"Anon."  wrote in message
news:bn3jkb$15nu$1{at}darwin.ediacara.org...
> John Edser wrote:
>
> > WA:-
> > Defining what is and is not an element of a set is among the most basic
> > aspects
> > of defining a set. To quote one math webpage:
> >
> > ======================================
> >
> > What is an element of a set? An element of a set A is a method which,
when
> > executed, yields a canonical element of A as result.
> >
> > When are two elements equal? Two elements a; b of a set A are equal if,
when
> > executed, they yield equal canonical elements of A as results.
> >
> > It is interesting to note that one cannot construct a set if (s)he does
not
> > know how to produce its elements
> >
> >    --www.math.unipd.it/~silvio/papers/TypeTheory.ps
> >
> >
> > JE:-
> > I disagree with noting in the above.
> > My point was: all the elements within one set are _mathematically_
> > equivalent. This equivalence has nothing to do with mathematics and
> > everything to do with a definitional process that lies outside
> > of mathematics. Godel's point was that propositions of mathematics
> > and propositions not of mathematics both exist, where mathematics
> > requires propositions from both. Within the set of fruit you can only
> > know that one element is a pear and not an apple by definition of what
> > each is.
>
> But you can get green apples and red apples, and both are apples, i.e.
> are members of the set of apples, but they are clearly not equivalent.
> They are also members of the sets of green and red fruit as well.  The
> fact that an an apple is green means that it is in the intersection of
> apples and green fruit.

Just to voice my *merely* profoundly percEPTive opinion on this discussion:

It is ultimately fruitless -- or, at least it *should* be realized that it
is.

All Edser says (underneath it all his lacklustre logic) is: "(1 unit
of)Fitness = (1 unit of) Fertility"; and vice versa.

That equation is not worth the electronic or wood-pulp paper it is written
on.

IOW, it falls *almost* completely flat! (I inserted "almost" only
because of
the thickness of ordinary writing paper.)

Yours only decEPTively joking,

P
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