On 08/05/2012 7:05 PM, Orchid Win7 v1 wrote:
> On 08/05/2012 05:04 PM, Jim Henderson wrote:
>
>> The error is when you've reached the end of the trail and keep going.
>
> If you set out to fail, and succeed, what have you done?

Become a gummy parrot. <Boom boom>

-- 
Regards
     Stephen

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On Tue, 08 May 2012 21:48:43 +0100, Orchid Win7 v1 wrote:

>>>>> If you set out to fail, and succeed, what have you done?
>>>>
>>>> You've taken a ride down the fail trail? ;)
>>>
>>> Does the set of all sets that do not contain their own complement
>>> contain itself?
>>
>> You do realise that I'm razzing you about your spelling again, right?
>> ;)
> 
> Yeah, I had noticed. :-P

Oh, good - sometimes stuff like that goes right past you - but you /are/ 
getting better at detecting it. ;)

> I was hoping to blind you with library science...

I'm not that easy to blind. ;)

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> 1) Does the set of all sets that do not contain their own complement
> contain itself?
>
> There is no such set, and thus the statement is vacuously true.

I'm not sure how you came to the conclusion that no such set exists.

Since /by definition/ a set can never contain its own complement (that's 
what I complement /is/), the set above contains all possible sets - 
including itself.

> 2) Now tell me, is the set of all sets that list themselves listed in
> itself?
>
> There are no sets which contain themselves, thus the set of all these
> sets it in fact the empty set. The empty set does not contain itself, so
> the answer is "no".

Again, I'm not sure how you come to the conclusion that a set cannot 
contain itself. Even if that were true, it would imply that the set in 
question /does not exist/, rather than that it is empty.

The answer of course is that the definition of the set is inconsistent. 
If the set does not contain itself, that implies that it does contain 
itself, and vice versa. So the answer is neither "yes" nor "no". The 
answer is "undefined".

>> Interestingly, in Portal 2 GLaDDOS poses nearly the exact same question
>> to Wheatly, who also responds with "false".
>
> Maybe an in-joke by some math-savvy writers? Assuming my reasoning is
> correct that is.

The actual statement was the liar paradox, to which Wheatly, being 
scientifically engineered to be the greatest moron ever, replies

"Er... false. Yes, definitely false. Although I think I may have heard 
this one before, to be fair."

The exasperated GLaDDOS retorts "There IS no answer, you idiot! It's a 
paradox!!"

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On 5/9/2012 1:21 AM, Invisible wrote:
>> 1) Does the set of all sets that do not contain their own complement
>> contain itself?
>>
>> There is no such set, and thus the statement is vacuously true.
>
> I'm not sure how you came to the conclusion that no such set exists.
>
> Since /by definition/ a set can never contain its own complement (that's
> what I complement /is/), the set above contains all possible sets -
> including itself.

Right, and such a "set of all sets" does not exist within standard set 
theory.  It appears, however, that you are unfamiliar with standard 
(ZFC) set theory, the your misconception is understandable.

I am, by the way, glossing over your use of "compliment" which strictly 
speaking isn't well defined the way you've used it.

>> 2) Now tell me, is the set of all sets that list themselves listed in
>> itself?
>>
>> There are no sets which contain themselves, thus the set of all these
>> sets it in fact the empty set. The empty set does not contain itself, so
>> the answer is "no".
 >
> Again, I'm not sure how you come to the conclusion that a set cannot
> contain itself.

Oh come on, it's one of the axioms of ZFC set theory! 
http://en.wikipedia.org/wiki/Axiom_of_regularity

> Even if that were true, it would imply that the set in
> question /does not exist/, rather than that it is empty.

Which is exactly what I said, you'll notice.  I'll quote to save you the 
trouble of reading: "thus the set of all these sets it in fact the empty 
set".

> The answer of course is that the definition of the set is inconsistent.
> If the set does not contain itself, that implies that it does contain
> itself, and vice versa. So the answer is neither "yes" nor "no". The
> answer is "undefined".

That was the answer at around 1901 before modern set theory existed, and 
it was sufficient to destroy the notion of "set" which led to it.  You 
appear to be using a notion of "set theory" like this which hasn't 
really been popular for over a century.  In ZFC set theory there is no 
paradox because you can't create the sort of sets needed for the paradox 
to happen.

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On 5/9/2012 1:21 AM, Invisible wrote:
> "Er... false. Yes, definitely false. Although I think I may have heard
> this one before, to be fair."
>
> The exasperated GLaDDOS retorts "There IS no answer, you idiot! It's a
> paradox!!"

Ohh right, I can't believe I forgot the content of that part of the game 
so quickly after playing it (which was just a few months ago).  Really 
good dialogue in that game all around though!

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Ok, also, if you're interested in learning more about this, but are 
philosophically attached to something like the "set of all sets" you 
might find it interesting to read up on Neumann–Bernays–Gödel set theory 
(http://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Bernays%E2%80%93G%C3%B6del_set_theory).

  It doesn't really 'fix' things like you might be hoping it would, but 
it's an interesting approach to the matter.

Cheers!

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>> "Er... false. Yes, definitely false. Although I think I may have heard
>> this one before, to be fair."
>>
>> The exasperated GLaDDOS retorts "There IS no answer, you idiot! It's a
>> paradox!!"
>
> Ohh right, I can't believe I forgot the content of that part of the game
> so quickly after playing it (which was just a few months ago). Really
> good dialogue in that game all around though!

I found Portal 2... not as enjoyable as I'd hoped. And I gather Wheatley 
was supposed to be funny, but I just found him irritating. But hey, each 
to their own.

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On 06/05/2012 08:01 PM, Orchid Win7 v1 wrote:
> Playing the violin: Now it sounds... still damned awful, actually. x_x

Well, a small amount of progress has been made tonight. I figured out 
how to make it sound less thin and scratchy. I can almost sort-of play 
in tune. And... yes, I used the Internet. So now I've corrected a few 
things.

Still doesn't sound fantastic, I'll be honest. :-P

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On 5/9/2012 15:11, Kevin Wampler wrote:
> On 5/9/2012 1:21 AM, Invisible wrote:
>> "Er... false. Yes, definitely false. Although I think I may have heard
>> this one before, to be fair."
>>
>> The exasperated GLaDDOS retorts "There IS no answer, you idiot! It's a
>> paradox!!"
>
> Ohh right, I can't believe I forgot the content of that part of the game so
> quickly after playing it (which was just a few months ago). Really good
> dialogue in that game all around though!

There's new user-generated test chambers available now, at least on Steam.

-- 
Darren New, San Diego CA, USA (PST)
   "Oh no! We're out of code juice!"
   "Don't panic. There's beans and filters
    in the cabinet."

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On Fri, 11 May 2012 09:47:38 -0700, Darren New wrote:

> On 5/9/2012 15:11, Kevin Wampler wrote:
>> On 5/9/2012 1:21 AM, Invisible wrote:
>>> "Er... false. Yes, definitely false. Although I think I may have heard
>>> this one before, to be fair."
>>>
>>> The exasperated GLaDDOS retorts "There IS no answer, you idiot! It's a
>>> paradox!!"
>>
>> Ohh right, I can't believe I forgot the content of that part of the
>> game so quickly after playing it (which was just a few months ago).
>> Really good dialogue in that game all around though!
> 
> There's new user-generated test chambers available now, at least on
> Steam.

Wish there was a way to play them on the console versions (PS3 in 
particular).

Jim

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