These are going to be some rough notes here.
1. For every statement (say, ~G, maybe? P:D) , there is a System, (S, or S' ?) for which it is valid.
(Are you prepared to wage a war across an infinite space of formal logics? That seems to be implied here! There is no single privileged logic that can be asserted as being the "One True Logic"!)
2. Any set of statements can be made into a logical system of greater or lesser formality. Example:
A. Statement (B) is valid. B. Statement (A) is invalid.
The reason this system cannot be resolved is that there is no third statement by which it can be resolved.
3. This is the reason for the distinction between the dichotomies of "valid" and "invalid" on one side, and "true" and "false" on the other: not all informal logical systems allow for the resolution of validity, and all resolutions of validity must refer to some other external systems for a sense of truth or falsehood. Values of Truth and Falsehood emerge from the values we hold in a level of Reality nearer to us entirely.
4. "Truth" simply indicates a form of validity that we value more highly than a simple conclusion of validity can warrant. They refer to conclusions of belief, experience, experimental data, consequence, risk, and safety, amongst many others. We also hold such conclusions to be more valuable when they are useful over a greater experiential domain; time, place, circumstance, and intentional stance, again, amongst many other variables.
5. Everyday language can create new systems of logic, a Linguistic Context, or speak within such a context, describing various premises within the context given;
"Superman has X-ray vision!!!"
or drawing conclusions;
"The bad guys might try to hide something behind lead!!!"
6. Cognitively, we make use of a multiplicity of Logics, slipping from one to the next as easily as we move from one perception to another. These mental frameworks allow us to interpret and re-interpret our perceptions until some sort of recognition takes place. A situation in which the "frame" could not match the "picture" would have a great emotional and physical effect, depending on its presentation. (Shock, fear, awe, wonder, strange beauty, etc.) This is the famous stream of consciousness, which changes not only in its contents, but in its processes! (Cue Rod Serling!)
7. What is the difference between suspension of disbelief (entertaining a fictional context) and other "serious" uses of language, such as lying, interrogation, brainwashing, and (perhaps empty) rhetoric? Do we store memories as percepts, or as logical frameworks in which percepts are then embedded? Does Luke Skywalker meet Obi-Wan on Tatooine, or on Arrakis? Why do you immediately know that is the stupidest question you were ever asked???
8. What is the relationship of special contexts of language and special contexts of experience, such as teaching, torture, Comparative Literature, and Analytic Geometry? (ucwutididthere? P:D)
9. How do Phenomenal Worlds train us to be critical of the world we live in, and the ways it is presented to us in various Linguistic Contexts? Do they help us to achieve new and more unusual ways to view the world and make otherwise unavailable observations of the (so-called) real world, and share them with others?
I'll bet they do! Wanna bet against me???