[lojban] A Proposed Explanation of {gunma}

[Kevin Reid <kpreid@mac.com>]

The problem, as I understand it, is: what is the type of the x2 place  
of {gunma}? Or, what are the selbri (as opposed to LAhEs) used for  
interconverting masses, sets, and individuals?

I have thought that the most sensible explanation is that the x2 of  
{gunma} is a set. Today, a discussion with Robin Lee Powell and John  
Cowan on #lojban resulted in the following complete list of  
conversions, which we agree is sufficient and consistent:

         x1 kind      x2 kind    relation
  gunma    mass       set        x2 is the set of all the parts of x1
  cmima    individual set        x1 is a member of x2
  pagbu    individual mass       x1 is a part of x2
  selgunma set        mass       se gunma
  selcmi   set        individual se cmima
  selpau   mass       individual se pagbu

The other simple explanation of {gunma}, that the x2 is all of the  
members as individuals, is incompatible with predicate logic.

Some notes, if the above is true:

{cmima} and {pagbu} may of course be used to specify an *in*complete  
list of multiple members/parts, using {.e}.

The x2 of {gunma} is indeed "complete", in the sense that in a bridi  
which specifies a value for it, that value must refer to some set  
which contains exactly all of the members.

To completely list the members of a set, use {ce'o} or {lu'i}. To  
completely list the members of a mass, use {joi} or {lu'i}, or some  
form of set description together with {gunma}.

The "individuals" which are parts of masses may be themselves masses,  
of course.

--
Kevin Reid                            <http://homepage.mac.com/kpreid/>




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