* Thursday, 2011-08-25 at 19:11 -0300 - Jorge Llambías <jjllambias@gmail.com>:
> On Thu, Aug 25, 2011 at 6:06 AM, Martin Bays <mbays@sdf.org> wrote:
> >
> > I think I now agree that Carlsonite Kinds are an appropriate way of
> > handling {lo'e} and can consistently be allowed as a reading of {lo}.
> >
> > I do still have a couple of questions about how Kinds should work in
> > Lojban.
> >
> > Firstly: there is the question of whether Kinds are in our domain of
> > quantification.
>
> My answer is that sometimes they are and sometimes they are not,
> depending on what "our domain of quantification" happens to be at the
> time.
Meaning that quantification can be over ordinary individuals, and it can
be over Kinds, but it can't be over a mixture of the two? So our
universe has multiple sorts, and {ro da} can be quantifying over any one
of them - but only one at a time? I'd be happy with that, and it seems
to deal with your "two favourite desserts" issue.
It would be nice to have a way of explicitly indicating that
quantification is over usual individuals and not Kinds. I'd say that {da
poi du} would do that (or {da poi zilmintu} if we want {du} to be
magic), as long as we ignore Kinds made from singletons.
You mention below "[not] just two levels of abstraction, concrete and
abstract, but lots and lots of levels with different degree of
abstraction"; could this mean more sorts? If so, what are you thinking
of? I guess you could have Kinds of Kinds, though maybe that's more
trouble than it's worth...
> > I think the answer has to be no, because it interferes with our usual
> > ideas of quantification. For example, if I have two children A and B, it
> > seems we would have to admit
> > mi rirni ci da .i je sa'e lo'i se rirni be mi cu du .abu ce by ce lo'e
> > se rirni be mi,
> > which is just silly.
>
> Right. Kinds aren't quantified together with their manifestations, and
> we rarely want to quantify over kinds of children, and especially in
> the panzi rather than the verba sense of "child".
>
> But that doesn't mean we never want to quantify over kinds. We should
> be able to say things like "I have two favourite desserts".
>
> > So we have to accept that {lo'e mulna'u du da} and {lo'e pemfinti cu
> > finti da poi pemci} are both false. This does seem to agree with English
> > bare plurals - "natural numbers are equal to something" and "poets write
> > some poems" are both false.
>
> Would you object to "natural numbers are equal to something (namely
> themselves)"
No, but I don't see how to analyse it with generics - I'd say that's
a clear case of quantification, i.e. that it's
{ro da poi mulna'u cu du de ne da}.
You can't say
"something (namely themselves) is/are equal to natural numbers"
(the problem isn't the pronoun position - you can say
"something (namely itself) is equal to any natural number"
)
> and "poets write some poems, but most poems are written by non-poets"?
I don't think 'poets' is a generic there, any more than 'non-poets' is.
> I wouldn't.
>
> > Secondly, there's the simple question of what *is* true of Kinds. This
> > doesn't seem to be seriously addressed by Carlson or his progeny, but we
> > have to address it.
> >
> > The non-commutativity example above narrows our options, but I see
> > nothing wrong with declaring:
> > lo'e broda cu brodi lo'e brodu
> > iff
> > the set { (x,y) | broda(x) /\ brodu(y) /\ brodi(x,y) } is Large in
> > { (x,y) | broda(x) /\ brodu(y) }
>
> But I want to be able to say "dogs have been known to eat carrots"
> even when the set { (x,y) | dog(x) /\ carrot(y) /\ eat(x,y) } does not
> seem to be Large in { (x,y) | dog(x) /\ carrot(y) }
Again, I don't think 'carrots' is a generic there.
Actually, doesn't it just mean
{se zgana lo nu su'o gerku su'o najgenja cu citka}?
If not, what did you mean by it and how would you like to Lojbanise it?
More generally, could you indicate (however vaguely) what you think the
truth conditions for {lo'e broda lo'e brodi cu brodu} should be?
> > where the Large subsets form a contextually defined filter - i.e. the
> > intersection of Large and Large is Large, and the empty set is not
> > Large.
> >
> > Working directly with the product like this avoids the non-commutativity
> > problems (failure of Fubini).
> >
> > Some predications will not be assigned a truth value (i.e. we don't
> > require the filter to be an ultrafilter); e.g. it would be reasonable
> > for {lo'e mulna'u cu mleca lo'e mulna'u} to be neither true nor false.
> > Similarly for {lo'e narmecmulna'u}.
> >
> > It's crucial that brodi was a basic predicate, not something involving
> > quantifiers, but that's fine.
> >
> > Problem: this doesn't give a natural translation of e.g. "poets write
> > poems". Under the above semantics, {lo'e pemfinti cu finti lo'e pemci}
> > is probably false, and so is {lo'e pemfinti cu finti su'o pemci}. {lo'e
> > pemfinti cu ckaji lo ka finti su'o pemci} would be true, but maybe
> > that's cheating.
> >
> > Thoughts?
>
> I think most of the problem is in getting levels of abstraction mixed
> up. (And by this I don't mean just two levels of abstraction, concrete
> and abstract, but lots and lots of levels with different degree of
> abstraction.)
Martin
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