Subject: [lojban] Re: loi preti be fi lo nincli zo'u tu'e

From: Martin Bays <[email-masked]>
Date: Fri, 24 Jan 2003 21:04:53 +0000 (GMT)

On Fri, 24 Jan 2003, Robin Lee Powell wrote:

> On Fri, Jan 24, 2003 at 07:36:21PM +0000, Martin Bays wrote:
> > On Thu, 23 Jan 2003, Robin Lee Powell wrote:
> > > On Thu, Jan 23, 2003 at 11:46:04PM +0000, Martin Bays wrote:
> > > > On Thu, 23 Jan 2003, Robin Lee Powell wrote:
> > > > > On Sun, Jan 19, 2003 at 01:33:18PM +0000, Martin Bays wrote:

> > > As an added bonus, "li pa ce re ce ci vu'u re" appears to be
> > > equivalent to the version with vei and ve'o, and satisfies my
> > > concerns about lojban not having all set operations; if anyone
> > > things that the above does *not* evaluate to "pa ce ci", please let
> > > me know.
> >
> > I don't see why it should... If you're using vu'u as a set subtraction
> > operator, surely it needs both sides to be sets. But {re} on its own
> > is "2", not "{2}". Would {lu'i li re} be "{2}"?
>
> I thought any value could be considered a singleton set containing only
> itself.

Not in set theory, it can't. And if it can in lojban, I've just gone off
lojban.

> Fortunately, "li pa ce re ce ci vu'u lu'i re" works, so it's
> irrelevant. Does that work for set subtraction IYO?
>

Hmm... I'm really not sure. I can see problems coming if we wanted to
start talk about numbers in the "proper", set theoretical way - but then
the same is true of the use of the symbol "-" for both operations... so I
guess it'll be ok.

> > > Now, on to the general set problems.
> > >
> > > Unfortunately, that doesn't fix the general set problems. In
> > > particular, if we have:
> > >
> > > le pamoi gerku ce remoi gerku ce cimoi gerku ku ku'a le remoi gerku
> > > ce vomoi gerku
> > >
> > > I'm not sure how to turn that into a set subtraction, without which
> > > we do *not* have a complete set (ha ha) of general set operators.
> > >
> > > Some ideas, comments requested:
> > >
> > > le pamoi gerku ce remoi gerku ce cimoi gerku ku ku'a ni'u le remoi
> > > gerku
> > >
> > > le pamoi gerku ce remoi gerku ce cimoi gerku ku ku'a da'a le remoi
> > > gerku
> > >
> > > le pamoi gerku ce remoi gerku ce cimoi gerku ku ku'a nai le remoi
> > > gerku
> > >
> > > I think I like da'a the best, but they all suck, IMO. Having a
> > > cmavo for set subtraction seems reasonable.
> >
> > da'a seems best... though this approach does mean you're taking an
> > intersection with a proper class, which might be something we'd rather
> > avoid (isn't it?).
>
> .oiro'a What's a proper class?

Oh dear... I'm not an expert on this, so please don't believe anything I
say. But basically, a proper class is a set that's too big to be a set.
You see, we have to set up set theory in a way which avoids paradoxes like
Russel's (consider the set of all sets which don't contain themselves
(lo'i da poi ke'a selcmi gi'e na cmima ke'a) - is it in itself? (xu ri
cmima vo'a)). If you're going to start allowing the set of all things, or
the set of all things except the second dog, you're quickly going to run
into that kind of paradox.

Of course the same is true of ro rarbau, and I wouldn't say lojban should
be built on aximoatic set theory (too late, for a start), but I do think
it'd be nice not to have use such an icky construction just to do set
subtraction.

>
> Does that mean you agree that a set subtraction cmavo is needed?
>

Well, we've got vu'u. But that's a completely different selma'o from ku'a
and jo'e.

One possibility would be to have the whole thing in mekso, perhaps with
su'i and pi'i for union and intersection when applied to sets. The problem
then is that sets in lojban are sumti rather than operands, so you'll need
{mo'e}'s all over the place. In fact I *think*, without being sure, that
your {lu'i re} (and my {lu'i li re}) above should actually be {mo'e lu'i
li re}... but the syntax is messing with my head right now and I can't
argue it clearly.

To be honest, I think the best solution is to stick with bridi, and define
some nice lujvo. And then if necessary, mexify them with na'u. Have you
seen this translation by Nick Nicholas of the start of an abstract algebra
book -
http://www.lojban.org/files/texts/algebra
- which goes some way towards doing that?

>
> A B.Math is a Bachelor of Mathematics, and it implies that your school
> has an actual Mathematics *Faculty*, which is very rare; most schools
> have a Mathematics *Department* underneath the Science or Arts
> faculties; in the former case you're getting a B.Sc., and a B.A. in the
> latter.
>
> It is in no way more prestigious, it is merely more rare. And since I
> never *wanted* a Math degree, and am in fact quite bad at advanced
> mathematics, it's something of a personal joke. 8)
>

Well, I'm impressed.

> > > > I have actually tried to do a little translation of logic/set
> > > > theory stuff into lojban... but not without difficulty. And I
> > > > found normal bridi more useful than mex - but then I haven't
> > > > really fully absorbed that chapter yet.
> > >
> > > <nod>
> > >
> > > I would like to translate something mathematical and substantial;
> > > got any contacts that would like to let us release a translated
> > > paper?
> >
> > Ummm... I guess I could ask someone. Can you be more specific? Do you
> > just want some random high-powered maths research?
>
> What I'd *really* like to do would be a textbook (or, more likely, a
> portion thereof), precisely for reasons of comprehensibility.
>

That's actually a very good idea. What kind of subject do you want? I
(very very vaguely) know the author of a nice+simple complex analysis
book, which should be suited to mex. Or else name a subject and I'll see
what I can do.

Personally I'd like to translate a proof of Godel... though obviously
that's a *rather* significant task.

> > Would it be comprehensible enough to be translatable? And how official
> > a "release"?
>
> I would like to able to make the lojban translation generally available.
> Obviously *only* the lojban translation would be so available, so
> there'd be very little fear of the author losing money.
>
> -Robin
>
>

---

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