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".

-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**

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.

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.

ju... at (no spam) diegidio.name wrote:
On 7 Jun, 23:32, John Jones <jonescard... at (no spam) aol.com> wrote:
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.

I am actually saying the opposite. I am stating a duality intrinsic to
the concept of sets, containers, properties, formulas, cars, shoes,
and whatever you might want to name.

Then I'm at a loss to know what is meant by duality in this case.

Your "a bunch is not a container" I get as an attempt to reduce the
discussion to the notion of emergent properties by means of a
paradoxical formulation, as you show below. But there is no need for
paradoxes, unless to remind us of our own limits.

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

Fine what?

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.

You adopt a paradoxical formulation, where what emerges is what was
already there, and you are fine with that. So what the problem is? And
where is it? Is that weird even?

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

Does that mean you agree?

-LV

There is a distinction between arrangements and containers of course.

There's no need to worry about an emergent property arising 'antecdent'
to its parts. Any misdescription that is there will fall upon 'property'
and not on anything else. I will start a new post on it.

ju... at (no spam) diegidio.name wrote:

Duality is duality in any case. Then, from the universal (logical)
duality: observer-observable, observer-observed in observer-
observable, and so on.

At a lower level, a set is (has the property of being) an element, and
an element is a set, with some specific properties at the boundaries.
There is no relative primality between element and set, part and
whole.

The "more" that the whole is said to have can track down to the notion
of "putting things together", that is how a whole happens to be made
of parts, and of "such and such" specific parts actually. This is what
we might call "embedding", and it is supposed to be our dual basic
notion.

Indeed, I'd say we do not proceed by regressing to the boundaries. We
rather progress from the generic notion of embedding, and from there
we develop a (logical) universe where we start from the empty
universe, and so on, by preserving containment! The whole procedure is
exception-less, or correctness-preserving.

  -LV

The only big author to tackle this topic is Kant, though there are
others appearing now, like Mark Sacks. Kant spoke of the synthesis of
parts and the conditions required for the existence of objects. Kantian
ontology (transcendental idealism) is unique. He is the only author who
used the idea that objects require conditions for their manifestation -
in other words for Kant objects do not announce or support themselves.
For science and logic, objects do support themselves. Your talk of parts
dips into the Kantian menagerie. The relevant topic is transcendental
philosophy/logic. It's a relatively new topic since Kant. Seehttp://www.essex.ac.uk/philosophy/tpn/

On 7 Jun, 23:32, John Jones <jonescard... at (no spam) aol.com> wrote:
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.


I am actually saying the opposite. I am stating a duality intrinsic to
the concept of sets, containers, properties, formulas, cars, shoes,
and whatever you might want to name.

Your "a bunch is not a container" I get as an attempt to reduce the
discussion to the notion of emergent properties by means of a
paradoxical formulation, as you show below. But there is no need for
paradoxes, unless to remind us of our own limits.


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


Fine what?


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.



You adopt a paradoxical formulation, where what emerges is what was
already there, and you are fine with that. So what the problem is? And
where is it? Is that weird even?


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


Does that mean you agree?

-LV

Duality is duality in any case. Then, from the universal (logical)
duality: observer-observable, observer-observed in observer-
observable, and so on.

At a lower level, a set is (has the property of being) an element, and
an element is a set, with some specific properties at the boundaries.
There is no relative primality between element and set, part and
whole.

The "more" that the whole is said to have can track down to the notion
of "putting things together", that is how a whole happens to be made
of parts, and of "such and such" specific parts actually. This is what
we might call "embedding", and it is supposed to be our dual basic
notion.

Indeed, I'd say we do not proceed by regressing to the boundaries. We
rather progress from the generic notion of embedding, and from there
we develop a (logical) universe where we start from the empty
universe, and so on, by preserving containment! The whole procedure is
exception-less, or correctness-preserving.
-LV