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
--
Philosophy is, after all, done ultimately in the first person for the
first person. --- H-N Castaneda
@[EMAIL PROTECTED]@^@
http://what-am-i.net
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