The Difference between a Set and an Element

Mathematics distinguishes between set and element and the formalisms
has proven useful. However, there is nothing physical about a set. A
set is simply a collection of unique memembers. Since a set of one
element is legitimate. What is the physical difference between me and a
set containing me?

Again I am thinking in the context of AI and the idea of AI by 1000
rules:

http://en.wikipedia.org/wiki/Cyc

In Cyc, the two most important predicate are "is a" to denote
instance and "genls" to denote the subset and super set
relationship. Clearly the distinction is useful in mathematics but do
we generally think in terms of the difference between me and the set
containing me? Is it helpful for an AI system to treat the two
separately in all cases when in common English they are essentially the
same thing. Might we treat the mathematical version of "is a" and
the mathematical version of genls as subtypes of the common idea of X
being Y.

Perhaps there are more then one type of notion of subset and superset
but the common English version in this rare case is the more general
and abstract idea. As a consequence we can define rules in terms of
"is a"::(common English) and they will apply to more specific
concepts of these ideas. This is known as generic programming.

.

Relevant Pages

  • The Difference between a Set and an Element
    ... Mathematics distinguishes between set and element and the formalisms ... has proven useful. ... separately in all cases when in common English they are essentially the ... the mathematical version of genls as subtypes of the common idea of X ...
    (sci.logic)
  • Re: Multiplication of Reals and Zero in programming languages
    ... You are bandying words in the sense of common English, ... to apply them to mathematics. ... But you fail to give definitions. ... ideas you present are fuzzy, ...
    (sci.math)
Loading