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. (01)
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'. (02)
But I do not see how "''nothing'', or
''nonentity'' or ''nonbeing'', interpreted as the empty set, is another
ontological category." (03)
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