2: if logic always has three directions, perhaps the map has four because it aspires to pretentions of being beyond knowledge. whether it wins or we do, shall the war between experience and language one day find out.
3: on triangles. note that all possible logic triangles, whether dialectical or syllogistic in nature, contain within their modeling analogies for the alternative lines and thus can model the total system. discourse is self revealing as well as self referential