Let me clarify a bit.

If the statement was true, it could be evaluated as true.

Maybe I haven't been clear enough. Taking "this statement is true" as an example, while an assumption that it is true or false leads to no contradiction, in order to ascertain that it is false, we would need to show that it cannot be true, and vice versa. We can't do that so we can't evaluate it either way. Maybe your interpretation is different, but by "evaluate as x" I mean to ascertain that x is the

only possible value. I'll think about rewording the OP for more clarity...

Anyway, bearing that in mind and going back to

**"This statement cannot be evaluated as true or false"**, our inability to evaluate it as true doesn't preclude the possibility that it may be true anyway. We just know that we

can't be certain that it is true.

Moving things forward a little, if we use "undefined" to denote the state where neither truth nor falsehood can be ascertained, we then run into difficulties when we consider this as being the answer. If we know that the statement is undefined, then the claim made by the statement is true. That takes us back into a contradiction. So the statement cannot be evaluated as true

*or* as undefined. Can we

*now* evaluate it as false?

We cannot evaluate (prove) the statement to be true.

We cannot evaluate (prove) that the statement even might be true.

Does that equate to falsehood? I don't think it does. The statement is not IMO proved false and yet we cannot even state with any certainty that it might possibly be otherwise.

If I'm right, we have a question without an answer. Even saying that we cannot know the answer is not a valid answer! Dang those pub quizzes, they can be pretty tough sometimes