Fuzzy Logic

(From Greek mithology)😲nce opon a time, two men came to the royal judge and wanted to sell him a machine that will answer True or False to any sentence she hears.
The judge was just about to give all his fortune to the two men, when his adviser ran shouting into the room and said that such machine could not exist!!!

The Question is: Why???
Clue: What sentence you can say to the machine and it will not have an answer?

This sentence is false.

The machine may only answer with "yes" and "no".

In that case, any sentence that cannot be logically answered with a "yes" or a "no" will stump the machine.

"What is my shoe size?"
"How old is my dog?"
"How does the caramel get into a Caramilk bar?"
etc.

-Ray.

That's right, the machine can not answer the sentence: "This sentence is false" or "I always lie" etc.
About the sentences: "What is my shoe size?", The machine is not supposed to ANSWER your QUESTIONS, but say if they are true or false, therefor you can't ask her questions.

The realy fun part begins when you try to think about HOW true is the sentence.
Let's take the sentence: "This sentence is false". mark it's
validity as x. we'll set x between 0 and 1, when 0 is completely false and 1 is completely true. then if x is it's validity, 1-x will be it's falseness. if you analize the sentence, you will get that by it's context
x=1-x. the only solution for this equasion is 0.5.

therefor, the sentence is half true.

p.s. sorry about the rutten spelling, I was in a hurry.

I think you left out a bit of information. Of course such a machine can exist!

The only thing the two men claim is that the machine answers 'true' or 'false' to every sentence. They don't claim that the answer has to be correct conform the sentence!