Most of our language suffers from two "disorderings", that is, application with one ordering type when another is need to facilitate communication.

The most useful language is univalently functional (as in an "id"), that is, one word has one referent, which is a simple (total) ordering in miniature. Instead, much of our language fails in the first condition (univalency) or in the second condition (functionality) or both:

• Much of our language is multivalently functional, that is, many different names for the same nameable, a disordering which I call preparordering, that is, parordering in the naming, which graphs as follows:

  
                     NAME1
                          \
                    NAME2__\_______NAMEABLE
                           /
                   NAME3__/

  (Some one made a game out of this condition.)
• Too much of our language is not functional at all, that is, one name invoking many different nameables, a disordering which I calL postparordering, that is, parordering in the nameables, which graphs as follows:

  
                           _________NAMEABLE1
                          /
                         /
                     NAME-----------NAMEABLE2
                         \
                          \_________NAMEABLE3

  We know that family naming is nonfunctional. There are many men out there answering to my name, "John Hays". That problem is bypassed by the "id" of social security number. Soon, it will be possible to improve on this by retinal image or dna identification. Meanwhile, we should try to "clean up our language".

  One of our greatest needs is for a univalent dictionary -- singling out, in a standard dictionary, those words which are univalently functional, and making them available in one book or at one Website. Each word in this univalent dictionary would graph as this miniature :

  
  
                              NAME--------NAMEBLE

  This would be of very value in implementing Search Engines ONLINE. Search Engines already achieve some degree of transitive closure by connecting, say, a particular transportation_id with a hotel_id. It would very much simplify and speed up transactions if a surfer could enter a keyword_id for her/his query.