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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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* Friday, 2011-11-04 at 22:51 -0300 - Jorge Llamb=EDas <jjllambias@gmail.co=
m>:

> On Fri, Nov 4, 2011 at 8:37 PM, Martin Bays <mbays@sdf.org> wrote:
> >
> > Suppose we have a forall-exists statement. Any at all will do;
> > let's consider
> > =A0 =A0"every French person wears a beret"
> > and render it in lojban as
> > =A0 =A0(A) {ro faspre cu dasni su'o ransedyta'u}.
> >
> > Then with malkinds, if (A) is true it would also be true that
> > =A0 =A0(B) {su'o ransedyta'u cu se dasni ro faspre},
> > i.e. we can just swap the quantifiers over and get another true
> > statement.
>=20
> The only way (A) and (B) can be logically equivalent is if
>=20
> (i) su'o faspre cu du ro faspre
>=20
> or
>=20
> (ii) su'o ransedyta'u cu du ro ransedyta'u
>=20
> If neither (i) nor (ii) are true, then (A) and (B) cannot be equivalent.

Not logically equivalent, no. But if (A) is true in one domain, then (B)
is true in another domain - and of course if (B) is true in a domain
then (A) is true in that domain too.

So "is true" was a simplification. Let me coin a new notion: a sentence
is metatrue if, were I to claim it out of the blue, you would reasonably
be able to interpret it in a way which made it true.

Then the point is that (A) is metatrue iff (B) is, and generally that
metatruthhood is not affected by permuting quantifiers.

Agreed?

> > If xorxes says (B) - or {ro faspre cu dasni lo ransedyta'u}, which
> > appears to be approximately equivalent
>=20
> The whole point of xorlo was to get away from the idea that "lo
> ransedyta'u" was equivalent to "su'o ransedyta'u".

[based on this and what you said below, I think you may have mistaken my
"(B)" for "(A)"]

> > - I don't know how, beyond my
> > prior knowledge of which was more likely, to tell whether he really mea=
ns
> > to make the surprising statement that all french people share a single
> > beret, or just the (za'a also false!) statement that every french person
> > wears a beret.
>=20
> If I say "ro faspre cu dasni su'o ransedyta'u" you can in no way
> conclude that that I mean to say that all french people share a single
> beret. They are different statements.

Agreed; the question was what to make of {su'o ransedyta'u cu se dasni
ro faspre}.

> If I say "ro faspre cu dasni lo ransedyta'u" the first thing you need
> to do is identify the referent or referents of "lo ransedyta'u". In
> this case, you could easily conclude that all French people wear the
> same headgear (but "sharing" implies more than that, perhaps that they
> take turns with it, or that it is big enough to cover all their heads
> at once, none of which is suggested by the original).

So I could conclude (A) and never more than that?

How about in a situation where the EA claim is more plausible - e.g.
when talking about the residents of some fictional country:
    {ro xabju cu se turni lo xabju} ;
would "some resident(s) govern all residents" not be a plausible
reading?

> > Generally, with malkinds, the order of quantifiers in a sentence gives
> > *no* information, at least until you bring in informal things like
> > emphasis and convention.
>=20
> The order of quantifiers gives all the information that quantifiers
> can provide. It is true that it doesn't give any information about
> what the contents of the domain of discourse are, or what the
> cardinality of the domain of quantification is, but that's not the job
> of a quantifier.

Indeed it isn't.

Martin

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