[lojban] Use and abuse of sets

["Jorge Llambias" <jjllambias@hotmail.com>]

From: "Jorge Llambias" <jjllambias@hotmail.com>

la adam cusku di'e

>What *is* the word for a mathematical set? The closest I can come
>up with is "selcmi", but that doesn't require complete specification
>of the set (and you've also already rejected that zo'o).

I guess {cmacykle} or something else with {klesi}.
For example:

     abu ca'e cmacykle lei prenu le ka ce'u clamau la djan
     Let A be the set of people who are taller than John.

I have no idea what to do with the places of {cmaci}.

>Consider these two sentences:
>
>le'i damba cu daxsi'u
>
>lei damba cu daxsi'u
>
>In my opinion, the first claims that each member of the group in
>question hits every other member, while the second only requires
>that some part of the group hits each other (but that it's
>presumably significant to mention it of the whole group).

Right, and the second is the useful one. When you say of
a group of people that they are hitting each other you
don't really mean to assert an exhaustive set of relationships
between each member with every other member.

>If, for
>example, there are two rival gangs in a brawl, it's obvious that the
>combatants don't hit members of their own gang, so the "le'i"
>version isn't correct. I think that the "lei" version expresses the
>situation well.

I agree. And even if it is not two gangs but a general
Hollywood-western bar-brawl you still don't want to claim
that every single person hits each and everyone else.

>OTOH, if you want to say that every member of a
>group performs some action on every other member, using a set is
>the most clear.

Yes, but does this situation ever come up? Or at least as
often as to require a whole set of cmavo to describe it?

>Officially, only "le'i" is allowed, but I think that using
>"lei" opens up interesting and useful distinctions such as this one.

I don't think that the gismu list suggesting a set
for a given place means that *only* sets are allowed
officially. I usually use masses where the gismu list
suggests sets. {mi'o} is {mi joi do}, so if only sets were
allowed with {simxu} you couldn't say something like
{mi'o daxysi'u}, you'd have to say {mi ce do daxysi'u}.

Loglanists use the word "set" to describe what we
call "mass". (And they use "mass" for something else.)
They had some discussion about whether their sets were
mathematical sets, or whether they were just collective
references like our masses, and they (sensibly) decided
that they are the latter. So they don't have any special
cmavo for mathematical sets. Hopefully Lojban will
eventually lose those cmavo, if I can convince people
not to use them...

co'o mi'e xorxes

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