On 7/26/07, Deborah MacPherson <debmacp@xxxxxxxxx> wrote:
> What "is not there" can be just as important as what is there.
> What mathematical system works without zeros and placeholders?
> "Nothing" merits a catagory.
> Deborah MacPherson
> On 7/25/07, Waclaw Kusnierczyk <Waclaw.Marcin.Kusnierczyk@xxxxxxxxxxx>
> > John F. Sowa wrote:
> > > Wacek,
> > >
> > > The question of how to or whether to represent a null value of
> > > some kind is a context-dependent issue about how to regularize
> > > the operators of some mathematical system.
> > >
> > > vQ> If you and me are just you and me, then nothing is nothing,
> > > > no entity at all, and not the empty set. You can well
> > > > interpret 'nothing' as a sheet of paper on which there is
> > > > no drawing, though there is the sheet -- how do such
> > > > interpretations help?
> > >
> > > The number 0, for example, simplifies the statements of many
> > > arithmetic principles. Similarly, the empty set simplifies
> > > many of the axioms of set theory. In lattices, the bottom
> > > symbol simplifies many axioms. In a Boolean lattice, the
> > > bottom corresponds to a proposition that is always false;
> > > such a proposition doesn't say anything useful, but it makes
> > > it possible to formulate the axioms more systematically.
> > >
> > > For some mathematical structures, a null value has no useful
> > > role. In most versions of mereology, for example, there is
> > > no empty part. An atom in mereology is defined to be something
> > > that has no part other than itself. In such systems, the word
> > > 'nothing' is just a way of saying 'no thing'. Unlike the empty
> > > set, which is assumed to exist in set theory, the word 'nothing'
> > > (or a formal symbol that represents it) would be a way of saying
> > > "It is false that there exists an x such that..."
> > >
> > > In short, the concept of 'nothing' or a 'null value' depends
> > > on the operations needed to regularize some system.
> > No doubt here. I thought we were talking about ontology there, and
> > interpreting 'nothing' as denoting the empty set (an entity in itself)
> > does not seem correct to me. Of course, you may build a mathematical
> > model of reality in which nothing is modelled as the empty set (and the
> > empty set is modelled as the set composed of the empty set), and such a
> > model may be used to interpret sentences containing the word 'nothing'.
> > But I do not see how "''nothing'', or
> > ''nonentity'' or ''nonbeing'', interpreted as the empty set, is another
> > ontological category."
> > vQ
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Paola Di Maio
School of IT
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