The negation of a contradiction is a validity or an open sentence?

Question

A contradiction is necessarily false. It has a truth-value. If you negate something that is necessarily false, i.e. in all possible worlds the bottom sign (┴)gets an "F", then it appears to be a necessary truth-- a validity.

But if you evaluate the negated terms of a FOL sentence that generates a contradiction, there is no necessity that the sentence be true in all possible worlds.

The question is about the semantics of the bottom sign: ┴

Answer 1

You are mixing terms. A "negation" means the opposite of a truth value: if something is TRUE than its negation is FALSE and if something is FALSE than its negation is TRUE.

According to the dictionary a "contradiction" means "a combination of statements, ideas, or features of a situation that are opposed to one another" [Apple's OS X's dictionary, version 1.0.1]. This means that a contradiction is neither true nor false because it appears to be both at the same time.

Therefore, it is not possible to apply negation to a contradiction.

On the other hand, you may try to unravel the contradiction; that is, take apart the contradicting elements and figure out away to avoid or resolve the contradiction. If you do so, you are not negating it.

Answer 2

more exactly please