Axiomatic Set Theory and Self-Asserted Self-Awareness
November 2nd, 2008, search relatedRelated posts :: Awareness :: Axiomatic Set Theory and Self-Asserted Self-Awareness :: The Collision of Fact and Principle? :: The Collision of Facts and Axioms
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)
Set membership and inclusion are complementary features of what a set is.
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).
Thus your analysis fails if you insist on using the empty set to represent
nothing(ness). Thus set theoretic representation fails to work with the
philosophical concept of nothing(ess).
regards
michaelP
