Think of the empty set as an empty paper bag, potentially fillable and the
null set as an absent
but potential paper bag that can be fetched or introduced, although the
procedures vary by which
version and variety of Set Theory one uses and by which operations performed
with and on sets vary,
as per usual. The hierarchy of sets goes further than Michaelp mentions as
called sets, sub and
supersets or classes, families and groups, although nomenclature or jargon
varies. Beyond that we
have infinite set theory with even more curious game rules. Actually the
analogy of sets with
concepts is quite close. Except for words you'd have to introduce false and
imaginary sets but no
great problem. And beyond all that we have proof theory and all that, not
supposed to be
understandable by ordinary mortals. Self-awareness is a paradox which needs at
least IST. Or one
needs at least process philosophy. Where you kids been for boot camp?
Tuttut
adrian.
Joseph Polanik wrote:
> michaelP wrote:
>
> >Joe on nothing(ness):
>
> >>alternately, one can state this axiom in the jargon of AST: it is
> >>impossible to attribute predicates to a member of the empty set ---
> >>because there are no such members.
>
> >Joe, this has been traversed earlier: the empty set, [], is not
> >nothing, it is a set (which is something) and thus has the sense of
> >inclusion, a boundary; that it has no members does not mean it is
> >nothing. Nothing is not a set that contains nothing. The empty set is
> >very much a something. Indeed it is possible to do some elementary
> >arithmetic with just (structures of) empty sets, when natural numbers
> >are representable thusly:
>
> >0 = [] the empty set
>
> >1 = [[]] i.e., it has just one member (the empty set)
>
> >2 = [[[]], []] i.e., it has two members, 1 ( [[]] ) and 0 ( [] )
>
> >3 = [[[[]], []], [[]], []] i.e., it has three members, 2, 1 and 0
>
> >etc
>
> >the operations to simulate addition, subtraction, etc are just
> >relatively simple set operations (e.g., union, intersection,
> >difference, etc)
>
> this is a good example of using set theory to model some other domain.
> I'm doing that, too.
>
> >Set membership and inclusion are complementary features of what a set
> >is.
>
> set inclusion (membership) and exclusion are mutually exclusive and
> collectively exhaustive.
>
> >Thus you cannot represent nothing(ness) (which is neither a set nor
> >a member of a set: it is nothing) by a set or the member of a set (both
> >of which are somethings).
>
> what I'm doing is using the relation between a set and its members to
> model the relation between a word and its referents.
>
> the empty set is a real set; but, it has no members.
>
> similarly, 'nothing' is a real word; but, it has no referent.
>
> more specifically, let us consider a linguistic frame of reference in
> which 'being' is the root predicate.
>
> in symbolic terms, where P = being,
>
> the predicate logic version, (x)(Px), would be translated as 'for any x
> that is, x is a being'.
>
> the set theory version, (x !<- {})(Px), would be translated as 'for any
> x that is not a member of the empty set, x is a being'.
>
> in such a linguistic frame of reference, anything that is is a being;
> so, the word 'non-being' would not have any referents.
>
> * * *
>
> now, the relevance of these points to issues under discussion is simple:
> one may only attribute predicates to an x that is not a member of the
> empty set --- because there are no members of the empty set to which one
> may attribute predicates.
>
> hence, in saying "I am self-aware", I am attributing a predicate to the
> referent of 'I'. hence, I am not a member of the empty set. hence, (pick
> one) of:
>
> in a linguistic frame of reference with 'being' as its root predicate, I
> conclude that I am a being.
>
> in a linguistic frame of reference with 'reality' as its root predicate,
> I conclude that I am a reality.
>
> in a linguistic frame of reference with 'existent' as its root
> predicate, I conclude that I am an existent.
>
> Joe
>
>
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