On Fri, Sep 13, 2013 at 12:06 PM, Craig Weinberg <whatsons...@gmail.com> wrote: > > > On Friday, September 13, 2013 5:31:40 AM UTC-4, telmo_menezes wrote: >> >> On Thu, Sep 12, 2013 at 5:47 PM, Craig Weinberg <whats...@gmail.com> >> wrote: >> > Which reasoning is clearly false? >> > >> > Here's what I'm thinking: >> > >> > 1) The conclusion "I won't be surprised to be hanged Friday if I am not >> > hanged by Thursday" creates another proposition to be surprised about. >> > By >> > leaving the condition of 'surprise' open ended, it could include being >> > surprised that the judge lied, or any number of other soft contingencies >> > that could render an 'unexpected' outcome. >> >> Ok but that's not the setup. The judge did not lie and there are no >> soft contingencies. The surprise is purely from not having been sure >> the day of the execution was the one when somebody knocked at the door >> at noon. Even if you allow for some soft contingencies, I believe the >> paradox still holds. > > > I don't understand why it's a paradox and not just contradiction. If I say > 'you're going to die this week and it's going to be a surprise when', that > is already a contradiction.
Ok, after a good amount of thought, I have come to agree with this. The judge lied. You convinced me! :) (with due credit to Alberto and Brent, who also helped convince me). A more honest statement would be "you're going to die this week and it will probably be a surprise when", or, "you'll probably die this week and it will be a surprise if you do". My thought process involves reducing the thing to a game. There are 5 turns in the game, and the attacker has to choose one of those turns to press a button. The defender also has a button, and its goal is to predict the action of the attacker. If both press the button. the defender wins. If only the attacker pressers the button, the attacker wins. Otherwise the game continues. The system is automated so that the attacker button is automatically pressed. Now the attacker (judge) is making the claim that he can always win this game. He cannot, there is no conceivable algorithm that guarantees this. Playing multiple instances of the game, I would guess the optimal strategy for the attacker is to chose a random turn, including the last. This will offer 20% of the games to the defender, but there's nothing better one can do. I read your post and now I think I understand you positions better. I am not convinced, but I will grant you that they are not easily attackable. On the other hand, this could be because they are equivalent to Carl Sagan's "invisible dragon in the garage" or, as Popper would put it, unfalsifiable. Do you care about falsifiability? If so, can you conceive of some experiment to test what you're proposing? The symbol grounding problem haunted me before I had a name for it. It's a very intuitive problem indeed. I tend to believe that the answer will actually look something like an Escher painting. Assuming that neuroscience is enough, one can imagine the coevolution of neural firing patterns with environmental conditions. This can lead to neural firing patterns that correlate with higher abstractions -- the symbols. Why not? Cheers, Telmo. > Adding the conceit of precise times doesn't > alter the fundamental contradiction that you can be surprised when someone's > true prediction comes true. The week already includes every hour of every > day of the week, so it can't be a surprise on that level, but if the judge > doesn't specify a single time then it also has to be a surprise on another > level. You just have to pick on which level you are talking about, or decide > that one level automatically takes precedence over the other. > >> >> > The condition of expectation >> > isn't an objective phenomenon, it is a subjective inference. >> > Objectively, >> > there is no surprise as objects don't anticipate anything. >> >> I would say that surprise in this context can be defined formally and >> objectively. The moment someone knocks at the door, the prisoner must >> have assigned a probability < 1 that he would be executed that day. >> This is clearly not the case for Friday, where p=1. > > > Even on Friday it can still be a surprise, a meta-surprise, when he finds > out the judge lied, or knocks on the door an hour later. If we say that > can't happen though, p=1 is still limited to Friday only if it's Thursday. > It doesn't accumulate. On Wednesday it's still 50-50 for Thursday and Friday > each. On Tuesday it's .33 for Wednesday-Friday each, so on Wednesday, when > the knock comes, he is 66% surprised - unless there's something I'm missing. > >> >> If we assume a >> rational prisoner, we can replace it with an object. Some computer >> running an algorithm. Here we can define the computer belief as some >> output it produces somehow. We can even make this problem fully >> abstract and get rid of the colourful story with hangings and judges. > > > That's a problem if you fall for the Pathetic Fallacy and assume that > computer 'beliefs' are literal rather than figures of speech. I posted more > about this here: > http://multisenserealism.com/2013/09/12/why-computers-cant-lie-and-dont-know-your-name/ >> >> >> > 2) If we want to close in tightly on the quantitative logic of whether >> > deducibility can be deduced - given five coin flips and a certainty that >> > one >> > will be heads, each successive tails coin flip increases the odds that >> > one >> > the remaining flips will be heads. The fifth coin will either be 100% >> > likely >> > to be heads, or will prove that the certainty assumed was 100% wrong. >> >> Coin flips are independent events. Knock/no-knock events are not >> independent. Each day that passes without a knock increases the >> probability of a knock the next day. > > > Ok, but his surprise is not independent either. In a Wednesday knock, that > means he is 33% unsurprised. From the outset he can only be 20% unsurprised > at the minimum just by virtue of his knowing it has to be 1 out of 5 > days...including Friday, because Friday is only p=1 on Thursday after noon. > On on level, the knocks are independent events also - they either happen or > they don't - so probability breaks down at any moment of incidence. The > probability is a subjective expectation, it cannot be relied on as an > object. Probability is an abstraction layer that is a posteriori to events. > Spacetime is a museum of causally closed tokens which can represent and > embody subjective experience, not the other way around. > >> >> > I think the paradox hinges on 1) the false inference of objectivity in >> > the >> > use of the word surprise >> >> Ok, let's replace the judge and the prisoner. A computer sits in a >> room for 5 days. One of those days, at noon, an input will be fed to >> the computer. If the computer fires an output at the exact same time >> that the input is received, it wins. The computer is only allowed to >> fire its response once. It's now a game between the programmer of the >> computer and the programmer of the system that emits the signal to the >> computer. How would you program these systems? It's clear that, if you >> are programming the computer, you will mostly certainly add a rule to >> fire the response if it's Friday. And then... > > > I don't see the problem. All the computer can to is computer a 20% > probability on Monday of all five days, and pseudorandomly pick one. Every > day that both programmer and computer do not pull the trigger, the odds go > up when it guesses again. It's the part about 'the judge/programmer was > right' that is arbitrary and omniscient. How can the programmer tell the > computer is not going to pick Friday until Thursday night? > >> >> >> > and 2) the false assertion of omniscience by the >> > judge. It's like an Escher drawing. In real life, surprise cannot be >> > predicted with certainty and the quality of unexpectedness it is not an >> > objective thing, just as expectation is not an objective thing. >> > >> > Or not? >> >> I am open to the possibility that this is a language trick, but not >> yet convinced. > > > See what you think of that post. These kinds of paradoxes don't really come > naturally to me, but I do feel very clear about the underlying nature of > symbol grounding and how it related generally. Think of an Escher drawing - > its the same thing - the paradox is only a paradox if you read a symbol as a > literal reality. No symbol has any objective reality outside of some > experience which interprets that way. > > Craig > >> >> >> Telmo. >> >> > Craig >> > >> > >> > On Thursday, September 12, 2013 5:33:24 AM UTC-4, telmo_menezes wrote: >> >> >> >> Time for some philosophy then :) >> >> >> >> Here's a paradox that's making me lose sleep: >> >> http://en.wikipedia.org/wiki/Unexpected_hanging_paradox >> >> >> >> Probably many of you already know about it. >> >> >> >> What mostly bothers me is the epistemological crisis that this >> >> introduces. I cannot find a problem with the reasoning, but it's >> >> clearly false. So I know that I don't know why this reasoning is >> >> false. Now, how can I know if there are other types of reasoning that >> >> I don't even know that I don't know that they are correct? >> >> >> >> Cheers, >> >> Telmo. >> > >> > -- >> > You received this message because you are subscribed to the Google >> > Groups >> > "Everything List" group. >> > To unsubscribe from this group and stop receiving emails from it, send >> > an >> > email to everything-li...@googlegroups.com. >> > To post to this group, send email to everyth...@googlegroups.com. >> > Visit this group at http://groups.google.com/group/everything-list. >> > For more options, visit https://groups.google.com/groups/opt_out. > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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