Bunches
> On 11/28/05, John E Clifford
> <clifford-j@sbcglobal.net> wrote:
> > --- Jorge LlambÃas <jjllambias@gmail.com>
> wrote:
> > > 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.
> >
> > Ahah! Yes, I think that that is true, though
> I
> > don't think your remarks prove it.
>
> Well, I guess you would first need to present
> it as a fomal
> thesis before a formal proof that it is not a
> theorem could
> be given.
My point is that the system presented differs
from mine in more than the one axiom and so can't
prove independence of that axiom.
> > > > > 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".
> >
> > Well, it turns out they aren't. The model
> > disconfirms a+a=a at least.
>
> Hmm, right. To have that property, take all the
> powers of a prime
But your countercase is about the reals; what
would be the corresponding move there?
> For the case with no individuals you can take
> for example
> the open sets on the real line, with union as
> "+".
Nice; that does look to give a case that fits all
the theses so far developed except the foundation
one and what follows from it. But it still has
nothing to do with bunches which are conceptually
exactly founded in the way stated: a bunch is a
bunch of things and when you get down to the
things that is the end of the process (actually a
step before, since in some versions unit bunches
are the singleton of the thing, not the thing
itself — but the thing is a member, not in in
the relevant sense, which tends to be like
inclusion in these versions). Can you think if a
Lojbanically relevant use for kinds, those
unfounded critters?