No proposition -- with the notable exception of a priori statements, which are about constitutive elements of our internal reality -- is about reality, but about our notion of reality – compare Kant. Reasoning is about synthetic propositions, which are necessarily only as conceived and represented in our internal reality. Logic is about what may be generalized in this, i.e., about forming synthetic judgements based on a posteriori data. Regarding this data, there is no chance to relate directly to reality, since nothing in our experience relates directly to reality, but is formed by our inner and outer senses. The same is true for any shared experience, commonly related to as 'reality' or 'truth'.

Since the truth of a proposition relates to a state of the world (reality), the notion of a contradiction relates to this as well. Hence, we have to shift our attention to the very nature of this world/reality and its representation, when facing a contradiction. A contradiction just refers to an ambiguous state, expressed as a non-exclusive duality of logical values. Now, we may ask, is it the world, which is ambiguous, (we may never know), or is it our representation, or, is there possibly more than a single representation/context at once?

A (very simple) example: If we subscribe to the notion of color as a property of an object, a solid colored object _is_ of a color, meaning, it may be either blue or red, but not both at once. But, if our description of the world includes the notion of a spectrum and mixed colors, it may be both blue and red at once, commonly related to as a shade of violet or purple. The very context may include the spectral description or not, it may be even ambiguous about this.

Well this is effectively meaningless. I can see why everyone went over to analytical philosophy. Color is the absence of light and all that. Anything you propose willl have some categorical membership grounded in something measured and observed. The only thing you get in the interpretive weirdness are rules that may or may not be consistent. Not to mention the more serious issue of incompleteness and undecideability. I think that’s the whole issue.

However, a proposition, like, "A says she knows it is raining, but A says at the same time that she does not believe that it is raining", is about a state of mind and a question regarding its logic is about what may be generalized. I can't see where analytical philosophy may be of help here, as the proposition would be just meaningless. (Let's say, Wittgenstein I wouldn't be of help, Wittgenstein II maybe. But I wouldn't consider the latter as analytical in the strict sense.)