Wednesday, December 17, 2008

Lying beliefs

Liar paradoxes are easy and fun to generate. Here is one that is fun: My latest belief, let us suppose, is that George's latest belief is false. And George's latest belief is that my latest belief is true. Who is right?

[Edited: Fixed a typo.]


jawats said...

More information is needed, and I think it needs to be temporal.

Brandon said...

I once had a class that kept pestering me to give them a true/false test instead of a short answer test. So I gave them a true/false quiz of twenty questions or so that consisted almost entirely of complicated liar paradoxes. (I didn't count it for a grade; I'm not quite that evil.) I don't think I have that quiz anymore, which is too bad; it was a beautiful work of art.

MG said...

If you're right, you're wrong. You and George must be married.

MG said...

Not to each other, of course. Man, that was a poorly executed joke.

Anyway, a neat way to do the liar paradox is to draw a box and write inside the box, "the sentence inside the box is not true." That's how my logic professor did it.

jawats said...

Wouldn't it be better to draw a box and put a sentence that says, "This sentence is not inside a box?"

Alexander R Pruss said...

"This sentence is not in a box" isn't actually paradoxical. It's just false.

Quirinius_Quine said...

"Liar paradoxes are easy and fun to generate."

Very true. :-)

You can even generate liar paradoxes that aren't statements. For example:

"Is the answer to this question 'no'?"

If the answer to the question is "no", then the answer should also be "yes", and if the answer to the question is "yes", then the answer should also be "no". If we assume "bivalence" for yes-or-no questions, then its answer must be either "yes" or "no", and hence both "yes" and "no".