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Topic: A fuzzy story (Read 784 times) |
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rhinoceros
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My point is ...
  
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A fuzzy story
« on: 2004-03-26 08:07:07 » |
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In a chat in #virus last night, after going through many topics such as cattle thievery, Apostle Paul and multivalued logic, the classic paradox of Epimenides the Cretan came up ("All Cretans lie" -- which eventually led to Goedel's theorem). Lucifer mentioned that fuzzy logic could resolve these paradoxes of self-referential statements by assigning a 0.5 truth value to them. For example
"This sentence is false"
Let's say p is the truth value of this statement by definition. Then 1-p is also the truth value of this statement by its content. This is impossible if a truth value must be either 0 (false) or 1 (true), but if p can take any value between 0 and 1 then we have:
p = 1 - p
2p = 1
p = 0.5
Which means that the statement is half true.
Hmm... I still don't get it completely. By reusing the content of the statement, could I prove that the truth value of "false" is 0.5?
Oh, I think I get it now! What I just claimed is half true, isn't it? 
Further efforts to get a better grip on fuzzy logic (courtesy google) led me here:
A Partly True Story
by Ian Stewart
http://www.tzingaro.com/artelectric/partlyTrue.html
Allow me to introduce myself: Epimenides, professional liar. Well, that's not quite true. My name is really Herman Fenderbender, and I work for a car insurance company. But my friends at the Paradox Club call me Epimenides, and when I'm with them, I always lie.
Last Thursday it was raining, so I got to the club a bit late. Socrates and Plato were leaning against the bar, and next to them was a chubby little fellow.
"This is our newest member, Lukasiewicz," Plato chimed.
Horrified to meet you," I said in disgust. My name's Zeno.
"He means he's delighted to meet you, and his name is Epimenides," Socrates explained. "Epimenides always tells lies."
"That's not true," I said. I opened my wallet and took out my business card. "This isn't my card," I commented and handed it over. Lukasiewicz read one side of the card: The sentence on the other side of this card is true. He turned the card over and saw: The sentence on the other side of this card is false.
"Socrates is right, however, I always tell lies," I boasted.
Lukasiewicz shook my hand warmly. "It's one third false that I'm pleased to meet you, and both sides of your card are half true."
"Pardon?" I said.
"Lukasiewicz is interested in fuzzy logic," Plato explained.
<snip>
The next one tells the rest about the above "Partly True Story"
About Fuzzy Logic
http://www.tzingaro.com/artelectric/aboutFuzzyLogic.html
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Blunderov
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"We think in generalities, we live in details"
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RE: virus: A fuzzy story
« Reply #1 on: 2004-03-26 10:59:16 » |
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From: owner-virus@lucifer.com [mailto:owner-virus@lucifer.com] On Behalf
Of rhinoceros
<snip>
Lukasiewicz read one side of the card: The sentence on the other side
of this card is true. He turned the card over and saw: The sentence on
the other side of this card is false.
</snip>
[Blunderov]
In a galaxy far, far away (London in the early 70's actually) I happened
to be searched in a vice squad raid on the Kensington market. (Just down
the road from the Albert Hall, it was a popular hangout).
The newbie vice squad cop who was turning out my pockets insisted on me
describing every item to him, no matter how innocent.
'Wot's this then?' 'It's a copy of 'Adventures in the Skin Trade' by a
very famous author named Dylan Thomas.'
'Wot's this then?' 'It's a packet of Rizla cigarette papers.' 'Don't
tell me, you roll your own, right?' 'Right!'
And then the magic moment; he happened upon a scrap of paper on which I
had written Zeno's paradox exactly as described, one statement on each
side.
'Wot's this then?' (What glee) 'It's a paradox!' I chirped.
I will never forget the sight of him turning and re-turning the piece of
paper and glaring at what he read with hostile suspicion!
Oh, and I wasn't busted - they found nothing else of interest.
Best Regards
---
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rhinoceros
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My point is ...
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Re:A fuzzy story
« Reply #2 on: 2004-04-01 11:14:58 » |
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[Blunderov]
In a galaxy far, far away (London in the early 70's actually) I happened to be searched in a vice squad raid on the Kensington market. (Just down the road from the Albert Hall, it was a popular hangout).
The newbie vice squad cop who was turning out my pockets insisted on me describing every item to him, no matter how innocent.
<snip>
[rhinoceros]
My own similar experience from London dates back to the late 70s, at 3 AM in the morning in the empty streets, dead drunk and walking back from Piccadilly Circus to a place called Camberwell.
I stood at a corner to take care of some quick business and here he was, a cop with a flashlight. I had an electronic part with me which I had purchased from a Heathkit dealer at noon, and he looked alarmed when I told him that it was "just an 11-position rotary switch". After trying hard to read my Greek ID card (I had left my passport at home) he gave up. He asked me my name, he scribbled something on his notebook, and he walked away.
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Blunderov
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"We think in generalities, we live in details"
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RE: virus: Re:A fuzzy story
« Reply #3 on: 2004-04-01 13:52:21 » |
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rhinoceros
Sent: 01 April 2004 06:15 PM
[rhinoceros]
My own similar experience from London dates back to the late 70s, at 3
AM in the morning in the empty streets, dead drunk and walking back from
Piccadilly Circus to a place called Camberwell.
I stood at a corner to take care of some quick business and here he was,
a cop with a flashlight. I had an electronic part with me which I had
purchased from a Heathkit dealer at noon, and he looked alarmed when I
told him that it was "just an 11-position rotary switch". After trying
hard to read my Greek ID card (I had left my passport at home) he gave
up. He asked me my name, he scribbled something on his notebook, and he
walked away.
[Blunderov]<hoots and chortles> Camberwell? Home of the dreaded
'Camberwell Carrot' as mentioned in 'Withnail and I'?
Best regards
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