Is the following a statement This statement is false?

The answer depends on your definition of statement, It is a grammatical correct English declarative sentence which may be a statement by one definition. However, in logic, a statement is defined to be a sentence that is either true or false but not both. This sentence is not a statement by this definition.

It is neither true nor false, because if is true, since it says it is false, it is false. If it is false. then is true since that is exactly what it says.

Please see the related question for more about this famous paradox.