Question

Not so tough...
Every statement you can make is either true or false...
For example:
"It is raining outside." is either true or false.

But what about this one:
"This statement is false."

Is it true or false?

Answer 1

its either true or false, perhaps the statement if true

Answer 2

By definition, that is not a statement.

Answer 3

Neither.

It can't be true because it says it is false, which would make it false.
But it can't be false because it says it is false, which would make it true.

So it is... FUE! :D

Answer 4

"This statement is false." is not a statement? please explain... what's the definition of being a statement?

Answer 5

This is related to a famous result
http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems#Relation_to_the_liar_paradox

Answer 6

fail link

Answer 7

Take the following "statement":

Justin Bieber is the sexiest man alive.

Is that a statement?

Answer 8

that's definitely false!

Answer 9

To his fans, that statement is true. However, to the rest of the world, I better run away before I get killed. So it is not a statement because it is subject to interpretation.

Answer 10

True for some people and false to others

Answer 11

@phi, right, so the statement that "Every statement is either true or false." is not correct then?

Answer 12

It is correct because for it to be a "statement" it has to be well-posed to begin with, so to speak.

Answer 13

Mathematicians define statements that have a truth value to be propositions. Your claim that every statement has is either true or false is not accurate.

Answer 14

*statement is*

Answer 15

Why is it not accurate? A mathematical statement, say "2+2=4" can only be either true or false. There is no such thing as "2+2 maybe 4!"

Answer 16

@pre-algebra , yes...

Answer 17

Take for example the statement "x+2=9". This statement can be true or false depending on the value of x. Thus it's NOT a proposition.

Answer 18

And it is not a statement, so that excludes it from our evaluation of his original question.

Answer 19

@Mr.Math , yes. that's called an open sentence.

Answer 20

neither true nor false.

Answer 21

Well then we're just differing in what a statement is, and this is not an issue. For me, a statement doesn't have to have a truth value.

Answer 22

I would say the statement is undecidable. You can not assert that it is true nor can you assert that it is false.

Answer 23

Perhaps you guys are taught differently, but here, by definition, a statement is a sentence that is either true or false. Everything else has another name which I cannot recall right now.

Answer 24

A sentence maybe?

Answer 25

Perhaps a conjecture.

Answer 26

It's not an issue, it happens a lot that mathematicians (or philosophers in this case) have different definitions for different terminology.

Answer 27

http://en.wikipedia.org/wiki/Proposition