R Hansen says: >I think getting the abstract notion of "implication" is critical for any of this to pan out
Of course, and the entire concept that we call "implication" in propositional logic is not something that somebody has a ingrained (or inbred) sense for. It is something that was discovered (, or if you like, invented,) worked out as a system with the other elements, and relies on cultural transmission to propagate to each new generation.
>Kids actually get double negatives, inclusive, exclusive etc. almost as soon as they get language.
Not in an entirely clear and consistent way. But like if..then.., of course the seeds are there. Its a matter of training to take any informally tossed off utterance: "I ain't never going to school again", "I could care less", and distort its meaning into the logician's.