This statement is false.

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Is the statement "This statement is false." true, or false?

I voted other. because it depends on the users perception of what it is to them

I'll say it's true.

If there was a second statement under it that said the first statement was false, then I would say it's false.

Interesting question.

The statement cannot be assigned a truth value. It is a fallacy to assume that any statement that can be made can be assigned a value of true or false.

The paradox lies in the fact that the statement is self-referential. (I thought about this first and then looked it up... the "self-referential part" I got from wikipedia).

Wouldn't saying that the statement cannot be assigned a truth value make it false (the statement asserts that it has a negative truth value, the reality is that it has no truth value, making its net truth value negative)?

Not sure, but that's not the way I'm interpreting it. The way I'm interpreting is simply there are two case:

1) The statement is true - well, this can't be possible, because the statement itself claims to be false.

2) The statement is false - if the statement is false, then that would mean that the statement "This statement is false" is not true - which would of course imply that the statement is not false (let's assume that not false means true for simplicity sake although it really doesn't change the problem)

So, whether you assign it true or false, you get a contradiction.

Unless you treat the choice as non-binary; in effect, as allowing different kinds of 'false'.

Yes, I suppose, but in that case the statement still wouldn't be false in the traditional sense, it would just be false under this new vocabulary we have created.

Let's say we had a statement that was really an opinion - something like "Obama is a good president." We cannot answer this with true or false but intuitively we know that this a grey area. It is not a paradox, it is just a subjective question.

The statement posted is simply a paradox and the only way to circumvent the paradox is to create a new language.

It's the same paradox as a person who says "I always lie." It is a self-contradicting statement.

As another example, Let's say a teacher tells everyone in the room to raise their hand if they are not raising their hand. The students are placed in a double bind. They have no way to honestly proceed other than to pretend they didn't hear the question.

I see your point but if we are talking about the way true and false is generally defined, I don't think we can get around the fact that this question cannot be answered truthfully.

So its true, about the fact that it is false.
Which would mean that it is indeed false.

So then how could it be "true"?

Self referential statements can be self-contradictory, and are thus undefined / nonsensical in terms of logic.

In truth the statement This statement is false is a meta-sentence. The self-referential paradox happens due to both the metalanguage and object language being the same in context and content.

Magritte used La trahison des images to illustrate self-referential recursion. He did say once that "perception always intercedes between reality and ourselves." Korzybski's map–territory relation describes the relationship between an object and a representation of that object, as in the relation between a geographical territory and a map of it. So its fair to say that self-reference is both the map and territory.

The statement is a lot like the following:

"This sentence contains thirty-eight letters." and Quine's paradox

Now is natural language recursion discretely infinite?

Anyway I'll end this with my favourite definitions of recursion: recursion, see recursion. To understand recursion, you must first understand recursion.

Edit: the statement in question for the OP is pseudomenon.

Last edited by Chipshorter on 14 May 2012, 10:03 am, edited 1 time in total.

The Liar Paradox restated.

Since the thing can neither be true nor false, it is not a statement.

ruveyn

Anyone interested in this thread will enjoy "Gödel, Escher, Bach" by Douglas Hofstadter.

edit: my two favourite self-referencing words: Pentasyllabic and Awkwardnessful.

Beware of sentences that refer to themselves. In that direction lies paradox, contradiction and error.

The first sentence of this posting does not refer to itself.

ruveyn

Yes, I'm assuming it's true that it is false.

If it says it's false, then I assume the falseness of it is true, how am I supposed to extrapolate that it isn't false? If there was a statement afterwards that said, "the first statement is false", then I'd say it was false.

Also, I guess you could go through it infinitely, being true one time and false the next, but what says I should?

I think its a paradox and I love paradoxes.