From: rhinoceros (rhinoceros@freemail.gr)
Date: Fri Mar 26 2004 - 06:07:08 MST
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 sentence 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? :P
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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