On Thu, Sep 12, 2013 at 5:47 PM, Craig Weinberg <whatsons...@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.
> 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. 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.
> 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.
> 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...
> 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
> 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:
>> 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?
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