Logical Confusion: A is True or False?

[varadgautam]

Consider a statement
A: Negation of A (~A) is true

Then,
~A: Negation of A is false


If A is true, that means that ~A is true too, but these can't be simultaneously true.
If A is false, ~~A is true, i.e. A is true. What is the problem?

 

[HallsofIvy]

The problem is that logic only applies to "propositions" which are defined as statements that are either true of false. What you have done is show that "the negation of this statement is false" is not a proposition.

It is, in fact, exactly the same as the common example of a statement that is not a proposition: "this statement is false".