Let's define logic as:
A statement and it's opposite, obtained by applying the "not" operator, both cannot be true. The not operator is applied to the part of the sentence describing action or attribute.
a) The apple is red. The apple is not red.
b) Swamy crossed over the fence. Swamy did not cross over the fence.
If in a set of statements, there exist two statements which are both true, and are opposites, then the set is inconsistent.
Do all paradoxes fall under the set of inconsistent statements or set of statements?
(Assuming of course that I have reasonably and objectively defined "logic", and other terms).