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From: Martin Bays <mbays@sdf.org>
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Subject: Re: [lojban] {zo'e} as close-scope existentially quantified plural variable
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* Monday, 2011-11-07 at 09:41 -0800 - John E Clifford <kali9putra@yahoo.com=
>:

> I'm still not sure I follow this problem.  In general the inference does =
not=20
> hold, of course, and the process by which it is made to appear to hold se=
ems to=20
> involve changing the meaning of terms in mid stream, so that quantifiers =
that=20
> made sense in one case make no (or certainly not the same) sense in the o=
ther. =20

If it seems that way to us, it's because we're not thinking Blobically
enough.

As I presented it, the problem is with an extreme raw form of Blobism,
which no-one is actually supporting - one where we work with a domain
which is closed under taking kinds; i.e. a domain which has the property
that for any unary predicate P(x) (defined without parameters, let's
say) there exists an element P' such that for any Q(x) (which is allowed
to use parameters from the domain), Q(P') holds iff
\exists x. ( P(x) /\ Q(x) ) does.

Then the impossible-seeming deduction goes like this:
suppose it holds in our bizarre domain that
\forall x. \exists y. R(x,y) ;
let P(y) :=3D \exists x. R(x,y)
then for each x, R(x,P') holds (as we see by considering Q(y) :=3D R(x,y))
so it holds in this bizarre domain that
\exists y. \forall x. R(x,y) .

(Of course this isn't a valid deduction in any standard logic; it
depends wholly on the bizarre properties of the domain.)

In fact, if we take this too literally, we can take Q(x,y) to be x=3Dy,
and find that the domain is a singleton... but nevermind that.

Hopefully consideration of the above gives an idea of what's screwy
about kinds, i.e. about mixing up elements and predicates.

> ----- Original Message ----
> From: Martin Bays <mbays@sdf.org>
> To: lojban@googlegroups.com
> Sent: Mon, November 7, 2011 11:19:40 AM
> Subject: Re: [lojban] {zo'e} as close-scope existentially quantified plur=
al=20
> variable
>=20
> * Monday, 2011-11-07 at 07:42 -0800 - John E Clifford <kali9putra@yahoo.c=
om>:
>=20
> > Why is there only one level in Ready-Made?  I suspect that this is a st=
raw man=20
>=20
> > you have set up, but the characterization of it -- and of blobular -- a=
re so=20
> > vague as to make a clear judgement difficult.  I suspect that the only =
problem=20
>=20
> > with levels is just that {lo broda cu klesi lo broda} shouldn't hold.  =
Or that,=20
> >
> > in the same context, {broda} is used sometimes for avatars (exemplars, =
slices,=20
>=20
> > ordinary things) and sometimes for kinds/masses/properties.  MB seems t=
o be=20
> > saying that you do do this, but his evidence is somewhat confusing itse=
lf=20
> >(using=20
> >
> > quantifiers inappropriately, for example), so I am not sure you do (or =
don't,=20
> > for that matter).  I do think, however, that there are limits as to how=
 far up=20
>=20
> > or don you can shove a predicate without some indication of the shove, =
but I am=20
> >
> > less sure what those limits are (using {cinfo} for what would normally =
be {ka=20
> > cinfo}, something about functions from worlds to sets, for example, see=
ms to=20
> >far=20
> >
> > up, using it for muscle fiber from a lion's leg muscle seems too far do=
wn --=20
> >but=20
> >
> > I am open to arguments either way).
>=20
> I proposing a simple test/definition of when level-mixing has gone too
> far:
>=20
> A unary broda is Sloppy if, in any domain containing everything which
> can broda, for any brode and brodi,
>     {brode ro brodi su'o broda}
> implies
>     {se brode su'o broda ro brodi}=20
>=20
> (Technical restriction: brode can not be taken to be {du}, because that
> has to be considered to be magic for the domain not to collapse.
> {mintu} and {dunli} are fine, though).
>=20
> If I understand xorxes and and correctly, they have every predicate
> being Sloppy - the witness for the existential in the second sentence
> can be taken to be the kind of broda which is broded by some brodi.
>=20
> They try to dodge this problem by introducing informal rules to avoid
> level-mixing within a single domain - in particular, they would never
> consider a domain like those in the definition of Sloppy.
>=20
> Martin
>=20
> --=20
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