Re: Me and David C. Ullrich
- From: David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx>
- Date: Mon, 10 Oct 2005 06:52:23 -0500
On 9 Oct 2005 13:05:09 -0700, john_ramsden@xxxxxxxxxxxxxx wrote:
>
>mareg@xxxxxxxxxxxxxxxxxxxxxxxx wrote:
>>
>> In article <1128873353.719646.144280@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
>> john_ramsden@xxxxxxxxxxxxxx writes:
>> >
>> >Christian Bau wrote:
>> >>
>> >> In article <1128860336.222209.307130@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
>> >> john_ramsden@xxxxxxxxxxxxxx wrote:
>> >>
>> >> > quasi wrote:
>> >> > >
>> >> > > If information is "given", how is it given? Someone tells you,
>> >> > > right? I can't think of any other way to interpret "given".
>> >> >
>> >> > Exactly, and the natural interpretation is that this condition
>> >> > is being given by the person stating the question. Even if not,
>> >> > one must assume that the information is equally accurate. So,
>> >> > although there may be a hairsplitting logical distinction in
>> >> > how the question is framed, the salient facts are the same.
>> >>
>> >> Lets say two coins have been thrown, I can't see the result, but you
>> >> can. I want to find out a bit more. I ask a question and you have to
>> >> answer thruthfully.
>> >>
>> >> Case 1: I ask "Is at least one coin heads?", and the only possible
>> >> statements that you can make are "None of the coins is heads" and "at
>> >> least one of the coins is heads". This is the same as "... given that
>> >> ..."
>> >>
>> >> Case 2: I tell you: "Please give me some true statement about the
>> >> coins". Now you have an infinite amount of choices. This is the
>> >> same as "... somebody told me that..."
>> >
>> >But once I've chosen to tell you truthfully that there's at least
>> >one head, your state of knowledge is the same as it is after my
>> >reply to case 1 - Different route, same destination which, in
>> >the context of the problem, you have already reached.
>>
>> I don't agree that your state of knowledge is the same after getting the
>> same replies in Cases 1 and 2. In Case 1 there is no ambiguity at all.
>> If the I reply "at least one coin is heads" then the proabbility of two
>> heads is 1/3.
>>
>> But in Case 2, you have no idea what policy I adopted in choosing
>> which statement to make.
>>
>> [...]
>
>I understand what you're saying, and it's obviously right
>if one takes policies and hidden motives into account.
>But, like Christian B with his incentives and lies, in
>just mentioning the word "policy" you're extending the
>problem beyond its original statement, reading between
>lines to introduce aspects which (by convention, we can
>assume) aren't there unless explicitly mentioned.
And in particular, once we introduce such factors
then we cannot possibly say anything about what the
answer to the question is. _If_ we're considering
questions of who said what and why they would say
that, but we're given no information about all that,
then saying that it follows that the probability is
anything specific is just stupid.
>If I asked someone "what is 2 + 2"? they would naturally
>reply "4". If I then said "Wrong, nitwit, my 'policy' is
>to only ask questions whose answer is to be calculated
>in base 3; so the answer is 1", they would be justified
>in thinking _I_ was the nitwit for not including this
>proviso in the statement of the question!
>
>In fact thinking about it some more, it seems to me
>that "X given Y" can quite reasonably be interpreted
>as "X assuming Y", even if in principle there is this
>meta-statement aspect to the first form.
************************
David C. Ullrich
.
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