A "set" per se is not an intelligble entity. A set must always be named.

The "name" of a set is always of a familiar, general form of a cluster,
arrangement or aggregate; for example, a "bouquet" of flowers.

A flower arrangement is not a set of flowers.

It would seem, therefore, that as the name of a set always references a
general form, the members of that named form or set cannot be
particulars. It would not then, be right to define numbers in terms of
set membership if numbers are particular (Platonic) forms.

A flower arrangement is not a set of flowers.
A war is not a set of battles.
A machine is not a set of parts.
A school is not a set of students.
A family is not a set of people.

The whole is more than the set of its parts.

A flower arrangement is not a set of flowers.
A war is not a set of battles.
A machine is not a set of parts.
A school is not a set of students.
A family is not a set of people.

The whole is more than the set of its parts.

On Sat, 26 Apr 2008, J Jones wrote:

A "set" per se is not an intelligble entity. A set must always be named.

The "name" of a set is always of a familiar, general form of a cluster,
arrangement or aggregate; for example, a "bouquet" of flowers.

A flower arrangement is not a set of flowers.
A war is not a set of battles.
A machine is not a set of parts.
A school is not a set of students.
A family is not a set of people.

The whole is more than the set of its parts.

It would seem, therefore, that as the name of a set always references a
general form, the members of that named form or set cannot be
particulars. It would not then, be right to define numbers in terms of
set membership if numbers are particular (Platonic) forms.

Riddle of the day. How come that member got into this set twice?

The whole is more than the set of its parts.

Yes, but the name of the emergent whole is the name of the set.

J Jones schrieb:
The whole is more than the set of its parts.

Yes, but the name of the emergent whole is the name of the set.


In ZFC sets do not have names. Because of the axiom of
extensionality there is no place for names. This is
a fact on the object level. Example:

The set named "anna", anna = {1,2,3}
The set named "bert", bert = {1,2,3}

Although the names are different, the sets are the same.

But in FOL we can have variables, and thus name sets.
Different variables are different, but they might refer
to the same set. This is a fact on the meta level. Example:

The set named "anna", anna = {1,2,3}
The set named "bert", bert = {1,2,3}

Although the sets are the same, the names are different.

All I can say is that you have shown that ZFC has changed the meaning of
the word set without knowing that it has changed it.

If the mathematical word 'set' is not the same as the common word 'set',
then what word does the mathematician use when talking about real-life
sets?

Or is mathematics not applicable to real life?

Similarly, if mathematics invents and uses only lines that can't exist,
then where is the applicability of mathematics?

Boolean algebra is a confluence of meaningless signs until it is hooked
up to an empirical situation.

J Jones schrieb:
All I can say is that you have shown that ZFC has changed the meaning
of the word set without knowing that it has changed it.

Yes the mathematical word "set" is not the
same as the common word "set".

Similar a mathematical line is an abstract object
that does not exist in reality. There is no
pen in reality that can draw a line as mathematics
defines it.

Because there is no pen only one point wide and
this will yield in a dimension-1 object. The
stroke of a pen will always occupy some area,
and thus be a dimension-2 object.

Best Regards

If the mathematical word 'set' is not the same as the common word 'set',

then what word does the mathematician use when talking about real-life
sets? Or is mathematics not applicable to real life?

Similarly, if mathematics invents and uses only lines that can't exist,
then where is the applicability of mathematics?

On Apr 30, 11:17 am, J Jones <jonescard...@aol.com> wrote:

If the mathematical word 'set' is not the same as the common word 'set',
then what word does the mathematician use when talking about real-life
sets?

Probably ordinary words such as 'set', 'collection', 'class', 'group
of', etc. That there is a special sense of 'set' in a field of study
does not preclude our also using that word outside the field of study.

Or is mathematics not applicable to real life?

Similarly, if mathematics invents and uses only lines that can't exist,
then where is the applicability of mathematics?

Among the practical uses is providing paradigmatic versions of
empirical situations, abstracting from the empirical particulars to
serve as the basis for calculations and predictions of empirically
observed events. You know this; even as you use technology spurred by
developments in abstract mathematics. A Boolean algebra, e.g., is an
abstract mathematical object, but that it is abstract doesn't stop us
from applying the concepts for practical use. You already know that,
so I wonder why you even ask this question.

MoeBlee

J Jones schrieb:
If the mathematical word 'set' is not the same as the common word 'set',

Hope this is nothing new to you!

then what word does the mathematician use when talking about real-life
sets? Or is mathematics not applicable to real life?

The same words, when he is talking to his customers.
pharao: pyramid
geometer: pyramid
But when in his tent, he will mentally transform the edifice into ?@#%!
And also call it pyamid.

Similarly, if mathematics invents and uses only lines that can't
exist, then where is the applicability of mathematics?

pharao: how many blocks do I need to build the pyramid
geometer: *approximately* 100'000 blocks

The $%^& signs he uses are meaningless untill they are associated with
the everyday term pyramid.