Re: masses, quantifiers, and ko'a

[jorge@phyast.pitt.edu]

> >To be consistent, {do} should always be a mass (because mi'o, ma'a, etc.
> >are defined as masses, not individuals), and the proper way of saying
> >"each of you" and "two of you" should be {ro lu'a do} and {re lu'a do}.
>
> Not generally a problem, since masses are quantified in fractions, and
> generally indefinite ones at that, while individuals are quantified in
> units.

It's not really a problem for {do}, true, but in general the quantifier
is not enough. {re lo gunma} have to be two masses, not two individual
components of {lo gunma}.

> >So what does this mean:
> >
> >        so'a da poi gerku cu se denci ije so'i da batci da
> >        Almost all dogs have teeth, and most of those bite (themselves?/
> >        those that bite?/those with teeth?)
>
> It means someone is trying to come up with a difficult case that is hard
> to understand, and has succeeded.
>
> I start with using instead of that final "da":
> ri = themselves (respectively or distributively is a bit ambiguous)

Respectively in my opinion. That is, if {ri} can refer back to {da}.
I think {ri} should refer back to any sumti whatever, but that's not
the canon.

> ra = those with teeth
> ru = dogs

How do you get these to be different? There is only one sumti
in the first sentence.


> It seems that if you are using quantifiers on previous "da"s, you need
> to explicitly use one here.  If you had said "ije so'i da batci so'u da"
> Cowan's rule would have been clear that you were subselecting from the
> biters.

Actually, Cowan's rule would say that you subselect from the
indentured ones, but I would prefer that it be from the biters.
But you can't use any quantifier to get the "themselves" meaning.

> Therefore "ije so'i da batci so'a da", though causing a
> double-take, must be a similar subselection, and "ije so'i da batci ro
> da" means that each of the biters bite each of the biters".

That's not what John said.

> Since unquantified "da" is so ambiguous as to quantification in this
> situation, I have no problem with assuming it to result in "themselves".

The whole point of {da} is its multiple use after one quantifier, the
problems arise when it is quantified more than once. In that case, I think
the {da} should be bound to the last quantification, not the first.
This is because you can't be expected to memorize all previous appearances
of {da}. You should be able to figure it out from the most recent.

> Perhaps the proper question is to ask pc what he would do to a logic
> student who used the corresponding notational structure in a logic paper
> %^) (or at least how he would interpret what that student had written).

I suppose he wouldn't admit two quantifications of the same variable,
which is what is causing the problem here.

> And if his answer is that it would not be considered good logical form
> for any of your selections, then that should be your answer.  Use of
> "da" in my book should match up pretty well with logical notation.

Then you should not allow subselections. I don't think we really need
to be so strict, as long as we have a clear rule for what it means
to quantify an already quantified variable and how are new appaerances
of the variable bound.

Jorge