Set Theory Woes

[Ashley Yakeley <AshleyB@HALCYON.COM>]

For a language that claims to be logical, Lojban really ought to have
better words for set theory. All I can find is "ce", "jo'e", "ku'a" and
"pi'u", and there do not seem to be words, even in mekso, for the empty
set, the set containing a single given element (except for "X ce X") or
the set difference operator (the set of objects in A but not B).

Worse still, "ce" is inconsistently defined in the refgram. On page 354,
"A ce B" is defined as the set with elements A and B (or {A, B}).
Logically, and together with the left-grouping rule, this means that "la
frank. ce la .alis. ce la djeimyz." means {{Frank, Alice}, James}, that
is, a set with the two members James and the set of Frank and Alice. Page
355 inconsistenly assigns this sumti to the more useful meaning {Frank,
Alice, James}.

The cmavo "ce'o" (but not "joi") is similarly inconsistenly defined.

As for masses, it should be made clear that there is no mathematical
concept that corresponds to "mass" as such, instead, one can consider
sumti as sets that when speaking of individuals contain one member, and
when speaking of masses contain typically more than one member. The
sumti-set of a sumti that referred to a set S would then be a set with
the one member S (itself a set).

Therefore, the "ce" (but probably not "ce'o") problem could be solved
with a set-making cmavo that when applied to a single item referred to
the set containing just that item, and when applied to a mass referred to
the set containing all the items in the mass. When does the baseline
period end?


--
fe'oca'emi'e tricrfraksizeicecmu ji'a mi'e .aclin.