SUO: *Date 09 Mar 2002 -- Set Theory
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I would like to note some of the finer points that are involved in the
axiom(s) of extent and the definition of a set that I quoted last time.
"Class" is an informal interpretive notion and remains
an unformalized intuitive notion from beginning to end.
A person could substitute, and people have substituted,
any other word for "class" -- "object" is one especial
favorite -- and the theory of sets tho' obscur'd would
not be affected in the slightest formal logical degree.
"Set" is from the very outset a relational concept.
The very idea of a set is defined by dint of a set
being in the membership relation to something else.
It is like the concept of an ancestor, a precedent.
If there is some "essence" to being a set, it does
not matter to set theory. To be a set, to possess
set-hood or to exemplify set-ness, is nothing less
than being an element or being a member, in effect,
a relational status, a membership in good standing.
Not entirely coincidentally, I would add,
this goes to say what is meant by "form".
It is my impression that the vast majority of the residual misgivings
that people continually exhibit with regard to this and other axioms
of set theory are due almost entirely to their misunderstanding of
the proper relationship between abstract forms, as they abide in
logical and mathematical realms, and concrete matters, as they
reside in physical reality.
"But tho' obscur'd, this is the form of the Angelic land."
http://www.blakearchive.org/cgi-bin/nph-1965/blake/erdman/erd/@Generic__BookTextView/5076
http://www.blakearchive.org/cgi-bin/nph-1965/blake/erdman/erd/@Generic__BookTextView/6037
Jon Awbrey
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