Why statement “either ”X is false“ or ”X is not false“” is not correct?

1. According to laws of logic either "X is false" or "X is not false". Let's call the statement1.
2. Let's consider well known statement "this statement is false", let's call it A. So A = "A is false".
3. Let's consider all two possible cases:
1. A is false. Substituting A here we have "It is false that A is false", or "A is not false". We conclude that this case is impossible.
2. A is not false. Substituting A here we have "It is not false that A is false", or "It is false that A is not false". So this case is impossible.
3. So A neither false or not false. So statement1. is not true...

How is this possible that statement "either "X is Y" or "X is not Y"" is not true?

• This is the liar's paradox: plato.stanford.edu/entries/liar-paradox – Dave Jun 19 '14 at 11:42
• You are assuming that truth is an essential property, derived from nothing in particular. What would it mean, for A to be false? What states of affairs would falsify A? – Niel de Beaudrap Jun 19 '14 at 12:00