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

From: Robin Lee Powell <[email-masked]>
Date: Fri, 24 Jan 2003 15:05:38 -0800

On Fri, Jan 24, 2003 at 09:04:53PM +0000, Martin Bays wrote:
> 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.

Heh. Ignore me, then. 8)

> > 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.

<nod>

Again, I want a new cmavo in JOI for set difference, but this is a
workable hack, I think.

> > > > 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)). 

<boggle>

> 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.

Granted.

> > 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.

It certainly is.

> 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.

<nod>

And I think that sucks anyways.

> To be honest, I think the best solution is to stick with bridi, and define
> some nice lujvo. 

cecyvi'u

<grin>

> 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?

I haven't yet read it. .u'uro'a

I'll do that now.

Hmmm. Nick seems to be using selcmipi'i for intersect, which is, umm,
insane, IMO. I prefer cec to selcmi, but even ignoring that, pi'i
doesn't even slightly match my concept if intersection; cecysi'umi'u is
my first try.

However, now I'm going to stop reading the English and go do my own
translation of the lojban without referring to the English, just for
fun. Of course, I've already cheated, but there you are. The result
will be at

http://www.digitalkingdom.org/~rlpowell/hobbies/lojban/algebra.txt

> > 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.

Heh. Thanks.

> > > > > 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.

Complex analysis would be cool. I'd also enjoy cryptography, set
theory, or subatomic physics. Game theory would be hella cool.

Hmmm...

My old Cryptography professor might actually be willing to let me do his
book. I was supremely fortunate to have
http://www.cacr.math.uwaterloo.ca/~ajmeneze/ as my crypto prof. 

Unfortunately, Handbook of Applied is already freely available, which
defeats part of my idea (translate something that people wouldn't be
able to easily get in English, at least without paying, and might
actually want).

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

Oh, the incompleteness proof isn't *that* long. Heh. There's an
interesting version here:

http://www.miskatonic.org/godel.html

-Robin

-- 
http://www.digitalkingdom.org/~rlpowell/ *** I'm a *male* Robin.
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