the dead cat without having opened the lid. It's about information of the cat's death escaping from the box by any means and reaching an observer. We can speak of a definite state of the cat only once it has been observed. The observer plays an active role in our Quantum Universe by turning the potential ("Dead or Alive" superposition) into the actual (a definite state of "Dead" or "Alive"). I like that you're thinking about Quantum Mechanics here...
@@keystoneperspectives But the information “escaping from the box” does not happen until the acid eats through the bottom which it cannot do until and unless the cat is dead and only dead. The problem (I think) arises because the cat’s death is not the last question in the line of deterministic events, i.e., the cat has to die to fall over and to tip over the vile and for the acid to have time to eat through the box. How could the cat be both alive and dead at once?
@@jamestagge3429 What you are describing is akin to the "Delayed-choice quantum eraser" where measurements in the present seem to alter events in the past. It's how our Quantum Universe works.
@@jamestagge3429 "How could the cat be both alive and dead at once?": Imagine that the cat lives in a simulated universe. For the time being let's not focus on the complexities of this universe, but instead say that all that matters is the state of the cat: alive or dead...1 or 0. Let's say the computer is going to simulate the cat's state for a week. It starts off alive (so we have a sequence of 1's) and then it dies on Wednesday around noon (so everything after that is 0's).
Do you think that the computer can give the cat a definite state every instant of the week? Take note that a week is composed of *infinite* instants, so that computer would have to produce a string of 0's and 1's having *infinite* digits. For a computer to produce such a string it must necessarily be infinite in memory and computing power. In other words, this computer must be MAGICAL.
I don't think we need magic to make sense of our world or of paradoxes. We can do just fine with what we know actually exists: finite computers. And a finite computer can only produce a finite string.
Q: But how can a finite string describe the continuum of events spanning a week?
A: By saying that the string only captures a few instants in that week and what's in between those instants (in particular, between the last 1 and first 0) is a superposition state where he is neither alive nor dead. Quantum Mechanics may violate our classical intuitions...but it's the only sensible way to describe a universe.
I may wind up with egg on my face, but I would say that this supposed paradox fails as such and seems more ridiculous than Russell’s paradox, which is not a paradox either. I will refer to it as one for the sake of expediency. So…I think that the resolution to this is the following; if they came for him on any day, before noon he would not know if they would and would be thus surprised, making the time of day as significant as the day itself in his calculations. Also, most significantly, in the paradox it is stated clearly that “IF” the man were not hanged on Thursday, he could not be on Friday for then it would not be a surprise. It is only for that reason that Friday is excluded from the possible days for the hanging. The meaning of this is clear in the definition of the paradox and carries a significant measure of weight in terms of the logic and structure. The “IF” conveys that the execution “COULD” take place on Thursday and the entire paradox collapses (this extends to each preceding day of the week). Additionally, that the paradox states that the hangman came on Wednesday, demonstrates an aspect to the logical structure which seems to be ignored by all who have contemplated the resolution.
So, “IF” the man were still alive on Wednesday, the possibility of Thursday still existed for the execution as stated above. I think that the hangman coming for him on Wednesday is because he was putting a buffer zone (day) between the date of the hanging and Friday, that day of the week under which circumstance it could not take place by definition. This in effect, broke the chain used in the defining of the paradox.
What do you all think? I am still working on this but I don’t see it as the big deal it is purported to be on the videos. Please comment. It’s a fun study.
Given that you think Russell's Paradox is not a paradox, I can only assume that you also think the Liar's Paradox is not a paradox. If that's the case, then there's no point talking about the Unexpected Hanging Paradox since it's just the Liar's Paradox wrapped in an entertaining story. And with more words to the story, I'm sure we'll just end up debating over the meaning of those words, like 'what exactly does it mean to be surprised?'
If I were the prisoner, I wouldn't be able to settle on the possible execution dates. Part of me would think I couldn't be executed on Wednesday and part of me would think I could. By you're definition of surprise, that means that I would be entirely surprised on Wednesday, so I could be executed. But your view doesn't accurately capture the depths of my confusion.
Part of me would be surprised and part of me wouldn't, so if we were precise on the matter only part of me could be executed...which is nonsensical. That's the paradox. And if you won't budge your definition of surprise, then perhaps we should scrap the word 'surprise' which contains all of your preconceived notions and create another word which aligns with my view of surprise. With this new word in place of surprise, is it then a paradox? Or as I alluded to in the beginning, perhaps we should be forget about all of this complexity and go to the heart of it all: why do you think the Liar's Paradox is not a paradox?
@@keystoneperspectives First, thanks very much for your response. I do love these kinds of discussions……anyway….The liars paradox I have heard expressed two ways; “I am a liar” and “this statement is false”. The former - this is purported to be a paradox because if whatever I say is a lie, then telling you I am a liar cannot be the truth, but if I am a liar and want to convey that I am…etc. This is childishly simple in the resolution. IF there are things I can say which cannot be lies such as, “I am” or “I am speaking” the paradox fails. The conundrum no longer exists. The latter - “this statement is a false” being supposedly paradoxical because if the statement is false it is because it is true, but cannot be true because it is false…etc. But as a statement, it is meaningless. The supposed paradox depends upon the fact that this statement does NOT reference some other utterance but rather itself. But the term “statement” in this statement has no meaning to which to refer. There is no value judgment which can be made about it. It can be neither true nor false. The claim that it is false cannot be made. In that there is no value to judge, there is no apparent contradiction. Sophomoric.
A quickie on Russell’s paradox to be clear - the paradox depends upon the barber having to be a member of the only two set of men, i.e., the set of men who shave themselves or the set of men who are shaved. His sign states that he shaves only those men who do not shave themselves, so he cannot shave himself but he must…etc. The revelation of the fraud which this is, is seen in the following; the barber cannot be a member of either the set of men who shave themselves or those who don’t so there is no paradox. Note, if there were no barber, there could be no set of men who are shaved, as per Russell’s outline of the scheme. The paradox would then fail. The two sets of men defined by Russell are members of their respective sets by the same three criteria, but one. Each is a man, each lives in town and each must be shaved. The defining characteristic in the one is that the men shave themselves and in the other, that they are shaved. Absent that one characteristic, there would be just one set of men and again, the paradox fails. So, what of the barber? He too is a man, he too lives in town and he too must be shaved. But the defining characteristic and only by which he would be a member of a set is that “he shaves others”. He is thus a member of a third set of men and the paradox fails. Now you might wish to deny this but in doing so you would deny the logic and means by which the first two sets of men were defined by Russell to begin with and the paradox fails. You would also be denying the very means of the set of men who are shaved to be so and the paradox fails. If then you accept my notion of the third set of men, the paradox fails. The point being that you cannot formulate such a conceptual contradiction, ever. Reality does not allow it.
As for the hanging paradox, which is also not a paradox, I based my reasoning on that which the author himself stated…”IF the man were not hanged by noon on Thursday, he could not be on Friday. What does this mean to you? To me, the statement means clearly that he could be hanged on Thursday and that Friday could only be taken out of the list of possible days IF the man were NOT hanged on Thursday. When the hangman came for him on Wednesday noon, the prisoner was surprised in any sense of the meaning of the word you might give it because he knew that he could be hung on that day or Thursday. The term IF and its application in the outline of the paradox is the only significant aspect which leaves an open door, as far as I can see thus far. It means what it means and cannot be ignored in the analysis. The author clearly wanted to convey that Friday was only eliminated as a day if the man were not taken by Thursday, a clearly stated condition.
Going all around the houses trying to invent some subtle meanings to the terms used to change the thrust of the paradox or the context in which the terms are considered is silly. The author of this piffle meant what he wrote and expected the context of the scheme to be sufficient to convey the apparent contradictions.
What do you think?
@@keystoneperspectives what do you think????
I’ve been notified a couple of times that you responded to my comment but I don’t see anything here. Perhaps you deleted your message but if not please try reposting.
@@keystoneperspectives First, thanks very much for your response. I do love these kinds of discussions……anyway….The liars paradox I have heard expressed two ways; “I am a liar” and “this statement is false”. The former - this is purported to be a paradox because if whatever I say is a lie, then telling you I am a liar cannot be the truth, but if I am a liar and want to convey that I am…etc. This is childishly simple in the resolution. IF there are things I can say which cannot be lies such as, “I am” or “I am speaking” the paradox fails. The conundrum no longer exists. The latter - “this statement is a false” being supposedly paradoxical because if the statement is false it is because it is true, but cannot be true because it is false…etc. But as a statement, it is meaningless. The supposed paradox depends upon the fact that this statement does NOT reference some other utterance but rather itself. But the term “statement” in this statement has no meaning to which to refer. There is no value judgment which can be made about it. It can be neither true nor false. The claim that it is false cannot be made. In that there is no value to judge, there is no apparent contradiction. Sophomoric.
A quickie on Russell’s paradox to be clear - the paradox depends upon the barber having to be a member of the only two set of men, i.e., the set of men who shave themselves or the set of men who are shaved. His sign states that he shaves only those men who do not shave themselves, so he cannot shave himself but he must…etc. The revelation of the fraud which this is, is seen in the following; the barber cannot be a member of either the set of men who shave themselves or those who don’t so there is no paradox. Note, if there were no barber, there could be no set of men who are shaved, as per Russell’s outline of the scheme. The paradox would then fail. The two sets of men defined by Russell are members of their respective sets by the same three criteria, but one. Each is a man, each lives in town and each must be shaved. The defining characteristic in the one is that the men shave themselves and in the other, that they are shaved. Absent that one characteristic, there would be just one set of men and again, the paradox fails. So, what of the barber? He too is a man, he too lives in town and he too must be shaved. But the defining characteristic and only by which he would be a member of a set is that “he shaves others”. He is thus a member of a third set of men and the paradox fails. Now you might wish to deny this but in doing so you would deny the logic and means by which the first two sets of men were defined by Russell to begin with and the paradox fails. You would also be denying the very means of the set of men who are shaved to be so and the paradox fails. If then you accept my notion of the third set of men, the paradox fails. The point being that you cannot formulate such a conceptual contradiction, ever. Reality does not allow it.
As for the hanging paradox, which is also not a paradox, I based my reasoning on that which the author himself stated…”IF the man were not hanged by noon on Thursday, he could not be on Friday. What does this mean to you? To me, the statement means clearly that he could be hanged on Thursday and that Friday could only be taken out of the list of possible days IF the man were NOT hanged on Thursday. When the hangman came for him on Wednesday noon, the prisoner was surprised in any sense of the meaning of the word you might give it because he knew that he could be hung on that day or Thursday. The term IF and its application in the outline of the paradox is the only significant aspect which leaves an open door, as far as I can see thus far. It means what it means and cannot be ignored in the analysis. The author clearly wanted to convey that Friday was only eliminated as a day if the man were not taken by Thursday, a clearly stated condition.
Going all around the houses trying to invent some subtle meanings to the terms used to change the thrust of the paradox or the context in which the terms are considered is silly. The author of this piffle meant what he wrote and expected the context of the scheme to be sufficient to convey the apparent contradictions.
What do you think?
God once said to human, you will die within a hundred year, but I will not let you know which date to come, otherwise you will become eternity. So all human live happily
Ah, I think I'm starting to get this, I was leaning to the same conclusions but needed someone to explain it clearly. If it's currently Sunday, the only day we can exclude with certainty is Friday, because we know with 100% certainy it's not going to be Sat/Sun. That's facts. But do we know for sure if it's going to be Monday? No. The entire idea is that we can't make certain 100% future predictions based on POTENTIAL events that didn't happen yet. Thus simply we can't exclude Thursday the same way we did with Friday. And if it's Wednesday night and we are still alive only and only then we have to assume it's Thursday and in that case Judge lied to us, because there wasn't any surprise. If we make it alive to Thursday night, the judge still lied to us, since we know it's Friday for sure. Uhh, am I getting confused again?
I don't think you have it quite yet. We can rule all cases out... Then all cases back in... Then back out... And so on to no end
@@keystoneperspectives How can one thing be two things at the same time? This contradicts logic :( It's either either. If we can rule them out, we can't rule them back in, since it's contradictory.
@@Gen_66 I agree that one thing can't *actually* be alive *AND* dead. I argue that it is *potentially* alive *OR* dead. In other words, until it's state is measured it is in an OR state. I believe that this is what happens in reality with superpositions in quantum mechanics (with Schrodinger's cat).
keystone Ok from a point of view on Sunday, the entire week is full of potential cases. But if the cat actually makes it alive until Wed night then the days Mon to Wed become a fact and reality no longer a possible or potential. Thus on Wed night we can judge bases on facts that Thu is the day when the cat dies. In that case Judge lied. If cat don’t die on Thu then it’s Fri in which case the judge lied as well, since the new cat beforehand the exact day of execution.
@@Gen_66 If we measure the cat to be alive on Wednesday then we can deduce that the cat was alive on all preceding days. As for Thursday it must remain unmeasured so it is 'alive or dead' and as for Friday we know that it will be 'dead' as promised. So all anybody can determine is that the cat was killed either Thursday or Friday. Surprise is maintained.
You mentioned that on Wed night that 'we can judge based on facts that Thu is the day' but we can't because right when we rule it in we must rule it out, and right when we rule it out we must rule it in.
do you see the comment now? Let me know. i reposted
This argument cannot be correct. In your construction you claim there is a 1/5 chance of being alive after noon on Thursday. That contradicts the premise which is that the execution will come as a surprise, because in those 1/5 of cases the execution on Friday would not be a surprise. That is the heart of the issue and cannot be sidestepped by thinking probabilistically or drawing quantum mechanical analogies.
The same mistake occurs even earlier when you are talking about "ruling in" the cases again. The case of living on Thursday afternoon cannot ever be ruled in.
In my construction I do claim that there is a 1/5 chance of being alive on Thursday evening. But I also claim that there must be a potential state between alive and dead. As such, we cannot measure his state on Thursday because that measurement might result in an inconsistency. His state on Thursday must either be "dead" or "dead or alive". "Alive" is not a valid option.
I think of this more of Sunday night judge picks a random day between Monday and Friday and just doesn’t tell the prisoner. As of Monday morning the cat has no idea.
The judge cannot pick ANY day between Monday and Friday because he cannot pick Friday. If Friday morning comes around the cat will not be surprised to be executed.
keystone yes he can. He picks a day on Sunday, each day has a 1/5 chance of being chosen. And the prisoner just isn’t told when even though the day is already selected. Even if we simplify it and look at Friday only, if he’s sure he’s going to be executed Friday then he believes that he’s not going to be hung at all thus being a surprise. If he’s unsure he’s going to be hung on Friday then he’s still surprised. Either way he’s surprised.
"If he's sure he's going to be executed... then he believes he's not going to be hung". Do you see any contradiction here?
Cheesus miced
He blinks so aggressively
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