Subject: [lojban] quantifying over imaginaries (was: Re: partial recantation in favour of solomonics

From: "And Rosta" <[email-masked]>
Date: Sat, 9 Nov 2002 00:06:53 -0000

xod:
> On Fri, 8 Nov 2002, And Rosta wrote:
[...]
> > How do we say "99% of Lojbanists are male"? I don't know, but
> > it ought to be doable along the same lines of so'e, "most",
> > which also expresses a fraction of a total extension. {so'e} makes
> > sense only with {so'e broda} and {so'e da poi broda} -- these
> > can't be paraphrased with unrestricted da 
> >
> > What are the truth conditions of "99% of Lojbanists are male"?
> > At the least they seem to require that there are at least
> > 100 Lojbanists (or at least 2 Lojbanists, if the claim was
> > that 50% of Lojbanists were male). So n% would seem to be
> > importing. But I think we also would like to be able to say
> > truthfully that "50% of unicorns are male". So it seems desirable
> > that we should be able to mark n% quantifiers as either
> > importing or nonimporting. Jorge already suggested a way to do
> > that: by adding ma'u/ni'u with no default when it is omitted,
> > and letting it be glorked from context when not used. This would
> > naturally extend to "100% of", which is equivalent to {ro}. I
> > therefore conclude that for all fractional quantifiers, including
> > {ro} and {so'e}, we want both importing and nonimporting versions,
> > and xorxes's suggestion is the best way to effect it 
> >
> > Is this something everyone could live with?
> 
> I don't like overloading the meanings of ma'u and ni'u. I don't like
> leaving it to context when it's not expressed. And you should probably
> read and meditate on what I closed message 17044 with, which shows why
> "50% of unicorns are male" is always a valid statement 

Okay. I was going to throw up my hands and give up, but I'll try
a different tack. It turns out that I agree with you (in 17044), 
but I think it means that John and pc are right about importingness....

Firstly, {pi mu lo(i) no pavyseljirna} really does seem nonsensical to
me -- taking 0.5 of 0 is daft, and is really not at all what we mean
to say when we say "50% of unicorns are male". I conclude from this
that the inner cardinality must be su'o.
Secondly, if we can talk about the set of Graces, lo'i cridrgreisa,
it seems proper that we can note that there were three of them:
{lo'i ci cridrgreisa}.

I conclude from this:
(i) fractional quantifiers entail cardinality su'o
(ii) the cardinality of an imaginary category is or can be also
imaginary

Applied to the general debate, this leads to the following conclusions:
(a) fractional quantifiers, including ro, are importing in the sense
that they entail cardinality su'o:
{ro broda} entails {ro lo su'o broda}
(b) the truth or falsity of claims involving {ro pavyseljirna} and
{lo ci cridrgreisu} depends on however we decide and signal whether
the universe of discourse includes only the real world, or also
imaginaries .
(c) {ro lo in-not-necessarily-real-world su'o broda} entails 
{in-not-necessarily-real-world: da broda}, but not
{in-necessarily-real-world: da broda}.

The upshot is as follows:
(d) {ro broda} IS importing
(e) it is not false to talk about {ro pavyseljirna}, even in belief
systems where these are purely imaginary. But it is false to talk
about {ro in-necessarily-real-world pavyseljirna}.

I was going to ask whether this at least could win agreement, but in
fact I have (temporarily at least) convinced myself that my reasoning
is actually correct, rather than merely a possible basis for
compromise.

--And.