On Sat, Sep 14, 2013 at 11:53 AM, Telmo Menezes <te...@telmomenezes.com> wrote:
> 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.

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.
>>> >
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