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On Thu, Nov 21, 2002 at 12:54:23PM +0000, Jorge Llambias wrote:
> la djorden cusku di'e
> > > {so'a} and {so'e} are clearly relative to {ro}, unless
> > > the keywords ("almost all", "most") are totally meaningless.
> > > It seems to me that they are necessarily less than ro, and
> > > also at least ro/2.
> >
> >As was being discussed on the wiki, this sort of way of looking at
> >things has issues for infinite sets. ro/2 can be ro in those cases.
>
> But then "almost all" and "most" will also be infinite.
Right, but they shouldn't be the same as "all" (or at least, in
english they aren't. I can't say "All numbers are divisible by
2"). So we can't consider them to be a fraction of ro, I don't
think, and we also can't consider "ro" to just be a cardinality
indicator when used as an outer quantifier.
> >I'd suggest viewing so'a and so'e as iterators along with ro. So,
> >while ro executes your propositional function for every x, so'a and
> >so'e execute for every x, but it should evaluate true for only every
> >N x's, and false for the rest.
>
> I suspect you meant to say something else there. so'a/so'e
> should evaluate true for an infinite number of cases when ro
> is infinite, so it can't be true for only a finite number of
> cases.
Right; and they also evaluate false for an infinite number of cases.
> You can't say either that for any finite subset it should evaluate
> as true for most of its members because for some selected
> subsets it will evaluate true for all members, for other
> selected subsets it will evaluate true for no members, etc.
I wasn't refering to a finite subset, just to the way the iteration
would work over the entire set. If I say {so'e namcu cu pilji lo
mulna'u li re}, I'm not really talking about how many namcu there
are which are pilji, but rather how many there are against the
background of numbers which aren't. So if we were to arrange the
elements in a particular order (in this case numerical order), and
then iterate over them, my function "it pilji lo mulna'u li re"
will be true every other time. (and there's an infinite number of
times).
I think this way of doing things can apply to ce'i actually without
requiring at least 100 elements. pace'i would mean that there is
an arrangement of the elements so that as you iterate over them you
hit 10 trues and then 90 falses, or any equivalent ratio. So if
there's only 10 elements, the arrangement where 1 is true and then
9 false will work.
> >[...]
> > > >3. CAhA, da'i, mu'ei etc.
> > >
> > > ka'e = su'omu'ei
> > > ca'a = <this>mu'ei
> > > nu'o = ka'e jenai ca'a
> > > pu'i = ?
> >
> >not {ka'e je ca'a}?
>
> With the above definition, that reduces to {ca'a}.
Actually with the way you give ka'e and ca'a, anything which ca'a
must also ka'e. So I don't see the problem. pu'i would just be
another way to say it (but you could've just said ca'a). However
I think bringing time tenses into this is neccesary.
> >Or perhaps nu'o as {pu naje ba ka'e} and pu'i as {pu je ba ka'e}?
>
> That brings in time, which should in principle be orthogonal
> to CAhA. I don't remember whether {pu na} meant "never in the
> past", or "at some point in the past, not".
I think the concept of "demonstrating" potential ("can and has")
really is about what has happened in the past.
These are probably a bit better though:
nu'o = pu ca'a naje ka'e
pu'i = pu ca'a je ka'e
On the point in the past thing, I think it means "it is false that
for some range of the past ...". I'd imagine "puze'e" gives you
the whole-past thing.
--
Jordan DeLong - fracture@hidden.email
lu zo'o loi censa bakni cu terzba le zaltapla poi xagrai li'u
sei la mark. tuen. cusku
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