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Topic: Matheology § 223: AC and AMS
Replies: 102   Last Post: Apr 18, 2013 12:26 AM

 Messages: [ Previous | Next ]
 fom Posts: 1,968 Registered: 12/4/12
Re: Matheology § 223: AC and AMS
Posted: Mar 14, 2013 6:16 PM

On 3/14/2013 4:42 PM, WM wrote:
> On 14 Mrz., 22:28, fom <fomJ...@nyms.net> wrote:
>> On 3/14/2013 2:58 PM, Virgil wrote:
>>

>>> In article
>>
>>> If that is what Zermelo said then he was wrong to say it because one
>>> does not ever "union" elements, only sets.

>>
>> I want to say that is technically incorrect.

>
> Of course it is not. He defined, the elements of the set T are
> disjoint sets.

>>
>> Surprisingly, the original 1908 paper introduced
>> a union that simply takes a union across the
>> elements of the set.

>
> You do not understand. The elements that Zemelo speaks of are sets. I
> give you an example: For instance all subsets of |N are elements of P(|
> N).

Obviously, van Heijenoort has deceived all
of the English speaking people who depend
upon his translation:

"Set theory is concerned with a
domain B of individuals, which we
shall call simply objects and among
which are the sets."

"An object may be called a set if
and -- with a single exception
(Axiom 2) -- only if it contains
another object as an element."

Hmm... Now those *might* be attributable to
a poor translation or a misunderstanding
on my part. However,

"9. Likewise, for several sets M, N, R, ...
there always exists an intersection
D=[M, N, R, ...]. For if T is any set whose
elements are themselves sets, then according
to axiom III there corresponds to every object
x a certain subset T_x of T that contains all
those elements of T that contain x as element.
Thus it is definite for every x whether
T_x=T, that is, whether x is a common element
of all elements of T; if X is an arbitrary
element of T, all elements x of X for which
T_x=T are the elements of a subset D of X
that contains all these common elements. This
set D is called the intersection associated
with T and is denoted D(T). If the elements
of T do not possess a common element, D(T)=null,
and this is always the case if, for example,
an element of T is not a set or if it is the
null set."

So, what is the important phrase?

"... an element of T is not a set..."

As I said before, one becomes so accustomed
to thinking in terms of "pure sets" because
that is the modern practice (V=WF, I think).

It is because I pay attention to anything
where denotation is an issue that I am
so aware of Zermelo's domain description.

The 1908 paper reflects Frege more than
Russell. The formal argument for ignoring
denotations is probably in Quine's "Word
and Object". But, as that is "not mathematics"
most are not aware of how it may be
significant to the model theory of set
theory.

Date Subject Author
3/14/13 Alan Smaill
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 Virgil
3/14/13 fom
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 fom
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 fom
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 fom
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 Virgil
3/15/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom
3/17/13 Virgil
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 Virgil
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 fom
3/19/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 fom
3/19/13 Virgil
3/19/13 fom
3/19/13 Virgil
3/19/13 Virgil
4/17/13 Virgil
3/18/13 Virgil
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 Virgil
3/19/13 fom
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/18/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/19/13 fom
4/17/13 Virgil
4/18/13 fom
3/18/13 Virgil
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/18/13 Virgil
3/18/13 Virgil
3/16/13 Virgil
3/16/13 Virgil
3/17/13 fom
3/15/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/15/13 Virgil
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 Virgil
3/15/13 fom
3/15/13 fom
3/15/13 Virgil
3/15/13 fom
3/16/13 Virgil
3/14/13 Virgil
3/14/13 Virgil
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom