* Wednesday, 2011-08-24 at 19:12 -0300 - Jorge Llambías <jjllambias@gmail.com>:
> On Wed, Aug 24, 2011 at 12:41 PM, Martin Bays <mbays@sdf.org> wrote:
> > * Tuesday, 2011-08-23 at 22:04 -0300 - Jorge Llambías <jjllambias@gmail.com>:
> >>
> >> For me the strongest argument for context dependent individuals comes
> >> not so much from all this distributivity issue but from kinds/generic
> >> reference (bare plurals in English).
> >
> > Right. I've avoided mentioning these things, not wanting to take too
> > much mud with the water sample, but since you bring them up...
> >
> > I don't think generics can be treated as individuals on par with the
> > other individuals in our universe.
> >
> > Indeed, we would then have to have
> > {lo'e mulna'u cu du da poi namcu}.
>
> Yes... but only when "namcu" is predicated of the members of the set
> {integers, rationals, reals, ...}, not when it is predicated of the
> members of {0, 1, 2, ...}
There was a text-editing error there, sorry; "namcu" was meant to be
"mulna'u" in both cases.
> > But since generics are generic, we would also have
> > {ro da poi mulna'u zo'u lo'e namcu cu na du da},
I see now that you wouldn't have accepted this, even without the
mistake. See below.
> > a contradiction.
>
> "ro da poi mulna'u" strongly suggests a context where there are many
> integers (infinitely many, of course), not a context where integers
> are just one kind of numbers. In the latter context (a strange context
> because we don't usually apply the universal quantifier over singleton
> sets) what you have there is false.
> > So I don't see that {lo broda} can be interpreted as a generic while
> > holding on to the idea that the interpretation of {lo broda} is
> > determined by its set of referents.
>
> In my understanding, "lo broda" has a single referent in such cases.
>
> > I think {lo'e broda} has to be read as introducing a quantifier:
> > {lo'e broda cu brode} -> "for x a generic broda: brode(x)"
> > (the semantics of this quantifier being hazy and context-dependent).
> >
> > Note also that two such quantifiers generally won't commute (e.g.
> > for generic natural numbers n: for generic natural numbers m: n<m
> > holds,
>
> I would say "natural numbers are smaller than natural numbers" is
> questionable at least,
Actually, I think this can (just) work in English - "natural numbers are
bigger than natural numbers" has a generic reading which is true in
a way that "natural numbers are smaller than natural numbers" doesn't. Not
that it's the kind of thing you're likely to say.
> but easily fixed to: "natural numbers are
> smaller than other natural numbers". But then "natural numbers" and
> "other natural numbers" are not the same individual, and the second
> one is in some sense a derivative of the first.
>
> > but
> > for generic natural numbers m: for generic natural numbers n: n<m
> > does not), so if {lo'e broda} is allowed as a meaning for {lo broda}
> > then the idea that {lo broda} should be immune to scope issues has to be
> > dropped too...
>
> I would say "other natural numbers are larger than natural numbers" is
> fine as a restatement of "natural numbers are smaller than other
> natural numbers". Just slightly unusual because "other" has to look
> forward to determine other than what, but still acceptable.
>
> > (Assuming scoping works as with other quantifiers, we'd have
> > {lo'e narmecmulna'u lo'e narmecmulna'u cu mleca} but not
> > {lo'e narmecmulna'u lo'e narmecmulna'u cu se mleca}.)
> >
> > Do you have a cunning way out of this?
>
> Not really mine. Are you familiar with Carlson's "A Unified Analysis
> of the English Bare Plural"? I'm sure there must be more modern
> analysis of generic terms, but I like that one very much.
Thanks. I looked through that and some of its successors.
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.
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.
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.
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) }
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?
Martin
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