On Saturday, September 14, 2013 5:53:01 AM UTC-4, telmo_menezes wrote: > > On Fri, Sep 13, 2013 at 12:06 PM, Craig Weinberg > <[email protected]<javascript:>> > 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 <[email protected]> > >> 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! :)
Ah cool! Thanks for posting the problem also, it helped me resurrect some lost mathematical-logical ability. > (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. Nice. > 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? > Falsifiability is nice - especially in public-facing physics, but since falsification itself is a sensory experience, we should not insist on the same kind of falsifiability for private physics that we have in public physics. > If so, can you conceive of some experiment to test what you're > proposing? > There may not be a test, so much as accumulating a body of understanding by correlating uses of information and qualities of sensation. It's more at the hypothesis stage than the testing stage. > > 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? > Still there's the hard problem. Why would neural firing patterns have a smell? Thanks, Craig > > 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 [email protected]. > >> > To post to this group, send email to [email protected]. > >> > 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 [email protected] <javascript:>. > > To post to this group, send email to > > [email protected]<javascript:>. > > > 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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