On Sat, Sep 14, 2013 at 11:53 AM, Telmo Menezes <[email protected]> wrote: > On Fri, Sep 13, 2013 at 12:06 PM, Craig Weinberg <[email protected]> > 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! :) (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.
I meant: automated so that the attacker button is pressed on turn 5. > 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 [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]. >> 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. 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