On Sun, 07 Jul 2013 18:02:48 -0600, Joe Niederberger <firstname.lastname@example.org> wrote:
> 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. > > Cheers, > Joe N >
This is especially so for kids who are born to an Indo-European language---in which, according to a linguist I talked to, "double" negatives occur naturally, grammatically, and as a matter of course. In these languages, you negate a statement by negating everything in sight.
English is a major exception in its prohibition of these constructions---and that prohibition was grafted onto the language by scholars of the Middle Ages. (The graft took only partially; witness the widespread use of double negatives among people who have been "properly educated" about their use.)
- --Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State University of Denver