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John Jones · Guest

The = sign doesn>t guarantee unreserved symmetry between expressions. It
can be a reminder or sign that is appended to one expression to show
that that expression is referencing another expression.

1) Taking the expression sq.rt4 = 2. Sq.rt4 refers to 2. 2 does not
refer to anything. 2 is the object itself. It is presented, we don>t
need to refer to it, it is there in front of us to use as we wish.

2) A = A (or A is equal to itself) is another asymmetric use of the =
sign. An object that references itself is not the object referenced by
another. Object properties are given by reference, but not by
self-reference.

herbzet · Guest

John Jones wrote:
[quote]
The = sign doesn>t guarantee unreserved symmetry between expressions. It
can be a reminder or sign that is appended to one expression to show
that that expression is referencing another expression.

1) Taking the expression sq.rt4 = 2. Sq.rt4 refers to 2. 2 does not
refer to anything. 2 is the object itself. It is presented, we don>t
need to refer to it, it is there in front of us to use as we wish.

2) A = A (or A is equal to itself) is another asymmetric use of the =
sign. An object that references itself is not the object referenced by
another. Object properties are given by reference, but not by
self-reference.
[/quote]
Hm.

======================
Just btw, when you say

An object that references itself is not the object referenced
by another

do you mean that in the expression 12 = 12, the object that references
itself is not the object referenced in the expression 12 = 3 * 4?

Or what exactly?

--
hz

John Jones · Guest

herbzet wrote:
[quote]
John Jones wrote:
The = sign doesn>t guarantee unreserved symmetry between expressions. It
can be a reminder or sign that is appended to one expression to show
that that expression is referencing another expression.

1) Taking the expression sq.rt4 = 2. Sq.rt4 refers to 2. 2 does not
refer to anything. 2 is the object itself. It is presented, we don>t
need to refer to it, it is there in front of us to use as we wish.

2) A = A (or A is equal to itself) is another asymmetric use of the =
sign. An object that references itself is not the object referenced by
another. Object properties are given by reference, but not by
self-reference.

Hm.

======================
Just btw, when you say

An object that references itself is not the object referenced
by another

do you mean that in the expression 12 = 12, the object that references
itself is not the object referenced in the expression 12 = 3 * 4?

Or what exactly?

--
hz
[/quote]

Does 12 reference itself in 12=12? Or does 12 reference 12? * (see note
at bottom) In either case, we see an asymmetric use of the = sign. In
the former case 12 is given in reference and self-reference, but in the
latter case it is given in reference and in presentation.

A number is presented or referenced, but I don>t think that
self-reference is a valid operation for a number. In self-reference an
object has no properties. In which case, 1) if a number is an object, a
number in self-reference reduces it to the general form of a number. But
if 2) a number is a property, then a number in self-reference isn>t a
number at all.

*(Normally, we would arrive at 12=12 at the end of a calculation to show
that 12 had been correctly referenced, as in the penultimate step
3x4=12. So 3x4 references 12, - it tells us how to find 12. Once found,
12 doesn>t reference anything.)

David C. Ullrich · Guest

On Sat, 25 Oct 2008 21:17:53 +0100, John Jones <jonescardiff@aol.com>
wrote:

[quote]The = sign doesn>t guarantee unreserved symmetry between expressions. It
can be a reminder or sign that is appended to one expression to show
that that expression is referencing another expression.

1) Taking the expression sq.rt4 = 2. Sq.rt4 refers to 2. 2 does not
refer to anything. 2 is the object itself. It is presented, we don>t
need to refer to it, it is there in front of us to use as we wish.
[/quote]
You>re never going to get anywhere with any of these deep
thoughts until you learn a few basic things. In another thread
those would be things like the definition of provability.
Here it>s the diference between 2 and "2". Possibly you
understand the difference - if so you should realize that
when you>re discussing this sort of thing you need to _say_
'"2"' when you mean '"2"'.

[quote]2) A = A (or A is equal to itself) is another asymmetric use of the =
sign. An object that references itself is not the object referenced by
another. Object properties are given by reference, but not by
self-reference.
[/quote]
David C. Ullrich

"Understanding Godel isn>t about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)

Peter Webb · Guest

[quote]when you>re discussing this sort of thing you need to _say_
'"2"' when you mean '"2"'.

[/quote]
I half suspect you were just looking for a way to use the character string
"'"2"'"

george · Guest

John Jones wrote:
[quote]The = sign doesn>t guarantee unreserved symmetry between expressions.
[/quote]
NOTHING creates symmetry between EXPRESSIONS.
It is THE SIGN that has symmetry. It is = ITSELF that *is*
symmetric.

[quote]I can be a reminder or sign that is appended to one expression to show
that that expression is referencing another expression.
[/quote]
It CAN>T avoid being PREpended to the "another" expression in THAT
context.
And whether you append or prepend fundamentally makes NO difference --
there
is no law requiring left (as opposed to right) to be "pre" or "first";
indeed a great
many languages OTHER than English do in fact do it the other way.

[quote]1) Taking the expression sq.rt4 = 2. Sq.rt4 refers to 2. 2 does not
refer to anything. 2 is the object itself. It is presented, we don>t
need to refer to it, it is there in front of us to use as we wish.
[/quote]
Since one of the uses we could wish is to remind people that it is
the
positive square root of 4, we CAN ALSO SAY 2=sqrt(4). THAT is because
*=* is symmetric. This has nothing to do with any preferred roles of
things
on the right as opposed to the left.

[quote]2) A = A (or A is equal to itself) is another asymmetric use of the = sign.
[/quote]
This article you just posted is another assholic use of public
stupidity.

[quote]An object that references itself is not the object referenced by
another.
[/quote]
But it STILL IS the object referenced by ITSELF, which, SYMMETRY being
what
we>re talking about here, IS a CONFIRMING example of symmetry.

[quote]Object properties are given by reference,
[/quote]
No, they>re not. You can refer to a thing without giving ANY of its
properties
other than the route by which it is referenced.

[quote]but not by self-reference.
[/quote]
In order to perceive the reference, you would have to HAVE ALREADY
BEEN
given SOME reference to the object. Whether that reference is or
isn>t self is something
you may OR MAY NOT be aware of. You have to EVALUATE the
reference. You have
to FOLLOW the reference.

The real asymmetry you are looking for involves evaluation, involves
getting closer
to some simpler or "normal" form. You need to google (or wiki) the
phrase
"rewrite rules". Believe it or not, for all your pretensions to
knowing enough to be
able to educate us (and they truly are pretense), YOU ARE NOT THE
FIRST person
to notice that = can be asymmetric. You are, perhaps, however, the
most incompetent.

Dan Christensen · Guest

On Oct 25, 4:17 pm, John Jones <jonescard...@aol.com> wrote:
[quote]The = sign doesn>t guarantee unreserved symmetry between expressions. It
can be a reminder or sign that is appended to one expression to show
that that expression is referencing another expression.

1) Taking the expression sq.rt4 = 2. Sq.rt4 refers to 2. 2 does not
refer to anything. 2 is the object itself. It is presented, we don>t
need to refer to it, it is there in front of us to use as we wish.

2) A = A (or A is equal to itself) is another asymmetric use of the > sign. An object that references itself is not the object referenced by
another. Object properties are given by reference, but not by
self-reference.
[/quote]

You are making this way too complicated with your "objects,"
"references," etc.

Formally, A=B just means that you can substitute string A for sting B,
and vice versa (taking into account any bracketing or precedence
conventions).

In your example, "sq.rt4 = 2" tells us that wherever we see "sq.rt4"
in a statement, we can substitute "2." And A=A is just a useful
identity. That>s how I look at it anyway.

Dan
Download my DC Proof software at www.dcproof.com

John Jones · Guest

george wrote:
[quote]
John Jones wrote:
The = sign doesn>t guarantee unreserved symmetry between expressions.

NOTHING creates symmetry between EXPRESSIONS.
It is THE SIGN that has symmetry. It is = ITSELF that *is*
symmetric.
[/quote]
The fullstop (or period) has symmetry too. And its use doesn>t guarantee
unreserved symmetry between its expressions either.

[quote]I can be a reminder or sign that is appended to one expression to show
that that expression is referencing another expression.

It CAN>T avoid being PREpended to the "another" expression in THAT
context.
[/quote]
The = sign never occurs in isolation. Nor does it occur between
expressions, except visually. The = sign is appended to only one
expression so

"sqrt.9=" 2
is correct,
and not
"sqrt.9= 2"

[quote]And whether you append or prepend fundamentally makes NO difference --
there
is no law requiring left (as opposed to right) to be "pre" or "first";
indeed a great
many languages OTHER than English do in fact do it the other way.
[/quote]
What about people who read through mirrors? Or what about looking at
equations upside down? Do these ways of looking spoil symmetry?

[quote]1) Taking the expression sq.rt4 = 2. Sq.rt4 refers to 2. 2 does not
refer to anything. 2 is the object itself. It is presented, we don>t
need to refer to it, it is there in front of us to use as we wish.

Since one of the uses we could wish is to remind people that it is
the
positive square root of 4, we CAN ALSO SAY 2=sqrt(4).
[/quote]
2=sqrt(4) wouldn>t mean anything, unless sqrt4 is used to come up with
another number. Nobody wants sqrt4, a reference, for its own sake.

[quote]2) A = A (or A is equal to itself) is another asymmetric use of the = sign.

This article you just posted is another assholic use of public
stupidity.

An object that references itself is not the object referenced by
another.

But it STILL IS the object referenced by ITSELF,
[/quote]
No it isn>t. An object that is given through a reference to itself has
no properties.

[quote]which, SYMMETRY being
what
we>re talking about here, IS a CONFIRMING example of symmetry.

Object properties are given by reference,

No, they>re not. You can refer to a thing without giving ANY of its
properties
other than the route by which it is referenced.
[/quote]
Object properties are given by reference. Objects are presented.
Spatiotemporally usually.

[quote]but not by self-reference.

In order to perceive the reference, you would have to HAVE ALREADY
BEEN
given SOME reference to the object. Whether that reference is or
isn>t self is something
you may OR MAY NOT be aware of.
[/quote]
Acts of self-reference are not surveyable.

[quote]You have to EVALUATE the
reference. You have
to FOLLOW the reference.

The real asymmetry you are looking for involves evaluation, involves
getting closer
to some simpler or "normal" form. You need to google (or wiki) the
phrase
"rewrite rules". Believe it or not, for all your pretensions to
knowing enough to be
able to educate us (and they truly are pretense), YOU ARE NOT THE
FIRST person
to notice that = can be asymmetric.
[/quote]
Ohhh, yes I am

[quote]You are, perhaps, however, the
most incompetent.
[/quote]
Ohhh, no I>m not

Mitch Harris · Guest

On Oct 27, 5:26 pm, John Jones <jonescard...@aol.com> wrote:
[quote]george wrote:

John Jones wrote:
The = sign doesn>t guarantee unreserved symmetry between expressions..
[/quote]
No symbol guarantees anything. We mutually agree to its properties. By
stipulation, most uses of '=' are symmetric. The English use of 'is'
is not.

[quote]2=sqrt(4) wouldn>t mean anything, unless sqrt4 is used to come up with
another number. Nobody wants sqrt4, a reference, for its own sake.
[/quote]
Maybe -you- don>t. What about sqrt(9801)? -Somebody- may want to refer
to that, use it, all for its own sake.

[quote]An object that is given through a reference to itself has
no properties.
[/quote]
no -other- properties, at least none that have yet been specified.

[quote] Object properties are given by reference,

No, they>re not. You can refer to a thing without giving ANY of its
properties
other than the route by which it is referenced.

Object properties are given by reference. Objects are presented.
Spatiotemporally usually.
[/quote]
Can>t objects be presented as themselves or by reference or by
description? Why does this matter as long as there is agreement?

[quote]In order to perceive the reference, you would have to HAVE ALREADY
BEEN
given SOME reference to the object. Whether that reference is or
isn>t self is something
you may OR MAY NOT be aware of.

Acts of self-reference are not surveyable.
[/quote]
What does that mean? DO you have some sort of technical or otherwise
specific meaning for 'surveyable'?

Mitch

David C. Ullrich · Guest

On Tue, 28 Oct 2008 00:31:15 +1100, "Peter Webb"
<webbfamily@DIESPAMDIEoptusnet.com.au> wrote:

[quote]
when you>re discussing this sort of thing you need to _say_
'"2"' when you mean '"2"'.

I half suspect you were just looking for a way to use the character string
"'"2"'"
[/quote]
Wasn>t "looking for" such a thing, it simply comes up. The
difference between 2 and "2" is crucial here. I wanted
to say something about how he needs to write the
string "2", including the quotes. So yes, I needed to
quote that string, including the quote marks.

[quote]
[/quote]
David C. Ullrich

"Understanding Godel isn>t about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)

Dan Christensen · Guest

On Oct 28, 3:34 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Dan Christensen wrote:
On Oct 25, 4:17 pm, John Jones <jonescard...@aol.com> wrote:
The = sign doesn>t guarantee unreserved symmetry between expressions.. It
can be a reminder or sign that is appended to one expression to show
that that expression is referencing another expression.

1) Taking the expression sq.rt4 = 2. Sq.rt4 refers to 2. 2 does not
refer to anything. 2 is the object itself. It is presented, we don>t
need to refer to it, it is there in front of us to use as we wish.

2) A = A (or A is equal to itself) is another asymmetric use of the > >> sign. An object that references itself is not the object referenced by
another. Object properties are given by reference, but not by
self-reference.

You are making this way too complicated with your "objects,"
"references," etc.

Formally, A=B just means that you can substitute string A for sting B,
and vice versa (taking into account any bracketing or precedence
conventions).

Yes, I know. It wasn>t me who extended that to make use of it as an
identity in A = A.

In your example, "sq.rt4 = 2" tells us that wherever we see "sq.rt4"
in a statement, we can substitute "2." And A=A is just a useful
identity. That>s how I look at it anyway.

I know that>s what Wittgenstein said, but there is a problem with that
idea.. a problem which he probably thought of. The substitution of signs
must be about a substitution of meaning. It can>t be about just
substituting signs. If it was, microscopic visual differences between 2
and 2 would make only one of them referenced by sqrt.4.- Hide quoted text -

[/quote]
In mathematics -- at least at a foundational level like this -- I
don>t find it is very useful to be talking about "meaning" in this
way. Hilbert, though talking specifically about geometry, said, “One
must be able to say at all times -- instead of points, straight lines,
and planes --tables, chairs, and beer mugs.” (I love that line!) He
argues that geometry, and I presume he meant all of mathematics,
should be based on pure abstractions completely devoid of any
"meaning" at this level.

As for microscopic, visual differences between 2 and 2, every formal
system begins with an "alphabet" of unambiguously distinct symbols
from which statements are constructed. I really don>t see any problem
with that idea.

Dan
Download my DC Proof software at www.dcproof.com

John Jones · Guest

Mitch Harris wrote:
[quote]On Oct 27, 5:26 pm, John Jones <jonescard...@aol.com> wrote:
george wrote:

John Jones wrote:
The = sign doesn>t guarantee unreserved symmetry between expressions.

No symbol guarantees anything. We mutually agree to its properties. By
stipulation, most uses of '=' are symmetric. The English use of 'is'
is not.

2=sqrt(4) wouldn>t mean anything, unless sqrt4 is used to come up with
another number. Nobody wants sqrt4, a reference, for its own sake.

Maybe -you- don>t. What about sqrt(9801)? -Somebody- may want to refer
to that, use it, all for its own sake.
[/quote]
Sqrt.x where x is any number has no real-time, everyday significance. 2
has a significance. That is why mathematics is constantly looking for
solutions. A solution is always a number and never a reference on how to
find a number.

[quote]An object that is given through a reference to itself has
no properties.

no -other- properties, at least none that have yet been specified.
[/quote]
I meant no properties at all. Anything measuring or viewing itself
measures and sees nothing.

[quote]Object properties are given by reference. Objects are presented.
Spatiotemporally usually.

Can>t objects be presented as themselves or by reference or by
description? Why does this matter as long as there is agreement?

In order to perceive the reference, you would have to HAVE ALREADY
BEEN
given SOME reference to the object. Whether that reference is or
isn>t self is something
you may OR MAY NOT be aware of.
Acts of self-reference are not surveyable.

What does that mean? DO you have some sort of technical or otherwise
specific meaning for 'surveyable'?

Mitch
[/quote]
An act of self-reference, like the brain viewing itself and eliminating
its material properties and gaining consciousness, is not reportable. A
report reports external properties.

John Jones · Guest

Dan Christensen wrote:
[quote]On Oct 25, 4:17 pm, John Jones <jonescard...@aol.com> wrote:
The = sign doesn>t guarantee unreserved symmetry between expressions. It
can be a reminder or sign that is appended to one expression to show
that that expression is referencing another expression.

1) Taking the expression sq.rt4 = 2. Sq.rt4 refers to 2. 2 does not
refer to anything. 2 is the object itself. It is presented, we don>t
need to refer to it, it is there in front of us to use as we wish.

2) A = A (or A is equal to itself) is another asymmetric use of the =
sign. An object that references itself is not the object referenced by
another. Object properties are given by reference, but not by
self-reference.

You are making this way too complicated with your "objects,"
"references," etc.

Formally, A=B just means that you can substitute string A for sting B,
and vice versa (taking into account any bracketing or precedence
conventions).
[/quote]
Yes, I know. It wasn>t me who extended that to make use of it as an
identity in A = A.

[quote]In your example, "sq.rt4 = 2" tells us that wherever we see "sq.rt4"
in a statement, we can substitute "2." And A=A is just a useful
identity. That>s how I look at it anyway.
[/quote]
I know that>s what Wittgenstein said, but there is a problem with that
idea.. a problem which he probably thought of. The substitution of signs
must be about a substitution of meaning. It can>t be about just
substituting signs. If it was, microscopic visual differences between 2
and 2 would make only one of them referenced by sqrt.4.

Mitch Harris · Guest

On Oct 28, 3:30 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch Harris wrote:
On Oct 27, 5:26 pm, John Jones <jonescard...@aol.com> wrote:

2=sqrt(4) wouldn>t mean anything, unless sqrt4 is used to come up with
another number. Nobody wants sqrt4, a reference, for its own sake.

Maybe -you- don>t. What about sqrt(9801)? -Somebody- may want to refer
to that, use it, all for its own sake.

Sqrt.x where x is any number has no real-time, everyday significance. 2
has a significance.
[/quote]
Don>t you think that>s a bit short sighted, in both ways?
- sqrt(2) is significant as the length of the hypotenuse of a
isosceles right triangle. That>s pretty 'everyday', at least for
carpenters.

- does 100 have everyday significance? not really that much, no one
ever -really- counts out 100 things (ecxpet when you>re 6 years old
and discover that it>s possible).

[quote]That is why mathematics is constantly looking for
solutions. A solution is always a number and never a reference on how to
find a number.
[/quote]
I disagree. A really good solution might be a number but there are all
sorts of solutions (really good ones) that are functions or algorithms
that take variables.

[quote]An object that is given through a reference to itself has
no properties.

no -other- properties, at least none that have yet been specified.

I meant no properties at all. Anything measuring or viewing itself
measures and sees nothing.
[/quote]
Right. -You- meant that, and I meant that your desription of such an
object certainly does have at least one property, that of referring to
itself. You might also then mean that that is not a true property
('not a true Scotsman'), but I think it is a perfectly fine property.

[quote]Acts of self-reference are not surveyable.

What does that mean? DO you have some sort of technical or otherwise
specific meaning for 'surveyable'?

An act of self-reference, like the brain viewing itself and eliminating
its material properties and gaining consciousness, is not reportable. A
report reports external properties.
[/quote]
Is that what 'surveyable' is supposed to mean? 'reportable'? 'has
external properties'? What does 'internal'/'external' property mean
here? Is this circular? (i.e. by definition 'surveyability' = 'non
self-referring'). What does surveyable or reportable mean without
reference to self-reference?

Mitch

Frederick Williams · Guest

John Jones wrote:
[quote]
The = sign doesn>t guarantee unreserved symmetry between expressions. It
can be a reminder or sign that is appended to one expression to show
that that expression is referencing another expression.

1) Taking the expression sq.rt4 = 2. Sq.rt4 refers to 2. 2 does not
refer to anything. 2 is the object itself. It is presented, we don>t
need to refer to it, it is there in front of us to use as we wish.

2) A = A (or A is equal to itself) is another asymmetric use of the =
sign. An object that references itself is not the object referenced by
another. Object properties are given by reference, but not by
self-reference.
[/quote]
Just for fun: Lejewski (and others) have considered a non-reflexive
identity.

--
He is not here; but far away
The noise of life begins again
And ghastly thro' the drizzling rain
On the bald street breaks the blank day.


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