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Date: Thu, 29 May 2014 20:24:34 -0700
From: Martin Bays <mbays@sdf.org>
To: lojban@googlegroups.com
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Subject: Re: [lojban] Individuals and xorlo
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* Thursday, 2014-05-29 at 15:42 -0700 - guskant <gusni.kantu@gmail.com>:

> Le jeudi 29 mai 2014 02:14:50 UTC+9, Martin Bays a =E9crit :
> >
> > * Tuesday, 2014-05-27 at 19:21 -0700 - guskant <gusni...@gmail.com=20
> > <javascript:>>:=20
> >
> > > Regarding {zo'e} as the outmost constant in a prenex of a statement i=
s a=20
> > > special case of {zo'e} as Skolem functions. As for the example=20
> > >=20
> > > {ro da broda lo brode},=20
> > > that is=20
> > > Ax B(x,f(x)),=20
> > >=20
> > > it says nothing about whether {lo brode} as a Skolem function f(x) is=
=20
> > > constant for all x or not. That is to say, xorlo allows both=20
> > > interpretations "EYAx B(x,Y)" and "AxEY B(x,Y)" as a statement before=
=20
> > > Skolemization, while CLL-lo restricts the interpretation to "AxEy=20
> > B(x,y)"=20
> > > (small y is a singular variable).=20
> >
> > Assuming I understand you correctly as wanting {lo broda se broda ro da=
}=20
> > to have only the "EYAx" interpretation, this is in direct conflict with=
=20
> > the gadri BPFK section, which says=20
> > "Any term without an explicit outer quantifier is a constant, i.e. not=
=20
> > a quantified term. This means that it refers to one or more individuals=
,=20
> > and changing the order in which the constant term appears with respect=
=20
> > to a negation or with respect to a quantified term will not change the=
=20
> > meaning of the sentence.".=20
> =20
>=20
> Then your assumption is false. I don't want {lo broda cu se broda ro da} =
to=20
> have only "EYAx B(x,Y)" interpretation. See the table at=20
> http://guskant.github.io/lojbo/skolem.png

Aha, thanks. I hadn't realised you were suggesting this only as
a special role for terms in the prenex.

> Le jeudi 29 mai 2014 05:21:56 UTC+9, xorxes a =E9crit :
> > On Wed, May 28, 2014 at 2:14 PM, Martin Bays <mb...@sdf.org> wrote:
> >> The statement "there exists a function f(x) such that for all x,
> >> P(x,f(x))" is logically equivalent to "for all x, there exists y such
> >> that P(x,y)".=20
> > There is, however, a difference between these two metalinguistic=20
> > statements:
> >
> > "There exists a function f(x) such that the speaker of the sentence is=
=20
> > claiming that for all x, P(x, f(x))" and  "the speaker of the sentence =
is=20
> > claiming that there exists a function f(x) such that for all x, P(x, f(=
x)".
> >
> > CLL-lo uses the second interpretation when interpreting such sentences.
> mi'usai

Agreed.

To return to the question of whether the referent of {zo'e} can be
non-constant wrt {da} in {ro da broda zo'e}: I understood xorxes
as adopting the contrary position when we discussed these things some
years ago (using generics as the constant values to make sense of things
like your S1), but perhaps that is out-dated or I over-interpreted.

In any case, the semantics you suggest seem sensible to me.

As for ways to specify that a {zo'e} is constant: an alternative to your
suggestion of introducing new rules for prenexes would be to pull tricks
like:
    su'oi da zo'u ro de broda lo du be da
(which may or may not be equivalent to
    lo du be su'oi da se broda ro da
).

A bit long-winded for something so important, though.


Meanwhile, a question. Under these semantics, the second (and only the
second!) {zo'e} in
    ro zo'e zo'e broda
depends functionally on the quantifier. But in
    ro zo'e ro zo'e broda
it doesn't make sense to say that each {zo'e} depends functionally on
the quantifier on the other. This seems to complicate matters?

Martin

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