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#1 bonanova

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Posted 23 February 2008 - 10:56 AM

So, what's he smiling for, all smug like? Jamie wondered.
He said he's goin' to mess with our minds tonight, Davey
replied, but I'll tell you, he's not gonna fool me. I'm pretty
much onto his tricks by now.

The subject tonight is logic,
Alex began, and as usual I'll
keep it nice and simple so you all can understand. That
caught Ian's attention, and now the three of them were
ready to take another challenge. Morty's was never so
lively as when the boys squared off in a battle of wits.

Tell me something that's true, Alex began, true today, true
tomorrow, true here, true down the street, true without
regard for time and place in any way. Davey scratched
his beard, as he often did, to give the appearance of deep
thought. But Jamie chimed in first. Well, take that stool
yer sittin' on, he said, it's got four legs. Four today, four
tomorrow, four where ever you take it. The number of
legs on that stool is four.
There's a true statement for you.

Excellent! cried Alex. Now let's talk a little bit about contradictions.
How would you say just the opposite of that? What statement
could you make that absolutely can't be true if that statement
is true? Can ya answer me that? Ian was all over this one.
C'mon, give us a challenge will ya? It's simple! A statement
that can't be true is just the opposite of what Jamie said.
The number of legs on that stool is NOT four.

You lads bring tears to me eyes, ye really do, continued Alex,
you're exactly right. There's no way those two statements
can ever both be true - no place, and no time. One has got to
be true, and the other has got to be false.

By this time Davey was wondering why he had bothered to
scratch his beard. Ya know, so far I'd have to say I'm not really
overwhelmed with the depth of this discussion. Have ya got
something for us, or not? And he looked wistfully across the
room at the dartboard.

I was just getting to it, Alex said. It's this: I'll put up a pound
against a month of drinks and tell you that I have a statement
that's true, just like Jamey's, any time, any place. But it's different.
Cuz when you make the contradictory statement like Ian-boy here
did, well, that statement is just as true as the first!

Now here's the challenge. You can take my bet, and end up buying
my cold ones for a month, or ... you can come up with a true statement
of your own, whose contradiction is every bit as true, and I'll do the
buyin'.

The beard scratching resumed - now in earnest. And Davey suggested
quietly that a sporting man just might drop a tiny clue. Alex smiled,
compassionately, and said, OK then, the statement goes like this. The
number .......... is nine.
And the contradiction goes like this: The number
.......... is NOT nine
. And the part where the dots are is exactly the same
in both statements. For you Yankee fans, it's not about spring training.... ;)

Davey slumped down into his chair, motionless. Ian quietly moved
back to the bar. Jamie closed his eyes for a moment and thought.
Yes, he said, I think I have it!

What was Jamie's idea?
Would you have taken the bet?
----------

"Use the spoiler, Luke."

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 jesusfreak1024

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Posted 23 February 2008 - 03:11 PM

Spoiler for possibly...

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#3 Aatif

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Posted 23 February 2008 - 04:10 PM

Spoiler for Number slumber

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#4 Duh Puck

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Posted 23 February 2008 - 04:11 PM

Almost any statement of truth has qualifications. You removed qualifications of time and place, but not ...

Spoiler for one solution


Incidentally, I wouldn't agree that the statement "the stool has four legs" is true anytime, if in a different time the stool doesn't exist.
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#5 Duh Puck

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Posted 23 February 2008 - 04:14 PM

Spoiler for Number slumber

Spoiler for i don't think so

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#6 bonanova

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Posted 23 February 2008 - 04:39 PM

... I wouldn't agree that the statement "the stool has four legs" is true anytime, if in a different time the stool doesn't exist.

Hi Duh Puck,

I mentioned your objection to Alex this morning.

Always the mind messer [well, mess isn't precisely the appropriate word] he said,
A stool that doesn't exist isn't built like an airplane just cuz it doesn't exist.

I think he was trying to suggest that a nonexistent stool could have four
nonexistent legs. And then he walked away, kind of muttering to himself.

Hope that helps.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#7 storm

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Posted 24 February 2008 - 02:10 AM

Spoiler for Number slumber


I think Alex indicated "If one is absolutely true then the other is also absolutely true"....so your solutions do not have a strong ground

Edited by storm, 24 February 2008 - 02:13 AM.

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#8 bonanova

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Posted 24 February 2008 - 06:52 AM

Spoiler for Number slumber

Kudos for traveling out of the box. ;)

But the suggested statements violate the condition of being
as true
as "The number of legs on that stool is four" is. -_-
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#9 Aatif

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Posted 24 February 2008 - 03:52 PM

Kudos for traveling out of the box. ;)

But the suggested statements violate the condition of being
as true
as "The number of legs on that stool is four" is. -_-

Hmmm .. perhaps true for the statements 2 and their corollaries, ie. indeterminate = determinate .. but what about 6 = 9 .. its the point of view statement, i mean 6 is 9 if seen upside down, just as much as the stool has four legs :) ..
Is your straight and contradictory statement independent of the point of view? Could you see my point of view in tht statement? :blink:
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#10 bonanova

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Posted 24 February 2008 - 06:53 PM

Is your straight and contradictory statement independent of the point of view? :blink:

Yes.
They are ordinary statements with which anyone would agree.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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