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Date: Sun, 6 Nov 2011 19:03:49 -0500
From: Martin Bays <mbays@sdf.org>
To: lojban@googlegroups.com
Subject: Re: [lojban] self-referential goi
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* Sunday, 2011-11-06 at 19:58 -0300 - Jorge Llamb=EDas <jjllambias@gmail.co=
m>:

> On Sun, Nov 6, 2011 at 6:57 PM, Martin Bays <mbays@sdf.org> wrote:
> > I thought this was cute, and it seems to be allowed by the BPFK section
> > definition of {goi}:
> >
> > {ko'a goi li pa lo'o ce'o ko'a ce'o ke li re lo'o ce'o ko'a zo'u pa
> > cimni je terkancu cu mleca lo se zilkancu be lu'i ko'a}
> >
> > It's the continuum hypothesis ;)
>=20
> I don't really quite know how either "lu'i" or "ce'o" are meant to work, =
but...
>=20
> Assuming ko'a is a set, wouldn't "lu'i ko'a" be a singleton, and so
> "lo se zilkancu be lu'i ko'a" be just one?
>=20
> And doesn't ko'a have only three members: 1, ko'a, {2, ko'a}?

Well, I was making up semantics for {lu'i} and {ce'o} which make this
work. Probably I shouldn't do that.

The goi phrase was meant to be read as
    A =3D=3D ((1,A),(2,A)) .

As for lu'i... actually, I guess it doesn't work.

Also there's no reason that A should be the *smallest* infinite binary
tree, which is needed for the continuum hypothesis bit.

Anyway, the real point was that self-referential goi is cool. If anyone
can see an actual use for them, that would be even cooler.


This does raise the more important question of how {ce} and {ce'o}
should work. If we want {.a bu ce'o by ce'o cy} to get (a,b,c), doesn't
that involve following LISP et al and defining (a,b,c) =3D <<a,b>,c>?

And if we want {.a bu ce by ce cy} to get {a,b,c}, rather that
{{a,b},c}, doesn't that involve blatant cheating?

Is this what "considered jointly" in the bpfk definitions is meant to
handle? It doesn't seem very clear.

Maybe it would be cleaner to explicitly have
    a ce b :=3D a \cup {b}  if A is a set
	      {a,b}	  otherwise
, and similarly for ce'o?

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