Is saying 'This statement is true' a logically valid statement?

Question

I understand how 'This statement is false' is not logically valid, but what about 'This statement is true'? I've always heard self-referential statements are not logically sound, but I can't really give a great explanation for why this one would not be. Anyone have a good argument one way or the other?

Answer 1

It could be consistently assigned either "true" or "false".

Interestingly enough, "this statement is provable" is provable (or more precisely, in a suitable formal system to which Gödel's theorems apply, a statement which asserts its own provability is in fact provable). See Löb's theorem