Subject: Re: [lojban] Re: [lojban Re: mei (was Pro-Sumti) In-Reply-To F64iZrAEXCUOGqcaZIc

From: [email-masked]
Date: Sun, 7 Jul 2002 20:41:14 EDT

<<la pycyn cusku di'e

>{piro} is no more transparent to negation boundaries or quantifier order 
>than
>{pisu'o} is -- {piro loi broda na brode} = {pisu'o loi broda cu naku brode}

I don't think that's true. The first does entail the second,
but {pisu'o loi broda naku brode} could be true and {piro loi broda
na brode} false. For example:

piro lei bolci na se culno le baktu FALSE
pisu'o lei bolci naku se culno le baktu TRUE

{piro loi broda} is transparent to negation boundaries because
it is a singular term.>>

I don't understand this: it is explicitly a quantified term. The fact that 
there is only one thing that fits it does not give it a special status. 
There is often only one thing that satisfies {lu'o loi broda}, too, but is 
still subject quantifier DeMorgan. I suspect that the examples work because 
of what is involved in a mass having a property or not. The second amounts 
to "there is a submass of the mass of these balls whose additive packing 
volume is less than the volume of the bucket" and the first is "it is not the 
case that the additive volume of the mass of all these balls is less than the 
volume of the bucket." It does not contradict the rule, obviously, because 
it is really not an instance of the rule. 
But it appears to contradict the rule, so we know that there is something 
wrong with the structure -- minimally that it is not yet fully in logical 
form. And the problem is, apparently, about the rules for claiming a mass 
has a property. Or else that we have misunderstood the quantifer here.
In fact, it is the latter (at least, the former may be involved as well). 
For {piro} is a double quantifier, in terms of the underlying set -- it is 
fractional and also whole: "some one somethingth of the whole" and {piro} 
then either "some whole of the whole" or "every whole of the whole." But 
these turn out to be equipollent.
DAMN! I've just convinced myself (I think) that {piro lei broda} IS a 
singular term (or indistinghishabe from one logically) . So {piro} and 
{pisu'o} are not exactly quantifiers, but {pisu'o} entails one. So the 
second sentence really says (closer to what is written here) "Some submass of 
these balls does not fill the bucket" and the negation shift of that is "Not 
every submass ... does fill the bucket," which isn't even expressible in 
Lojban in any direct way that I can think of.

Thanks. Maybe there is another way out of the mess wherein intensionality 
threatens.

<<>(I know that you probably allow {piro} on empty masses, but skipping that
>oddity for now -- it just means we have to use the marked forms here).
>And the choice of the default quantifier, it it has any reason other than
>"something has to be default" is likely tied up with the nature of masses
>and thus affects every word that deals with masses.

But it has no other reason than "something has to be default"
as far as I can see.>>

Well, minimally it ought to say something about the kinds of masses we are 
most likely to meet, which is a relevant fact about the nature -- if not of 
masses, then of how language deals with them, which has to be important for 
language construction. So, generic masses tend to act through submasses -- 
because we want to assign them properties now but not all the members are 
present now, and so on. (While selected masses are all present now and 
further we often selected them just to say something about this particular 
group -- pace the Book.)

Back to logic for a minute (I am trying things out, please excuse the 
wandering). 
We can't readily get that hidden quantifier to light, the easiest is {su'o lo 
pisu'o loi broda} -- and this {lo} cannot be dropped. And a specific 
submass would be {le pisu'o loi broda} or (to be really safe) {le pa le 
pisu'o loi broda} (we can't just tuck the {pa} inside the first {le} either 
or we get a supermass).

<<
>{ko'a joi ko'e joi ko'i} stands for some mass {lei ...
>[whatever predicate fits exactly these three things]} in a fundamental way
>and thus -- by the admitted rule about implict quantification -- stands for
>some unspecified submass from that set of things (my preferred reading of
>{mei} in any case) . To say it is the whole mass is either to say that the
>default quantifer on {loi} is {piro}, which you don't want, or to say that
>{ko'a joi ko'e joi ko'i} is not equivalent to {loi du be ko'a be'o ja du be
>ko'e be'o ja du be ko'i} (to pick the most boring -- and safest -- unique
>property of this cluster).

Right. It is equivalent instead to {piro loi du be ko'a be'o ja
du be ko'e be'o ja du be ko'i}. Why is that a problem?
I meant {loi} instead of {lei} in the first line. And we don't need the 
{be'o} -- in this case. 
I don't suppose it is a problem except for getting some consistency in mass 
expression (what I am about, after all). If the basic way of referring to 
masses refers to their submasses, then this basic reference spelling out the 
members with {joi} should also do so. (Of course, naming the members is a 
clear way of selecting a mass and so, if the quantifier on {le} were {piro} 
the identification suggested would be the consistent one.)

<<
Is the difference between {piro loi broda} and
{pisu'o loi broda} intensional? Because that's the
difference between the {joi} form and the {pisu'o loi}
form
No, that difference is extensional (I think -- I'm feeling very uncertain 
about that whole {piQ} business at the moment). But I don't see that that is 
the difference between the {joi} and the {ja} forms. I could be so in your 
language, but it would be an anomaly in Lojban. {le cimei}, because it comes 
at the issue from another direction -- not indicating anything about members 
of the mass but their number (closer thus to sets) -- may be subject to 
different rules (though I really don't think so).

>I admit that {le cimei} may be different because I
>can't see any disaster happening if it is -- yet.

And what disaster happens if {joi} is equivalent to {piro loi}?

I meant {loi} instead of {lei} in the first line