Is there any phrase of the form "A and not-A" that is meaningful?
We can imagine vernacular expressions with that form that carry meaning. I could say, "I do like France and at the same time I don't like France ... I like it as a place to visit but I wouldn't want to live there." Perhaps the truth of the terms used in a statement can vary in the time it takes to make the utterance. If I'm flicking a switch, I could say, "The light is on and ... the light is off (hence not on)" and say something not only meaningful but true.
But here we are talking about the sense of a proposition not statements made in ordinary language, which have looser requirements for carrying meaning. If we are speaking of the logical sense of a proposition, we strip away this vagueness and the contingencies of expression. Both instances of the term are supposed to carry precisely the same sense. The "indexicals" in the proposition, such as I, here, and now are translated into their referents. The above examples would be rendered as something like:
"I (Person A) like France (in the sense of being a place to visit) and I don't like France (in the sense of being a place to live)"
"The light is on (at t1) and the light is off (at t2)"
So they are not cases of "A and not-A".
Let's take the last example and change it so that we are forming an 'A and not-A' proposition. "The light is on and the light is off". Is it meaningful or just false?
I am assuming that different theories of language and meaning will have different answers to this so I am open to all approaches.