Re: [lojban] More about quantifiers

["Jorge Llambias" <jjllambias@hotmail.com>]

la pycyn cusku di'e

> > What do you mean by "actual quantification"?
> >
> Quantity and quality (universal-particular, affirmative-negative) as well 
> as
> import.

So, in:

   ro broda su'o brode cu brodi
=   no broda me'iro da poi brode cu brodi

What is the "actual quantification" of broda and brode?
I can tell what the actual import is: - for broda and + for brode
in my system, ++ in yours. But what is the "actual
quantification"?


> <Which one is the traditional system?>
>
> All + with the  assumption that all classes mentioned as subject are 
> non-null
> (and maybe a few less certain things as well).

That sounds exactly like (A-,E-,I+,O+) with the assumption
that all classes mentioned as subject are non-null. Indeed,
with that assumption we can drop the +/- distinction, as it
becomes irrelevant.

> Well, I didn't read the whole book, just a few sections that talked about
> restricted quantification.  I never saw any evidence that it was developed 
> as
> a separate system.

This is where he defines things:

http://www.wabash.edu/depart/Phil/classmaterials/Phil3F99/Phil3txt/Phil3txt7/Phil3txt72/Phil3txt723.html


> Obversion is just a device for making
> "not every" a bit more readable, as I read him.

But for "not every" to be equivalent to "some not",
"every" and "some" must have opposite import.

> But I will look at some more
> (and of course it works for an all positive set as well -- under the 
> standard
> condition -- no empty subjects).

Of course. Under that condition, the +/- distinction is pointless.

> Of course, the restricted quantifier is -, since it just is the ultimate 
> form
> in a minorly gussied up way.  Part of the gussying is, alas, to hide the 
> real
> subject of the of the final quantifier, namely the universal class.

Do you agree or disagree that in Lojban these are equivalent:

1. ro da poi broda cu brode =||= ro da zo'u ganai da broda gi da brode

2. su'o da poi broda cu brode =||= su'o da zo'u ge da broda gi da brode

They have to be defined that way if obversion is to work for the
{poi} forms. And that gives A- and I+ for the {poi} forms.

> Every universal quantifier (in a non-empty universe) entails every instance
> of  its matrix, every matrix with a free term entails its particular 
> closure
> on that term:
> AxFx therefore Fa therefore ExFx.  That is about as thorough a working out 
> as
> I can think of.

Assuming a non-empty universe (and you are assuming it by bringing
up a), I have no problem with that.

But of course that does not mean that
{ro da zo'u ganai da broda gi da brode} entails
{su'o da zo'u ge da broda gi da brode}. It does not.

So, if, as I believe, these hold:

1. ro da poi broda cu brode =||= ro da zo'u ganai da broda gi da brode

2. su'o da poi broda cu brode =||= su'o da zo'u ge da broda gi da brode

then we cannot say that {ro da poi broda cu brode} entails {su'o
da poi broda cu brode}. You may not like 1. and 2. as definitions,
but they seem to me fairly standard. At least they are presented
as valid in the page I found (from a random search I did for
"restricted quantification").

mu'o mi'e xorxes



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