Is every statement true?
Consider the following argument:
If a statement is true, then it is a member of the set of true statements.
If a statement is false, then it implies a contradiction. Since anything follows from a contradiction, it follows that the statement is true. Thus the statement is a member of the set of true statements.
Since a statement is true or false, all statements therefore belong in the set of true statements. All statements are true, with the set of false statements being a subset of the set of true statements. A statement thus is either true and true only, or both true and false.
Does this mean that all statements are true?