What makes something 'empty'?

What makes something 'empty'? Here's a bunch of bananas. A "bunch" of
bananas is a particular type of set of bananas.

I then eat all the
bananas. Which of these describes my now "empty set"?

1. The bunch is "empty".

2. The bunch of bananas has the property of "emptyness".

3. There is no bunch of bananas.

None of the above offers a coherent description of emptyness as it
pertains to a set, because:

1. is a contradiction on its own terms,

2. is unintelligible without a definition of 'empty property',

3. is barely intelligible in this context. It can only mean that if no
bunch of bananas is an 'empty' set then 'empty' must refer to a
container which holds the bananas. No container is proffered or suggested.

On 5 Jun, 22:37, John Jones <jonescard... at (no spam) aol.com> wrote:

What makes something 'empty'? Here's a bunch of bananas. A "bunch" of
bananas is a particular type of set of bananas.

Isn't "a particular type of set of" bananas anything but "a set",
namely the set of bananas?

I then eat all the
bananas. Which of these describes my now "empty set"?

1. The bunch is "empty".

Well, maybe your set of bananas is now 'empty'; that is, 'an "empty"
set of bananas' is "zero bananas", while it is not 'the-empty-set'
which sort of "zero" tout-court, so quite another notion.

2. The bunch of bananas has the property of "emptyness".

You could maybe say "it is 'empty'", still why strech terminology?

3. There is no bunch of bananas.

That is? Otherwise, ditto.



None of the above offers a coherent description of emptyness as it
pertains to a set, because:

1. is a contradiction on its own terms,

Is it really?

2. is unintelligible without a definition of 'empty property',

That I can understand, otherwise how to put "empty" into 'empty'?

3. is barely intelligible in this context. It can only mean that if no
bunch of bananas is an 'empty' set then 'empty' must refer to a
container which holds the bananas. No container is proffered or suggested.

The very moment you say "I finished my bananas", you are the
container.

-LV

None of the above offers a coherent description of emptyness as it
pertains to a set, because [...]

On 5 Jun, 22:37, John Jones <jonescard... at (no spam) aol.com> wrote:
Here's a bunch of bananas.

On 5 Jun, 22:37, John Jones <jonescard... at (no spam) aol.com> wrote:
What makes something 'empty'? Here's a bunch of bananas. A "bunch" of
bananas is a particular type of set of bananas.

Isn't "a particular type of set of" bananas anything but "a set",
namely the set of bananas?

I then eat all the
bananas. Which of these describes my now "empty set"?

1. The bunch is "empty".

Well, maybe your set of bananas is now 'empty';

that is, 'an "empty"
set of bananas' is "zero bananas", while it is not 'the-empty-set'
which sort of "zero" tout-court, so quite another notion.

2. The bunch of bananas has the property of "emptyness".

You could maybe say "it is 'empty'", still why strech terminology?

3. There is no bunch of bananas.

That is? Otherwise, ditto.

None of the above offers a coherent description of emptyness as it
pertains to a set, because:

1. is a contradiction on its own terms,

Is it really?

2. is unintelligible without a definition of 'empty property',

That I can understand, otherwise how to put "empty" into 'empty'?

3. is barely intelligible in this context. It can only mean that if no
bunch of bananas is an 'empty' set then 'empty' must refer to a
container which holds the bananas. No container is proffered or suggested.

The very moment you say "I finished my bananas", you are the
container.

ju... at (no spam) diegidio.name wrote:
On 5 Jun, 22:37, John Jones <jonescard... at (no spam) aol.com> wrote:
What makes something 'empty'? Here's a bunch of bananas. A "bunch" of
bananas is a particular type of set of bananas.

Isn't "a particular type of set of" bananas anything but "a set",
namely the set of bananas?

A set is always of a particular type. You can't have merely 'a set of
bananas' - no-one knows what that is.
A set is a generic name for particular sets.

I then eat all the
bananas. Which of these describes my now "empty set"?

1. The bunch is "empty".

Well, maybe your set of bananas is now 'empty';

How can a bunch be empty? That was my point. A bag can be empty. But a
bag signifies another object. An 'empty' set confuses an arrangement
with a container.

that is, 'an "empty"
set of bananas' is "zero bananas", while it is not 'the-empty-set'
which sort of "zero" tout-court, so quite another notion.

2. The bunch of bananas has the property of "emptyness".

You could maybe say "it is 'empty'", still why strech terminology?

Because saying it has the property of emptyness holds out more hope of
being an intelligible description. I can't attach any meaning to an
empty bunch unless we confuse an arrangement with a container.

3. There is no bunch of bananas.

That is? Otherwise, ditto.

None of the above offers a coherent description of emptyness as it
pertains to a set, because:

1. is a contradiction on its own terms,

Is it really?

A bunch signifies at least a positive number, yet the number of bananas
is zero.

2. is unintelligible without a definition of 'empty property',

That I can understand, otherwise how to put "empty" into 'empty'?

3. is barely intelligible in this context. It can only mean that if no
bunch of bananas is an 'empty' set then 'empty' must refer to a
container which holds the bananas. No container is proffered or suggested.

The very moment you say "I finished my bananas", you are the
container.

Yes but that presupposes that the bananas are still with us only in
another description. In other words it amounts to a denial that we can
remove something.

What makes something 'empty'? Here's a bunch of bananas. A "bunch" of
bananas is a particular type of set of bananas. I then eat all the
bananas. Which of these describes my now "empty set"?

1. The bunch is "empty".
2. The bunch of bananas has the property of "emptyness".
3. There is no bunch of bananas.

None of the above offers a coherent description of emptyness as it
pertains to a set, because:

1. is a contradiction on its own terms,
2. is unintelligible without a definition of 'empty property',
3. is barely intelligible in this context. It can only mean that if no
bunch of bananas is an 'empty' set then 'empty' must refer to a
container which holds the bananas. No container is proffered or suggested.

ju... at (no spam) diegidio.name wrote:
On 6 Jun, 20:35, John Jones <jonescard... at (no spam) aol.com> wrote:
A set is always of a particular type. You can't have merely 'a set of
bananas' - no-one knows what that is.
A set is a generic name for particular sets.

I have then qualified that notion. My point there is simply that I
don't need "types" for your riddle as the U set for reference is quite
enough to avoid any of those foundational problems.

A U (universal) set inherits the same problem as an empty set. Both a
universal set and an empty set treat particular arrangements as if they
were containers. A bunch is not a container, a set that encompasses
other sets does not enfold or contain them.

I then eat all the
bananas. Which of these describes my now "empty set"?
1. The bunch is "empty".
Well, maybe your set of bananas is now 'empty';
How can a bunch be empty? That was my point. A bag can be empty. But a
bag signifies another object. An 'empty' set confuses an arrangement
with a container.

Ok, maybe now I get it. Indeed, the paradoxical nature of coformality
(as I would put it), based on the empty coclass, is in the
formalization of that dual nature of sets: the whole is more than the
sum of its parts.

It is the dual nature of sets (treating a type of arrangement and a
container as being equivalent)that brings us confusions:

Wholes and parts can't yield a dual nature. They are not aspects of
anything. If we declare wholes and parts to be aspects of something then
they must have a common property. But wholes and parts have no common
properties between them.

A whole and a part are independent of each other. A whole is not a
summation of parts. A whole emerges antecedently from its parts.

A bunch signifies at least a positive number, yet the number of bananas
is zero.

If we start counting from zero, all the structure simplifies. You are
here confusing the informal and linguistical usage of 'bunch' with a
formal theory on 'sets' and related notions.

A consistent and formal set theory can STILL stumble at the point where
it is applied to the world if, for example, that whole formal system
fails to distinguish between arrangements and containers. A failure to
acknowledge shortcomings in particular applications, in either worldly
or technical domains, can't be good for the discipline.

Similarly, you use

"emptyness" improperly exactly because it is a term of philosophy,
already and maybe not only.

I'm doing a bit of philosophy, but its technical terms are a bugbear
that I avoid wherever possible. Thank god there aren't too many. The
tradition of plain speaking is an old one, the Greeks, Nietszhe and
Wittgenstein to mention a few, spoke plainly. Technical terms are only
ellipses for a set of instructions or plain meanings. The danger is that
technical terms can become reified.

2. is unintelligible without a definition of 'empty property',
That I can understand, otherwise how to put "empty" into 'empty'?
3. is barely intelligible in this context. It can only mean that if no
bunch of bananas is an 'empty' set then 'empty' must refer to a
container which holds the bananas. No container is proffered or suggested.
The very moment you say "I finished my bananas", you are the
container.
Yes but that presupposes that the bananas are still with us only in
another description. In other words it amounts to a denial that we can
remove something.

In a sense that is the case, although unlimited in principle.

I didn't want to include anything in a bunch of bananas that wasn't
specifically mentioned. Except where technical terms are employed,
propositions are plainly presented, they are plain speaking - what you
see is all you get.
I don't want or need to consider the role of eyebrows before talking
about the eye of God.

In sci.logic, John Jones
jonescard... at (no spam) aol.com
 wrote
on Thu, 05 Jun 2008 22:37:55 +0100
g29mb1$av... at (no spam) aioe.org>:





What makes something 'empty'? Here's a bunch of bananas. A "bunch" of
bananas is a particular type of set of bananas. I then eat all the
bananas. Which of these describes my now "empty set"?

1. The bunch is "empty".
2. The bunch of bananas has the property of "emptyness".
3. There is no bunch of bananas.

None of the above offers a coherent description of emptyness as it
pertains to a set, because:

1. is a contradiction on its own terms,
2. is unintelligible without a definition of 'empty property',
3. is barely intelligible in this context. It can only mean that if no
bunch of bananas is an 'empty' set then 'empty' must refer to a
container which holds the bananas. No container is proffered or suggested.

I'll admit I have no idea how one would model your considerations
in logic, apart from some rather pedantic observations.

[1] The bunch of bananas includes connective wood
-- for lack of a better term -- which connects the
bananas together on the tree or in the store.  When the
insides of the bananas are eaten, the wood is generally
discarded, usually as part of the last banana peel.
The peels are discarded as well [*], which for bananas is
standard procedure (as opposed to, say, apples or pears).
Admittedly, most people, when confronted with this little
piece of wood, would not think in such terms.

[2] I make a distinction between an empty property-list
(a list with no properties) and a property-list with an
"empty" entry.  Neither one makes much sense in this case,
though.

[3] is true enough, except for that little piece of wood,
which in this case is a bit of an accident anyway.

Best I can do is:

bunch of bananas = wood + banana skins + stuff that comes
out later after the banana flesh is digested

I should also point out that it's not your empty set;
it's *the* empty set.  Briefly put, A != B if there's an
element in A that's not in B, or vice versa; since, if
both A and B are empty, neither A nor B has any elements,
they are of necessity equal.

Of course one might quibble as to whether one can have an
empty set of bananas versus an empty set of cars, depending
on whether one's discussing shopping cart or car carrier,
but sets are rather abstract notions anyway.

[*] a generally good idea, AFAIK, as they are laden with
pesticide residue, unless someone knows something about
pesticide-free bananas out there.

--
#191, ewi... at (no spam) earthlink.net
Useless C++ Programming Idea #7878218:
class C { private: virtual void stupid() = 0; };
** Posted fromhttp://www.teranews.com**

In sci.logic, ju... at (no spam) diegidio.name
ju... at (no spam) diegidio.name
 wrote
on Sat, 7 Jun 2008 14:07:40 -0700 (PDT)
cb0814bb-bc76-40de-a680-34b745e16... at (no spam) 8g2000hse.googlegroups.com>:

On 7 Jun, 03:18, The Ghost In The Machine
ew... at (no spam) sirius.tg00suus7038.net> wrote:
In sci.logic, John Jones
jonescard... at (no spam) aol.com
 wrote
on Thu, 05 Jun 2008 22:37:55 +0100
g29mb1$av... at (no spam) aioe.org>:

What makes something 'empty'? Here's a bunch of bananas. A "bunch" of
bananas is a particular type of set of bananas. I then eat all the
bananas. Which of these describes my now "empty set"?

1. The bunch is "empty".
2. The bunch of bananas has the property of "emptyness".
3. There is no bunch of bananas.

None of the above offers a coherent description of emptyness as it
pertains to a set, because:

1. is a contradiction on its own terms,
2. is unintelligible without a definition of 'empty property',
3. is barely intelligible in this context. It can only mean that if no
bunch of bananas is an 'empty' set then 'empty' must refer to a
container which holds the bananas. No container is proffered or suggested.

I'll admit I have no idea how one would model your considerations
in logic, apart from some rather pedantic observations.

[1] The bunch of bananas includes connective wood
-- for lack of a better term -- which connects the
bananas together on the tree or in the store.  When the
insides of the bananas are eaten, the wood is generally
discarded, usually as part of the last banana peel.
The peels are discarded as well [*], which for bananas is
standard procedure (as opposed to, say, apples or pears).
Admittedly, most people, when confronted with this little
piece of wood, would not think in such terms.

[2] I make a distinction between an empty property-list
(a list with no properties) and a property-list with an
"empty" entry.  Neither one makes much sense in this case,
though.

[3] is true enough, except for that little piece of wood,
which in this case is a bit of an accident anyway.

Best I can do is:

bunch of bananas = wood + banana skins + stuff that comes
out later after the banana flesh is digested ;-)

In this list you indeed miss the one who is carrying them, who is
gonna eat them, and who is gonna count them back. That is "the bunch".

Well, that's an interesting subpoint, to be sure; of course
one can make adjustments:

bunch of bananas + eater = wood + banana skins +
satisfied eater + stuff that comes out later

That's one of the three; dunno how precisely to model
the other two without introducing more symbolism.  This
is admittedly a vast oversimplification anyway, as
there are also considerations as airborne oxygen, carbon
dioxide, urine, water, sweat, the potassium in the
banana flesh, etc.





-LV

I should also point out that it's not your empty set;
it's *the* empty set.  Briefly put, A != B if there's an
element in A that's not in B, or vice versa; since, if
both A and B are empty, neither A nor B has any elements,
they are of necessity equal.

Of course one might quibble as to whether one can have an
empty set of bananas versus an empty set of cars, depending
on whether one's discussing shopping cart or car carrier,
but sets are rather abstract notions anyway.

[*] a generally good idea, AFAIK, as they are laden with
pesticide residue, unless someone knows something about
pesticide-free bananas out there.

--
#191, ewi... at (no spam) earthlink.net
Useless C++ Programming Idea #7878218:
class C { private: virtual void stupid() = 0; };
** Posted fromhttp://www.teranews.com**

--
#191, ewi... at (no spam) earthlink.net
Useless C/C++ Programming Idea #1123133:
void f(FILE * fptr, char *p) { fgets(p, sizeof(p), fptr); }
** Posted fromhttp://www.teranews.com**

In sci.logic, ju... at (no spam) diegidio.name
ju... at (no spam) diegidio.name
 wrote
on Sat, 7 Jun 2008 13:58:46 -0700 (PDT)
76a59b69-e0e1-4c9f-b6bc-269682d1d... at (no spam) k13g2000hse.googlegroups.com>:

On 7 Jun, 14:18, John Jones <jonescard... at (no spam) aol.com> wrote:
ju... at (no spam) diegidio.name wrote:
On 6 Jun, 20:35, John Jones <jonescard... at (no spam) aol.com> wrote:
A set is always of a particular type. You can't have merely 'a set of
bananas' - no-one knows what that is.
A set is a generic name for particular sets.

I have then qualified that notion. My point there is simply that I
don't need "types" for your riddle as the U set for reference is quite
enough to avoid any of those foundational problems.

A U (universal) set inherits the same problem as an empty set. Both a
universal set and an empty set treat particular arrangements as if they
were containers. A bunch is not a container, a set that encompasses
other sets does not enfold or contain them.

Now I can see you are just playing with words, and I must tell you:
this is not philosophy either. If you are interested in mathematics,
stop playing with words and try to put your thoughts into formulas.

And the difference between a word and a symbol in a formula
is ... ?

One of the tougher problems in mathematics is not a problem
at all, but the setup of a problem, the finding of the
right formulas to solve a problem that is initially given
in English.  As an example:

A bridge is able to hold 200 pounds weight.  A 198-pound
individual carrying a sack of 3 1 pound pumpkins wants to
cross the bridge.  How should he do it?

It turns out the answer of juggling the pumpkins doesn't
work, as throwing a pumpkin into the air means the man
has to apply more force to the pumpkin than the pumpkin is
applying to him, and therefore more force gets transmitted
through the man's body to the bridge surface.

Assuming of course that the man is worried that 201 pounds
will actually collapse the bridge (most bridges and such
have a certain safety margin), the best answer is to
leave one of the pumpkins behind, cross, leave one or both
pumpkins behind (it doesn't matter as long as there's no
thief nearby), cross back, retrieve the pumpkin, cross a
third time, pick up the bag and move on.

Admittedly, no formula is involved here but you can see
problem setup/formulation is very important.  A lot of
word problems are easily solvable once one sees a "trick"
or gimmick:

   A man is being chased by a bear.  He runs 1 mile south,
   1 mile east, then 1 mile north, and is now back
   at his starting point.  What color is the bear?

Answer: white.  It's a polar bear and the man starts out
at the North Pole, describing a triangle with curved sides.
But the original problem is enthymemical in nature, not
specifying all of its assumptions -- one has to know that
polar bears inhabit the frozen North, and that the North
is frozen (Uranus would have some very interesting flora and
fauna, were it moved farther into the solar system without
changing its axial tilt).

Once one has in fact reduced the problem to a series of
formulas, one has to properly manipulate the symbols in
the formulas -- in other words, one has to understand the
language of math.  For example, one cannot make assumptions
such as

sqrt(2 + 3) = sqrt(2) + sqrt(3)
3^2 + 4^2 = (3+4)^2
1/2 + 1/3 = (1+1)/(2+3)

or "proofs" such as:

a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a + b) (a - b) = b(a - b)
Therefore a + b = b

(division by zero)

or nonsense such as

a + b/c)1023++xyzzy//[10

Don't get me wrong; I agree with you in general.  The
previous poster is making some strange assumptions -- one
of them being that sets are anthropomorphic.


I then eat all the
bananas. Which of these describes my now "empty set"?
1. The bunch is "empty".
Well, maybe your set of bananas is now 'empty';
How can a bunch be empty? That was my point. A bag can be empty. But a
bag signifies another object. An 'empty' set confuses an arrangement
with a container.

Ok, maybe now I get it. Indeed, the paradoxical nature of coformality
(as I would put it), based on the empty coclass, is in the
formalization of that dual nature of sets: the whole is more than the
sum of its parts.

It is the dual nature of sets (treating a type of arrangement and a
container as being equivalent)that brings us confusions:

The dual nature of sets does not bring anything, on the contrary it
expresses the inherent dual nature of foundational notions like
observables with observers. You have to grasp the nature of
coformality and intrinsic duality if you wanna really dive into
foundational mathematics. But again, your line of reasonning is not
even valid as a philosophy.

Wholes and parts can't yield a dual nature. They are not aspects of
anything. If we declare wholes and parts to be aspects of something then
they must have a common property. But wholes and parts have no common
properties between them.

Just playing with words. What are you exactly talking about? Can you
name it?

Confusion?

A whole and a part are independent of each other. A whole is not a
summation of parts. A whole emerges antecedently from its parts.

Nice, the whole comes before! And so where it comes from? And so, how
does it give birth to the parts? You just play with empty words. Try
give them substance.

It also depends on the whole, as well.  If one breaks a
rock into chunks, the whole is greater than the sum of the
chunks, even were one to locate them all and put them back
in the right order, unless one believes that nanosurfaces
can join together with any cohesion (an interesting notion
in materials science and suggested in Asimov's _Foundation_
trilogy at one point).  However, one can theoretically
disassemble an automobile and then put it back together
again.  It was even possible at one point to sell the
parts thereof for a *greater* amount than the entire car.
There's that pesky problem formulation issue again.

A bunch signifies at least a positive number, yet the number of bananas
is zero.

If we start counting from zero, all the structure simplifies. You are
here confusing the informal and linguistical usage of 'bunch' with a
formal theory on 'sets' and related notions.

A consistent and formal set theory can STILL stumble at the point where
it is applied to the world if, for example, that whole formal system
fails to distinguish between arrangements and containers. A failure to
acknowledge shortcomings in particular applications, in either worldly
or technical domains, can't be good for the discipline.

So you want a theory where that distinction is taken into account,
but! you don't think there is such a distinction to begin with. This
is called incongruency in logic, and stands for the fact that you are
actually saying nothing apart from the noise.

I'm confused here...why does one need arrangements and containers when
one already has sequenceable lists and sets?

Similarly, you use

"emptyness" improperly exactly because it is a term of philosophy,
already and maybe not only.

I'm doing a bit of philosophy, but its technical terms are a bugbear
that I avoid wherever possible. Thank god there aren't too many. The
tradition of plain speaking is an old one, the Greeks, Nietszhe and
Wittgenstein to mention a few, spoke plainly. Technical terms are only
ellipses for a set of instructions or plain meanings. The danger is that
technical terms can become reified.

As said, you are right: yours is not even philosophy, which is another
serious discipline, even more complex than math and logic if I can
dare say -- despite, and couldn't be otherwise, what happens in the
newsgroups.

2. is unintelligible without a definition of 'empty property',
That I can understand, otherwise how to put "empty" into 'empty'?
3. is barely intelligible in this context. It can only mean that if no
bunch of bananas is an 'empty' set then 'empty' must refer to a
container which holds the bananas. No container is proffered or suggested.
The very moment you say "I finished my bananas", you are the
container.
Yes but that presupposes that the bananas are still with us only in
another description. In other words it amounts to a denial that we can
remove something.

In a sense that is the case, although unlimited in principle.

I didn't want to include anything in a bunch of bananas that wasn't
specifically mentioned. Except where technical terms are employed,
propositions are plainly presented, they are plain speaking - what you
see is all you get.
I don't want or need to consider the role of eyebrows before talking
about the eye of God.

When you say "a bunch of bananas", you have said it already: a "bunch"
plus a "bananas". What you "want" is irrelevant, and nobody can really
talk about "the eye of God".

I'm still wondering what he wants to do with the bunch of
bananas.  Unless one is the size of an elephant or whale,
eating the entire bunch at once is a bit problematic.

-LV

--
#191, ewi... at (no spam) earthlink.net
Windows Vista.  Now in nine exciting editions.  Try them all!
** Posted fromhttp://www.teranews.com**

ju... at (no spam) diegidio.name wrote:
On 7 Jun, 14:18, John Jones <jonescard... at (no spam) aol.com> wrote:
ju... at (no spam) diegidio.name wrote:
On 6 Jun, 20:35, John Jones <jonescard... at (no spam) aol.com> wrote:
A set is always of a particular type. You can't have merely 'a set of
bananas' - no-one knows what that is.
A set is a generic name for particular sets.
I have then qualified that notion. My point there is simply that I
don't need "types" for your riddle as the U set for reference is quite
enough to avoid any of those foundational problems.
A U (universal) set inherits the same problem as an empty set. Both a
universal set and an empty set treat particular arrangements as if they
were containers. A bunch is not a container, a set that encompasses
other sets does not enfold or contain them.

Now I can see you are just playing with words, and I must tell you:
this is not philosophy either. If you are interested in mathematics,
stop playing with words and try to put your thoughts into formulas.

I'm deadly serious. A bunch is not a container. If you think that
eliminating the difference between sets and containers can be
accomplished in a formula, then I agree with you. But translating into
that sort of formalism restricts applicability.

It is the dual nature of sets (treating a type of arrangement and a
container as being equivalent)that brings us confusions:

The dual nature of sets does not bring anything, on the contrary it
expresses the inherent dual nature of foundational notions like
observables with observers. You have to grasp the nature of
coformality and intrinsic duality if you wanna really dive into
foundational mathematics. But again, your line of reasonning is not
even valid as a philosophy.

Wholes and parts can't yield a dual nature. They are not aspects of
anything. If we declare wholes and parts to be aspects of something then
they must have a common property. But wholes and parts have no common
properties between them.

Just playing with words. What are you exactly talking about? Can you
name it?

Fine

A whole and a part are independent of each other. A whole is not a
summation of parts. A whole emerges antecedently from its parts.

Nice, the whole comes before! And so where it comes from? And so, how
does it give birth to the parts? You just play with empty words. Try
give them substance.

An emergent property is a manifesting condition expressed in terms of
objects. Emergent properties like bouquets and cutlery emerge antecedent
to their parts (ie are independent of them). I'm fine with that. There's
no weirdism involved there.

A bunch signifies at least a positive number, yet the number of bananas
is zero.
If we start counting from zero, all the structure simplifies. You are
here confusing the informal and linguistical usage of 'bunch' with a
formal theory on 'sets' and related notions.
A consistent and formal set theory can STILL stumble at the point where
it is applied to the world if, for example, that whole formal system
fails to distinguish between arrangements and containers. A failure to
acknowledge shortcomings in particular applications, in either worldly
or technical domains, can't be good for the discipline.

So you want a theory where that distinction is taken into account,
but! you don't think there is such a distinction to begin with. This
is called incongruency in logic, and stands for the fact that you are
actually saying nothing apart from the noise.

woof

On 7 Jun, 14:18, John Jones <jonescard... at (no spam) aol.com> wrote:
ju... at (no spam) diegidio.name wrote:
On 6 Jun, 20:35, John Jones <jonescard... at (no spam) aol.com> wrote:
A set is always of a particular type. You can't have merely 'a set of
bananas' - no-one knows what that is.
A set is a generic name for particular sets.

I have then qualified that notion. My point there is simply that I
don't need "types" for your riddle as the U set for reference is quite
enough to avoid any of those foundational problems.

A U (universal) set inherits the same problem as an empty set. Both a
universal set and an empty set treat particular arrangements as if they
were containers. A bunch is not a container, a set that encompasses
other sets does not enfold or contain them.


Now I can see you are just playing with words, and I must tell you:
this is not philosophy either. If you are interested in mathematics,
stop playing with words and try to put your thoughts into formulas.

I then eat all the
bananas. Which of these describes my now "empty set"?
1. The bunch is "empty".
Well, maybe your set of bananas is now 'empty';
How can a bunch be empty? That was my point. A bag can be empty. But a
bag signifies another object. An 'empty' set confuses an arrangement
with a container.

Ok, maybe now I get it. Indeed, the paradoxical nature of coformality
(as I would put it), based on the empty coclass, is in the
formalization of that dual nature of sets: the whole is more than the
sum of its parts.

It is the dual nature of sets (treating a type of arrangement and a
container as being equivalent)that brings us confusions:


The dual nature of sets does not bring anything, on the contrary it
expresses the inherent dual nature of foundational notions like
observables with observers. You have to grasp the nature of
coformality and intrinsic duality if you wanna really dive into
foundational mathematics. But again, your line of reasonning is not
even valid as a philosophy.



Wholes and parts can't yield a dual nature. They are not aspects of
anything. If we declare wholes and parts to be aspects of something then
they must have a common property. But wholes and parts have no common
properties between them.


Just playing with words. What are you exactly talking about? Can you
name it?

A whole and a part are independent of each other. A whole is not a
summation of parts. A whole emerges antecedently from its parts.


Nice, the whole comes before! And so where it comes from? And so, how
does it give birth to the parts? You just play with empty words. Try
give them substance.

A bunch signifies at least a positive number, yet the number of bananas
is zero.

If we start counting from zero, all the structure simplifies. You are
here confusing the informal and linguistical usage of 'bunch' with a
formal theory on 'sets' and related notions.

A consistent and formal set theory can STILL stumble at the point where
it is applied to the world if, for example, that whole formal system
fails to distinguish between arrangements and containers. A failure to
acknowledge shortcomings in particular applications, in either worldly
or technical domains, can't be good for the discipline.


So you want a theory where that distinction is taken into account,
but! you don't think there is such a distinction to begin with. This
is called incongruency in logic, and stands for the fact that you are
actually saying nothing apart from the noise.

Similarly, you use

"emptyness" improperly exactly because it is a term of philosophy,
already and maybe not only.

I'm doing a bit of philosophy, but its technical terms are a bugbear
that I avoid wherever possible. Thank god there aren't too many. The
tradition of plain speaking is an old one, the Greeks, Nietszhe and
Wittgenstein to mention a few, spoke plainly. Technical terms are only
ellipses for a set of instructions or plain meanings. The danger is that
technical terms can become reified.


As said, you are right: yours is not even philosophy, which is another
serious discipline, even more complex than math and logic if I can
dare say -- despite, and couldn't be otherwise, what happens in the
newsgroups.



2. is unintelligible without a definition of 'empty property',
That I can understand, otherwise how to put "empty" into 'empty'?
3. is barely intelligible in this context. It can only mean that if no
bunch of bananas is an 'empty' set then 'empty' must refer to a
container which holds the bananas. No container is proffered or suggested.
The very moment you say "I finished my bananas", you are the
container.
Yes but that presupposes that the bananas are still with us only in
another description. In other words it amounts to a denial that we can
remove something.

In a sense that is the case, although unlimited in principle.

I didn't want to include anything in a bunch of bananas that wasn't
specifically mentioned. Except where technical terms are employed,
propositions are plainly presented, they are plain speaking - what you
see is all you get.
I don't want or need to consider the role of eyebrows before talking
about the eye of God.

When you say "a bunch of bananas", you have said it already: a "bunch"
plus a "bananas". What you "want" is irrelevant, and nobody can really
talk about "the eye of God".

-LV