  Mathematicians still use Naive Set Theory when generating sets without danger
of producing any contradiction. Therefore their working method can be
considered as a consistent inference system with an experience of over 100
years. My conjecture is that this method works well because mathematicians use
only those predicates to form sets, which yield closed hereditary consistent
predicate extensions. And for every open formula they use in the process of
constructing of a certain (special) set (bottom up), we can always find an
"almost-closed" formula (i.e. a parameter-free formula with only the free
variable "x") which yields the same certain (special) set as predicate
extension as constructed in the bottom up process before. Therefore the use of
predicates with free parameters in the Comprehension Scheme does not cause any
difficulties and can be "lifted" by meta-mathematical considerations.
  KEYWORDS: naive set theory, Quine, new foundation, NF, universal sets,
comprehension schema, predicate extension, philosophy of set theory, Zermelo,
Fraenkel, ZF, complement. CT is the Class-Theoretical frame: logic + "=" +
Church Schema + Extensionality Axiom.
