Deborah MacPherson wrote:
> What "is not there" can be just as important as what is there.
> What mathematical system works without zeros and placeholders? (01)
How does it relate to the point? Of course, a mathematical system may
use zeros or whatever to model nothing -- to say that there is nothing
somewhere there. But this is not making nothing something; it is the
zero in the system which is something. (02)
If you think of ontological categories as elements of synthetic (perhaps
abstract) models, then of course you may have the category 'nothing',
which is the zero, th empty set, whatever. If you think of ontological
categories as kinds (concepts, classes, universals, whatever your view
here) of entities that exist in reality, then 'nothing' is no category,
since there exist no nothings. (03)
It seems to me that you, John, and some others support the former
interpretation of 'ontological category'. Then I agree with you. I
thought Azamat was using the other sense, and hence my objection. (04)
> "Nothing" merits a catagory.
> Deborah MacPherson
> On 7/25/07, Waclaw Kusnierczyk <Waclaw.Marcin.Kusnierczyk@xxxxxxxxxxx> wrote:
>> John F. Sowa wrote:
>>> 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."
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Wacek Kusnierczyk (07)
Department of Information and Computer Science (IDI)
Norwegian University of Science and Technology (NTNU)
Sem Saelandsv. 7-9
tel. 0047 73591875
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