First, let's take a special case of paradoxes. I'll describe it as "negation selfreffering" statements. One exemple might be Russel's parodox.
I will take the most simple example, "The liar's paradox", wich states:
P: "This statement is false." ("This" reffers exactly to the statement it belongs to.)
Now let's take a false statement:
F: "The sky is green."
Ok. I'm interested in the character of the conjunction and disjunction of the two statements. (I know it's more philosophy than math, but I think I found a way to mathematicaly model it; I wouldn't post the model yet, to not influence your opinion).
My opinion is:
(P and F) is paradoxical,
(P or F) is false.
What's your opinion?