Your attempt at justifying contradictions is like performing neurosurgery to remove a hangnail--it's both overly complex, and misapplied.
We are talking about simple truth values. We need no more than a simple predicate calculus. A contradiction always has a truth value of false. It occurs with a conjunction of statements that cannot both be true. It is a fundamental of all rational logic. "A and not A" is false in all rational set theory, grammars, automatons--even Chomsky's (despite his political absurdities he apparently does not deny the law of noncontradiction, at least in his linguistic theories). That you have construed ways in which you think a contradiction is at times NOT false shows your misapplication of the fundamentals upon which the theories you think you understand are founded.
Besides. I don't fall for diversions.
What is the truth value of this predicate:
"This sentence is FALSE"?
A statement with a truth value of FALSE would not be a contradiction--it has an unambiguous value--what do you think "contradiction" means?
It occurs with a conjunction of statements that cannot both be true. It is a fundamental of all rational logic.
It is a fundament of all historical formal logic, and it has limited application to the real world. It works pretty well for gross physical objects and relationships, and most formal maths. It fails conspicuously for sets that commit type violations, such as "the set of all sets", it fails conspicuously in subnuclear physics to explain the 2-slit experiment, and it fails conspicuously to explain many subjective phenomena, such as, for example, my ability to be both happy and not(happy) that my mother has died. It is just one of several mathematical descriptions of how elements in well-formed sets behave. As such, it does not constitute the entire warp and weave of the universe. It is a useful tool for many purposes, it is not a ghost that inhabits every corner of the universe.
"A and not A" is false in all rational set theory, grammars
Chomsky level 0 (or 4, I always forget which direction the grammar heirarchies are stacked in) grammars permit exactly such contradictions, as do my dreams and fancies, as do individual molecules going through the slits of the 2-slit one at a time.
That you have construed ways in which you think a contradiction is at times NOT false shows your misapplication of the fundamentals upon which the theories you think you understand are founded.
Kindly just answer the question: is "This sentence is FALSE" FALSE? If we assume the sentence is FALSE, (as you say, because it is contradictory), than upon evaluation, we find it declares itself to be TRUE, which we must believe, because we declared it to be FALSE. If it is true, it must therefore be FALSE, therefore, it must be TRUE...are you getting the drift here? Contradiction does not necessarily just mean FALSE--it could mean you cannot get a value. You hang up if you try. You are using a loose and inadequate notion of contradiction as if it were ubiquitous. It is not, it is quite easy to have validly formed predicates that are neither TRUE nor FALSE in any formally acceptable sense. That is what most of 20th century formal mathematics was about.
Besides. I don't fall for diversions.
Unless you supply them, I assume.