This sentence is false

[Aion]

This sentence is false.

Classify this sentence as either a statement or not a statement at all.


My reasoning:

A statement must be true or false. If this atomic statement is false then it would be true. And if it were true it would be false. Hence it must be a statement. But according to my answer key, I'm wrong. And this is actually not a statement, although it certainly looks like one. So what's wrong in my reasoning?

 

[Dr.Peterson]

This sentence is false.

Classify this sentence as either a statement or not a statement at all.


My reasoning:

A statement must be true or false. If this atomic statement is false then it would be true. And if it were true it would be false. Hence it must be a statement. But according to my answer key, I'm wrong. And this is actually not a statement, although it certainly looks like one. So what's wrong in my reasoning?

You've demonstrated that it can't be either true or false, haven't you? So it doesn't fit the definition you were given.

 

[Aion]

You've demonstrated that it can't be either true or false, haven't you? So it doesn't fit the definition you were given.

Aw and so it can never actually take on any truth value even if it really wanted to. Now I think I get it.

 

[Dr.Peterson]

Aw and so it can never actually take on any truth value even if it really wanted to. Now I think I get it.

That's an interesting way to put it: It's a wannabe statement that doesn't manage to assert anything.

It's actually a paradox that philosophers discuss; for your purposes in your class, you just avoid it by not considering it a statement.