Bunches
On 11/27/05, John E Clifford <clifford-j@sbcglobal.net> wrote:
> --- Jorge LlambÃas <jjllambias@gmail.com> wrote:
> > I was thinking of special abstract things like
> > the number seven.
> > Any kind of seven is seven, at least from some
> > point
> > of view.
>
> I don't think I follow this. The number seven is
> a kind in that there is a natural seven and a
> rational one and a real one and so on,
That's why I hedged "at least from some point of view".
If natural sevens, rational sevens and real sevens are
different kinds of sevens, then obviously sevens are not
an ultimate kind.
> but that
> seems to be breaking down in ultimate kinds,
> pretty much any way you extend the list.
I'm not sure that if sevens can differ like that then
natural sevens won't in turn be able to differ in some other
way, but it doesn't really matter.
> And of
> course anything is some subkind is also a thing
> of the kind itself. So I have missed the point
> here.
The point was that the restriction "every bunch breaks down
completely into individuals" for the system of bunches is an
independent restriction of all the other thesis listed, it doesn't
follow from them but must be imposed. There are systems
where it need not hold.
(I said that whereas it may be the case that *some* kinds
might break down completely into ultimate kinds, not all kinds
do. "Sevens" or "naturals sevens" *might* be an example of
ultimate kinds, or perhaps there are no ultimate kinds, depending
on your point of view. But whether or not sevens or natural sevens
are ultimate kinds, not all kinds break down completely into ultimate
kinds.)
> ("kind" is ambiguous between
> intensional and extensional versions; I suppose
> you mean this as inrtensional).
Yes.
> In any case, the
> fact that it can be divide indefinitely only
> complicates the claim that we always get to the
> bottom; it does not deny it.
You can impose it as an additional condition, but it does
not follow from the rest of the thesis.
> At the bottom level, the next lowest kind has
> only individuals as subkinds, each "one of a
> kind."
That is, if you assume there is a bottom level.
> But some might object to taking
> individuals as kinds. In that case the lowest
> kinds would have no subkinds and so are the
> sought lowest level into which the kind divides.
> I gather I am still missing your point.
My point is that you need not assume a bottom level.
> > The natural numbers greater than one follow the
> > same rules
> > as bunches, with "+" being the product and "in"
> > being "is a divisor of".
> > Then the primes are the individuals and "every
> > bunch breaks down
> > completely into individuals". Kinds are more
> > like the real numbers.
>
> I do hope this is true, relative consistency
> proofs using set theory are always a bit chancey.
> But I still don't get the kinds claim: it would
> seem that every number is then "in" every other
> and so there are no individuals.
Well, I was keeping the "greater than one" restriction, so
every number is "in" every number greater than or equal to
itself. And indeed this is an example where there are no
individuals, there is no bottom level.
mu'o mi'e xorxes