Subject: RE: sets, masses, &c. (was: RE: [lojban] Re: [jboske] RE: Anything but tautol...

From: "And Rosta" <[email-masked]>
Date: Sun, 3 Mar 2002 19:32:09 -0000

pc:
> [email-masked] writes:
> A sequence can be either a set or a mass; you just add ordering
> to the set or to the mass.
> 
> But sequences seem to have properties (beyond order) that neither of 
> these have -- they don't seem to collaborate and yet the individuals 
> seem to still function significantly.

Sequences can have properties derived from the members but not 
shared with the members. E.g. "The alphabet takes 1 minute to
recite".

> <BTW, personally I would prefer to talk of "groups" rather than
> "masses", when we talk about logcarrying. I find it more intuitive.
> 
> BTW2, do {lo'i} and {le'i} serve any function that cannot be
> served by {loi} and {lei}? For example, do {loi} and {lei} have
> a definite cardinality? If, as the term 'mass' implies, {loi} and 
> {lei} don't a definite cardinality, then I would favour using
> {le'i} and {lo'i} loglanically to denote groups, that can carry
> logs and have discrete denumerable members.>
> 
> Well, I always liked the term "team" for masses. But masses pretty 
> clearly have cardinalities -- they are derived from sets or somethig 
> therelike, which do (I forget if or what the interior quantifer 
> assumed for these things is). 

We might want to distinguish between masses that don't necessarily
have discrete members (e.g. apple, in diced pureed form), and masses
that do (e.g. apples, filling a bowl). 

> But masses or groups or whatever are 
> still very different things from sets -- and things we talk about 
> much more often. (I suppose that a mass of waters would be hard to 
> cardinalize unless you took ups some notion of the size of a water, 
> whichj, at least inm principle, you can do in Lojban.)

My point is that, as Jorge often reminds us, we hardly ever need
to talk about sets in the strict sense, so the lV'i gadri are
wasted. But we do often want to talk about groups/teams (appies
filling a bowl), and, I think, anything that can be described
in terms of sets can also be described in terms of sets/teams
-- all properties that sets have are also properties that groups/
teams have. Hence if we did want to distinguish between a bowl
full of apple and a bowl full of apples, I would suggest making
the first be full of lei apple and the second full of le'i apple.

--And.