Bunches
> On 11/27/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > I'm not sure that it will work out that there
> are
> > kinds that do not break down into subkinds.
> The
> > tendency to dichotomize is pretty strong
> after
> > all. I can't think of a real case, anyhow.
>
> 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, but that
seems to be breaking down in ultimate kinds,
pretty much any way you extend the list. And of
course anything is some subkind is also a thing
of the kind itself. So I have missed the point
here.
> More normal kinds can be refined indefinitely:
> dogs > fat dogs > fat ugly dogs > fat ugly dogs
> that bark > fat
> ugly dogs that bark at trees > ...
No, at a certain point you get down to
individuals and, although they can be specified
in a variety of ways, it is not clear that they
are new kinds ("kind" is ambiguous between
intensional and extensional versions; I suppose
you mean this as inrtensional). 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.
> > Of
> > course, this does require in some cases,
> taking
> > individuals as infima species (a hallowed
> > practice).
>
> Not sure what that means.
At the bottom level, the next lowest kind has
only individuals as subkinds, each "one of a
kind." 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.
> 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. But the bit
about every number being in every number tells me
that the characterization of kinds is incomplete,
for it is not in any sense fitting that every
kind should be a subkind of every kind. At
least, I don't know of a notion of kinds in which
this would happen. Still missing the point?