Science and Technology news... :: View topic

John Jones · Guest

Mitch wrote:

[quote]By my account, I>d guess that to call anything a middle one must have
ends respect to which it is a middle, but the empty string or null
string (the string of zero length) may have two ends the left and the
right (of course they don>t go anywhere) but no middle. or maybe the
middle of of length zero. I>ll leave that up to you.
[/quote]
I don>t know whether 'a line of zero length' means the absence of a
line, or describes a line as being independent of its length, or is a
vanishingly small, but not completely gone, line.

[quote]A string can have a middle if it is a finite line.

'can' is not 'must' (you were saying 'must' before'; I agree with
"...can...if...finite line" though)
[/quote]
It couldn>t if the line was a circle.

[quote]Are you talking about strings that are like shoe-laces? or like
sequences of characters in text? or some curve in space? or what?
[/quote]
I>m taking a string as a sequence of individual, spatially or temporally
fixed elements. But I don>t think the idea is coherent because in order
to fix the elements, I need a higher organising structure (like 'left
and right').

[quote]If all the beads are the same I will be unable to differentiate them and
make a reliable count. If I can>t make a reliable count then I don>t
have a sequenced line. Woof.

What do you mean by same? indistinguishable? Then logically, you>d
have to say that if you have a set of indistinguishable items, then
you really only have 1 (or 0) items.
[/quote]
In fact, I wouldn>t be able to tell one from infinity.

[quote]As to making a reliable count, I>d say that is built in to the
definition of a string, the position of items along the string. Even
if they are otherwise identical, the position along the string is
enough to allow counting.
[/quote]
But once I have counted an element and want to move on to the next
element, I don>t know whether or not I am counting the next element or
the one before it. That>s because I can>t see the whole string, because
to see the whole string would mean that a count has already been tacitly
made.

Herbert Newman · Guest

Am Sun, 12 Oct 2008 23:54:58 +0100 schrieb John Jones:

[quote]
By my account, I>d guess that to call anything a middle one must have
ends respect to which it is a middle, but the empty string or null
string (the string of zero length) may have two ends the left and the
right (of course they don>t go anywhere) but no middle. Or maybe the
middle of of length zero. I>ll leave that up to you.

I don>t know whether 'a line of zero length' means the absence of a
line, or describes a line as being independent of its length, or is a
vanishingly small, but not completely gone, line.

It might be considered a (single) point. (Or a set consisting of a single[/quote]
point, especially when we consider lines to be sets of points.)

Herb

Mitch · Guest

On Oct 12, 6:54 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch wrote:
By my account, I>d guess that to call anything a middle one must have
ends respect to which it is a middle, but the empty string or null
string (the string of zero length) may have two ends the left and the
right (of course they don>t go anywhere) but no middle. or maybe the
middle of of length zero. I>ll leave that up to you.

I don>t know whether 'a line of zero length' means the absence of a
line, or describes a line as being independent of its length, or is a
vanishingly small, but not completely gone, line.

A string can have a middle if it is a finite line.

'can' is not 'must' (you were saying 'must' before'; I agree with
"...can...if...finite line" though)

It couldn>t if the line was a circle.
[/quote]
Possibly. But I 'could' imagine a definition of a line that is a
circle that might have a middle. But we>re being so fuzzy about
everything, trying to extrapolate definitions from single ambiguous
examples, I don>t think we could tell one way or the other.

Take a look at Heath, A History of Greek Mathematics, and the Euclid
edition with his comments. Lots of explanation about what 'line' means
in particular, but also lost of stuff about defining in general.

[quote]Are you talking about strings that are like shoe-laces? or like
sequences of characters in text? or some curve in space? or what?

I>m taking a string as a sequence of individual, spatially or temporally
fixed elements. But I don>t think the idea is coherent because in order
to fix the elements, I need a higher organising structure (like 'left
and right').
[/quote]
How about just 'start element' and 'end element', or just 'natural #
position'? That>s pretty coherent.

[quote]If all the beads are the same I will be unable to differentiate them and
make a reliable count. If I can>t make a reliable count then I don>t
have a sequenced line. Woof.

What do you mean by same? indistinguishable? Then logically, you>d
have to say that if you have a set of indistinguishable items, then
you really only have 1 (or 0) items.

In fact, I wouldn>t be able to tell one from infinity.
[/quote]
I think you>re mixing up counting abilities here. Your counting
primitive of using entire distinguishability would just say you have 1
item no matter what. That>s all you>d have. If by some other
distinction ability you have a greater # of things (even infinity),
that>s a different counting scheme. Sure you>d be able to tell one
from infinity in the first scheme as long as you can distinguish
elements in a given way, and also with the other counting scheme.
Within a scheme, you>d know the difference between zero, one, and
anything else.

[quote]As to making a reliable count, I>d say that is built in to the
definition of a string, the position of items along the string. Even
if they are otherwise identical, the position along the string is
enough to allow counting.

But once I have counted an element and want to move on to the next
element, I don>t know whether or not I am counting the next element or
the one before it.
[/quote]
Always go in one direction? define string first, then you>ll be able
to answer these questions.

Mitch

Mitch · Guest

On Oct 13, 5:23 pm, John Jones <jonescard...@aol.com> wrote:
[quote]
In a presentation of indistiguishables I wouldn>t be able to make a
count at all, not even a count of one. I might be able to count a
concept, but I wouldn>t be able to count an object.
[/quote]
What>s the difference between a concept and an object?

Mitch

John Jones · Guest

george wrote:

[quote]Strings with 2 ends have 2 orientations; every string has a reverse.
[/quote]
Strings have no orientations or reversals. They are not spatial entities.

[quote]Strings of length 0
[/quote]
So now lines can have a zero length.

[quote]and length 1 are EQUAL to their reverses, though
they
of course are not the only strings with this property.
[/quote]
What about box strings, like numbers on dice.

John Jones · Guest

Herbert Newman wrote:
[quote]Am Sun, 12 Oct 2008 23:54:58 +0100 schrieb John Jones:

By my account, I>d guess that to call anything a middle one must have
ends respect to which it is a middle, but the empty string or null
string (the string of zero length) may have two ends the left and the
right (of course they don>t go anywhere) but no middle. Or maybe the
middle of of length zero. I>ll leave that up to you.

I don>t know whether 'a line of zero length' means the absence of a
line, or describes a line as being independent of its length, or is a
vanishingly small, but not completely gone, line.

It might be considered a (single) point. (Or a set consisting of a single
point, especially when we consider lines to be sets of points.)

Herb
[/quote]
In that case a line is independent of its length. But perhaps what we
are doing here is starting out with the concept of a line and then
constructing points on it. And THEN, when we have constructed only one
point on the line, we say that a line can be a point.

Aside from the seeming trickery involved in that, I might note that we
don>t construct points on a line, we construct positions. And where we
have constructed only one position, we still don>t construct a line, or
even a point.

John Jones · Guest

Mitch wrote:
[quote]On Oct 12, 6:54 pm, John Jones <jonescard...@aol.com> wrote:

I>m taking a string as a sequence of individual, spatially or temporally
fixed elements. But I don>t think the idea is coherent because in order
to fix the elements, I need a higher organising structure (like 'left
and right').

How about just 'start element' and 'end element', or just 'natural #
position'? That>s pretty coherent.
[/quote]
I suppose that we can exchange spatial metaphors (left and right) for
temporal or mixed spatial/temporal metaphors (start, end etc)

[quote]In fact, I wouldn>t be able to tell one from infinity.

I think you>re mixing up counting abilities here. Your counting
primitive of using entire distinguishability would just say you have 1
item no matter what. That>s all you>d have.
[/quote]
In a presentation of indistiguishables I wouldn>t be able to make a
count at all, not even a count of one. I might be able to count a
concept, but I wouldn>t be able to count an object.

[quote]If by some other
distinction ability you have a greater # of things (even infinity),
that>s a different counting scheme. Sure you>d be able to tell one
from infinity in the first scheme as long as you can distinguish
elements in a given way, and also with the other counting scheme.
Within a scheme, you>d know the difference between zero, one, and
anything else.
[/quote]
In fact, I think in a presentation of indistinguishables I wouldn>t be
able to distinguish zero from one or infinity. A count would be impossible.

[quote]But once I have counted an element and want to move on to the next
element, I don>t know whether or not I am counting the next element or
the one before it.

Always go in one direction?
[/quote]
I don>t have an element in the string that is an 'element of direction'.
If each element was also an element of direction then the string would
be a line perhaps or would have a structure. But again, I argue that a
string cannot support such a structure. It must come from outside, from
the operator, who can, for example, distinguish left from right and
impose it on the string.

george · Guest

On Oct 13, 2:32 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Strings have no orientations or reversals.
[/quote]
They DO SO TOO, DUMBASS.

[quote]They are not spatial entities.
[/quote]
I NEVER SAID THEY WERE.
We are talking about 1st and 2nd here.
That IS NOT spatial but it IS STILL one of two opposite
orientations (the other being 2nd and 1st of the same two
things).

[quote]
Strings of length 0

So now lines can have a zero length.
[/quote]
We ARE NOT TALKING about LINES, DUMBASS!
LINES are from the CONTINUUM! THEY have UNcountably
many points! STRINGS are DISCRETE! They have AT MOST
COUNTABLY many elements! A STRING is A LIST of characters!

[quote]What about box strings, like numbers on dice.
[/quote]
You GENERALIZE those from THE ORIGINAL LINEAR version
by ADDING A SECOND DIMENSION. A box string is a string OF strings.
It is a 2-d MATRIX of characters.
Equivalently/alternatively, you could take the face of the die as an
atomic symbol and DENY that it has bit-strings-in-dimensions as
parts.

John Jones · Guest

Mitch wrote:
[quote]On Oct 13, 5:23 pm, John Jones <jonescard...@aol.com> wrote:
In a presentation of indistiguishables I wouldn>t be able to make a
count at all, not even a count of one. I might be able to count a
concept, but I wouldn>t be able to count an object.

What>s the difference between a concept and an object?

Mitch
[/quote]
A concept wouldn>t have any spatial or temporal boundaries or
structures. It would not be a sensory object. I would have only a
general case.

John Jones · Guest

george wrote:
[quote]On Oct 13, 2:32 pm, John Jones <jonescard...@aol.com> wrote:
Strings have no orientations or reversals.

They DO SO TOO, DUMBASS.

They are not spatial entities.

I NEVER SAID THEY WERE.
[/quote]
Orientation and reversal are spatial.

[quote]We are talking about 1st and 2nd here.
[/quote]
There>s nothing that makes the left-most element the 'first'. There is
nothing that makes any element 'the first'.

How can a string, or anything for that matter, tell us which of its
elements is 'the first'? The 'first' is not part of the structure of the
string, or of the line. The first isn>t even part of a count. Same goes
for 'start'. It is we who start, not the string or the line.

[quote]That IS NOT spatial but it IS STILL one of two opposite
orientations (the other being 2nd and 1st of the same two
things).

Strings of length 0
So now lines can have a zero length.

We ARE NOT TALKING about LINES, DUMBASS!
[/quote]
Good. So a string isn>t a line. Yet you like to think it has a middle.

[quote]LINES are from the CONTINUUM!
[/quote]
Waffle.

[quote]THEY have UNcountably
many points!
[/quote]
So lines are made of counted and uncounted points. The uncounted points
aren>t placed. That means that a line is discontinuous, fragmented.

[quote]STRINGS are DISCRETE! They have AT MOST
COUNTABLY many elements!
[/quote]
You can count them, yes. But don>t think that your count defines the
string. Your count defines only itself.

[quote]A STRING is A LIST of characters!

What about box strings, like numbers on dice.

You GENERALIZE those from THE ORIGINAL LINEAR version
by ADDING A SECOND DIMENSION. A box string is a string OF strings.
It is a 2-d MATRIX of characters.
Equivalently/alternatively, you could take the face of the die as an
atomic symbol and DENY that it has bit-strings-in-dimensions as
parts.
[/quote]
So where>s the middle of a box string die with 6 sides?

Mitch · Guest

On Oct 14, 2:48 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch wrote:
On Oct 13, 5:23 pm, John Jones <jonescard...@aol.com> wrote:
In a presentation of indistiguishables I wouldn>t be able to make a
count at all, not even a count of one. I might be able to count a
concept, but I wouldn>t be able to count an object.

What>s the difference between a concept and an object?

Mitch

A concept wouldn>t have any spatial or temporal boundaries or
structures. It would not be a sensory object. I would have only a
general case.
[/quote]
So is the number 2 a concept or an object?

Mitch

John Jones · Guest

Mitch wrote:
[quote]On Oct 14, 2:48 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 13, 5:23 pm, John Jones <jonescard...@aol.com> wrote:
In a presentation of indistiguishables I wouldn>t be able to make a
count at all, not even a count of one. I might be able to count a
concept, but I wouldn>t be able to count an object.
What>s the difference between a concept and an object?
Mitch
A concept wouldn>t have any spatial or temporal boundaries or
structures. It would not be a sensory object. I would have only a
general case.

So is the number 2 a concept or an object?

Mitch
[/quote]
Frege would have it that the number 2 is an object. An object that
presumably points out two objects. Number per se (but not any named
number like 2) looks like a concept.

Also according to frege the number 2, like all numbers, have unique
identities if they are objects. But the unique identity of the number
two is that it is a pair, which is a definable, single object or entity.
But then we lose the distinction between a pair and two singletons, so I
would say that 2 is not a pair and hence is not an object.

Mitch · Guest

On Oct 15, 3:11 pm, John Jones <jonescard...@aol.com> wrote:
[quote]Mitch wrote:
On Oct 14, 2:48 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 13, 5:23 pm, John Jones <jonescard...@aol.com> wrote:
In a presentation of indistiguishables I wouldn>t be able to make a
count at all, not even a count of one. I might be able to count a
concept, but I wouldn>t be able to count an object.
What>s the difference between a concept and an object?
Mitch
A concept wouldn>t have any spatial or temporal boundaries or
structures. It would not be a sensory object. I would have only a
general case.

So is the number 2 a concept or an object?

Mitch

Frege would have it that the number 2 is an object. An object that
presumably points out two objects. Number per se (but not any named
number like 2) looks like a concept.

Also according to frege the number 2, like all numbers, have unique
identities if they are objects. But the unique identity of the number
two is that it is a pair,
[/quote]
I don>t see that. The number 2 describes collections that are pairs
(pardon any circularity), but is not necessarily a pair itself. (like
the guy over in the sci.math thread who thinks that zero is nothing
when really 0 -describes- the null set.)

[quote]which is a definable, single object or entity.
But then we lose the distinction between a pair and two singletons, so I
would say that 2 is not a pair
[/quote]
the conclusion, yes, 2 is not a pair, but that doesn>t follow from the
lack of distinction between a pair and 2 singletons (there -is- a
distinction?).

[quote]and hence is not an object.
[/quote]
and that doesn>t follow either from all those previous statements,
whether right or not.

Mitch

John Jones · Guest

Mitch wrote:
[quote]On Oct 15, 3:11 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 14, 2:48 pm, John Jones <jonescard...@aol.com> wrote:
Mitch wrote:
On Oct 13, 5:23 pm, John Jones <jonescard...@aol.com> wrote:
In a presentation of indistiguishables I wouldn>t be able to make a
count at all, not even a count of one. I might be able to count a
concept, but I wouldn>t be able to count an object.
What>s the difference between a concept and an object?
Mitch
A concept wouldn>t have any spatial or temporal boundaries or
structures. It would not be a sensory object. I would have only a
general case.
So is the number 2 a concept or an object?
Mitch
Frege would have it that the number 2 is an object. An object that
presumably points out two objects. Number per se (but not any named
number like 2) looks like a concept.

Also according to frege the number 2, like all numbers, have unique
identities if they are objects. But the unique identity of the number
two is that it is a pair,

I don>t see that. The number 2 describes collections that are pairs
(pardon any circularity), but is not necessarily a pair itself. (like
the guy over in the sci.math thread who thinks that zero is nothing
when really 0 -describes- the null set.)
[/quote]
I meant that if 2 has a single identity, then I must know what it is,
and I must look for that identity. But I can>t say that it>s 'twoness'.
The only candidate I can think of, for good or bad, is that the single
identity of 2 is a pair.

[quote]which is a definable, single object or entity.
But then we lose the distinction between a pair and two singletons, so I
would say that 2 is not a pair

the conclusion, yes, 2 is not a pair, but that doesn>t follow from the
lack of distinction between a pair and 2 singletons (there -is- a
distinction?).
[/quote]
I don>t know what the identity of two is, if it>s a single identity,
except that it might be a pair. The mystics said that numbers had
identities, but why Frege said that numbers had identities well I just
don>t know.

[quote]and hence is not an object.

and that doesn>t follow either from all those previous statements,
whether right or not.
[/quote]
I don>t know what it could mean for a number to have a single identity.
Objects can be regarded as numbers, voided of the differences that make
them qualititaively different. What makes a number distinctive in that
case is Space, which allows us to discern similar objects. But even that
would not mean that numbers have unique identities.


www.GetXFactor.com Leading Technology, Science, Agriculture News and information	Part of the Identityscape.com network... getxfactor.com jmoodmusic.com smartbusinesschoices.com mintdepot.com lowfaresalways.com evangelicalview.com shoppingpodder.com soproudlywehail.com webnews.ws currenthumor.com

Science and Technology news... Forum Index -> Logic Forum	Goto page Previous 1, 2
Page 2 of 2