Here it is.

Burt Hopkins


On Aug 29, 2006, at 8:31 AM, Lancelot R. Fletcher wrote:

> I am trying to find the following article from the Journal of the
> History of Ideas which, based on an abstract, seems to discuss Klein's
> ideas about mathematics.
>
> Page, Carl 1957- "Symbolic Mathematics and the Intellect Militant: On
> Modern Philosophy's Revolutionary Spirit"
> Journal of the History of Ideas - Volume 57, Number 2, April 1996, pp.
> 233-253
> University of Pennsylvania Press
> <http://muse.jhu.edu/about/publishers/upenn>
>
> If anybody here has a hard copy of the article and could fax it to me
> at: 1-202-478-0278 I would be very grateful. Or if you have access to
> the electronic version via Project Muse (which some academic libraries
> have), please send it to me and I will post it to the group file
> library.
>
> Lance Fletcher
>
>



[Non-text portions of this message have been removed]

I am trying to find the following article from the Journal of the
History of Ideas which, based on an abstract, seems to discuss Klein's
ideas about mathematics.

Page, Carl 1957- "Symbolic Mathematics and the Intellect Militant: On
Modern Philosophy's Revolutionary Spirit"
Journal of the History of Ideas - Volume 57, Number 2, April 1996, pp.
233-253
University of Pennsylvania Press
<http://muse.jhu.edu/about/publishers/upenn>

If anybody here has a hard copy of the article and could fax it to me
at: 1-202-478-0278 I would be very grateful. Or if you have access to
the electronic version via Project Muse (which some academic libraries
have), please send it to me and I will post it to the group file library.

Lance Fletcher

Does discussion of jacob klein's work assume that the fundamentals of
modern algebra, such as spencer-browns's laws of form, have masked the
greek meaning of number to the extent that viewing and understanding
of information content transferred can be either misconstrued or lost.
len

dear moderator
i am changing my address from
chofborg1@...
to
pieiphi@...

thanks
len gallagher

picard wrote:

>Worreller
>Perhaps you could answer a question for me wrt something klein says
>near the end of his introduction, a look ahead so to speak.
>Klein says, "...we show that the revival and assimilation of greek
>logistic in the sixteenth century are themslves prompted by an
>already current symbolic understanding of number, and we attempt to
>clarify the conceptual structure of the algebraic symbolism which is
>its product..."
>Does klein infer that- not only is our modern view (physics=math)
>our expression of mind but it's structure is at our behest.
>len
>
>
>
>
Yes.

J

ps. Did you notice the other comments below in my pervious post? I am
reluctant to point them out only because I do not have much time.

>--- In klein@yahoogroups.com, "picard" <chofborg1@y...> wrote:
>
>
>>Worreller
>>Yes agreed; to 'have read' one must think the author's thoughts.
>>Klein, in the introduction i think, wants us to appreciate that
>>wrt our world and minds we and ancient thinkers are not that
>>different. Maybe this is just my thought (but that's the point of
>>discussion), mathematics has never really been simply about theory
>>on one hand and application on the other, no, in and of itself it
>>has always condensed to an examination of our individual conscious
>>progress.
>>len
>>
>>
>>--- In klein@yahoogroups.com, worreller <worreller@c...> wrote:
>>
>>
>>>Mr. Picard,
>>>
>>>I will tell you some points that Mr. Klein made in various
>>>
>>>
>places.
>
>
>>>When reading the words of any thinker ( and there are not so
>>>
>>>
>many
>
>
>>>thinkers as we tend to believe) one's own habits of thought are
>>>insufficient. This means that if one is going to read, as
>>>
>>>
>opposed
>
>
>>to
>>
>>
>>>"that book is a good read," one must submit to the habits of
>>>
>>>
>>thought of
>>
>>
>>>the author. These days people are quick to attack this
>>>
>>>
>suggestion
>
>
>>as one
>>
>>
>>>that undermines "critical thinking." But, of course, critical
>>>
>>>
>>thinking
>>
>>
>>>is impossible without judgment and judgment impossible without
>>>discernment. If one has not thought the thought which affords
>>>understanding of the text one has not finished reading it. And
>>>
>>>
>>better
>>
>>
>>>than critique, having submitted to the text long enough to think
>>>
>>>
>>it one
>>
>>
>>>is free to occupy the office which the composition is as well as
>>>establish another such should it prove worthy to do so.
>>>
>>>picard wrote:
>>>
>>>
>>>
>>>>Bill
>>>>My apologies, my thoughts, my obtuse language. Scientific, as a
>>>>
>>>>
>>word
>>
>>
>>>>and wrt social perspective, was meant to indicate that all of
>>>>
>>>>
>us
>
>
>>>>have (in some way) have been made physicists and questioners;
>>>>
>>>>
>>even
>>
>>
>>>>the most religious do not deny they share the 'stage' with
>>>>
>>>>
>logic
>
>
>>and
>>
>>
>>>>reason. (Were things ever otherwise?, apperently there still
>>>>
>>>>
>>remain
>>
>>
>>>>corners of our world that are)
>>>>
>>>>
>>>>In my understanding, thus far, mathematics was a gift of the
>>>>
>>>>
>world
>
>
>>>>to man. Mathematics and the world were one.
>>>>
>>>>
>>>>
>>>Yes, if you are indulging a certain way of speaking. There was a
>>>
>>>
>>time
>>
>>
>>>when everything they saw they could count. But than they saw the
>>>continuous. With the theorem called Pythagorean comes the
>>>
>>>
>>discovery that
>>
>>
>>>there is no unit, no means, with which to count the side of a
>>>
>>>
>>square
>>
>>
>>>that will count its diagonal as well. Until than it looked to
>>>
>>>
>>those who
>>
>>
>>>liked counting so much that number and the world were one.
>>>
>>>But math had proved to these people that a thing could be
>>>
>>>
>learned,
>
>
>>that
>>
>>
>>>is to say understood, which meant that a thing could be known.
>>>
>>>
>>This
>>
>>
>>>model for learning and knowledge was never betrayed by the
>>>
>>>
>Greeks.
>
>
>>It is
>>
>>
>>>fair to point out that Plato, for instance, was not "the Greeks."
>>>
>>>
>>>
>>>>It is true today, but
>>>>in the sense that the mathematics system sought is both logical
>>>>
>>>>
>>and
>>
>>
>>>>applicable (to the physical).
>>>>
>>>>
>>>>
>>>>
>>>Yes. Although some argue that natural history (he peri phuseos
>>>
>>>
>>historia)
>>
>>
>>>was always a silent fifth art never far from the quadrivium
>>>
>>>
>>(arithmetic,
>>
>>
>>>geometry, music, astronomy) the inquiry into nature never did
>>>
>>>
>>admit of
>>
>>
>>>the kind of reflection which makes an art worthy of the name
>>>
>>>
>>liberal.
>>
>>
>>>Here liberal education is understood as the acquisition of the
>>>
>>>
>>pursuits
>>
>>
>>>that make it possible for a man to be a free one. As the
>>>
>>>
>teachers
>
>
>>began
>>
>>
>>>to fear for their way they compensated with the addition of the
>>>
>>>
>>trivial
>>
>>
>>>supplments (logic, rhetoric and grammar). This trend drifted
>>>
>>>
>from
>
>
>>those
>>
>>
>>>arts concerned with the mathema proper to the study  and
>>>
>>>
>>generation of
>>
>>
>>>-ologies.
>>>
>>>Skipping over a great deal I will conclude this confirming reply
>>>
>>>
>>by
>>
>>
>>>pointing out that today all four of the original liberal arts
>>>
>>>
>>labor on
>>
>>
>>>behalf of  physics and have probed so far into the nether
>>>
>>>
>regions
>
>
>>that
>>
>>
>>>this mathematical physics affords no account apart from its
>>>
>>>
>>symbolic
>>
>>
>>>formula. Not only does submission to the rules of modern physics
>>>
>>>
>>not
>>
>>
>>>afford any human being a reflection which could be called
>>>
>>>
>>liberating,
>>
>>
>>>its results do not have sufficient semblance to anything anyone
>>>
>>>
>>had ever
>>
>>
>>>know to be knowledge to be worthy of the name.
>>>
>>>
>>>
>>>>There are many systems available for people to compare, combine
>>>>
>>>>
>>and
>>
>>
>>>>use, and these bring with them certain inherent problems such as
>>>>contradiction and paradox.
>>>>
>>>>
>>>>
>>>The Greek cognate of system meant an ordered arrangement and was
>>>
>>>
>>used of
>>
>>
>>>many things, a row of columns, the unites in a number, the beams
>>>
>>>
>>rowers
>>
>>
>>>set on in the ships but it was never said of thought. It did not
>>>
>>>
>>occur
>>
>>
>>>to them to speak of systems of thought because they thought
>>>
>>>
>about
>
>
>>things
>>
>>
>>>in the world, their thought was open to the world, their thought
>>>
>>>
>>was the
>>
>>
>>>world insofar as they had through thinking brought the world
>>>
>>>
>with
>
>
>>in.
>>
>>
>>>When you say this word "mind" what is it that you say? If you
>>>
>>>
>>speak as
>>
>>
>>>the moderns speak you mean some kind of a box which is by
>>>
>>>
>>definition
>>
>>
>>>(note what Bill said of definition) ever separate from any thing
>>>
>>>
>>and
>>
>>
>>>anything that could be called a world. Mind is a terrible word
>>>
>>>
>to
>
>
>>utter
>>
>>
>>>on behalf of the Greeks but the only thing that could be vaguely
>>>identified with this awful word was understood as that which was
>>>
>>>
>>open to
>>
>>
>>>the world, that by means of which one brought  the world within.
>>>
>>>
>>It was
>>
>>
>>>this alone and nothing else.
>>>
>>>In part two of this text Mr. Klein makes a suggestion concerning
>>>
>>>
>>modern
>>
>>
>>>conceptuality which  made the modern mind, the algebra, systems
>>>
>>>
>of
>
>
>>>thought and so much else follow.
>>>Take care,
>>>
>>>J Keyser
>>>
>>>
>>>
>>>>At this point an individual might choose
>>>>to ignore something(s) so as to say "this the world"
>>>>
>>>>
>(definitions
>
>
>>to
>>
>>
>>>>masquerade as cause), when it is better asked "what is it that
>>>>determines all else, here?"
>>>>Wrt senses and thoughts: let a mind be a set M, in itself it is
>>>>
>>>>
>a
>
>
>>>>universal because it cannot deny any aspect of it's own
>>>>
>>>>
>knowledge,
>
>
>>>>physical or otherwise.
>>>>len
>>>>
>>>>
>>>>--- In klein@yahoogroups.com, "Bill Oates" <boates@e...> wrote:
>>>>
>>>>
>>>>
>>>>
>>>>>Len
>>>>>
>>>>>Sorry but I am not following you. Perhaps you could expand on
>>>>>
>>>>>
>>some
>>
>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>this
>>>>
>>>>
>>>>
>>>>
>>>>>or perhaps I am just obtuse.
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>>-To the scientific.
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>Sorry still not understanding - in fact this only confuses
>>>>>
>>>>>
>more.
>
>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>Maybe
>>>>
>>>>
>>>>
>>>>
>>>>>you could start over and expand on this. What is scientific?
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>>>How is mathematics given by the world different from a world
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>that
>>>>
>>>>
>>>>
>>>>
>>>>>>>is inseparable from the mathematics?
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>-Fundamentally there is no difference, the exception being in
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>those
>>>>
>>>>
>>>>
>>>>
>>>>>>minds which tend now toward thinking of determination as
>>>>>>
>>>>>>
>cause.
>
>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>AS opposed to the Aristotle four fold?? What on earth is
>>>>>
>>>>>
>>>>>
>>>>>
>>>>determination?
>>>>
>>>>
>>>>
>>>>
>>>>>>>How do our eyes and thoughts tell us anything about goals?
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>-Senses and thoughts are elements in the set.
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>Not as far as I can see....
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>>>How does mathematics (ancient or modern) act as an
>>>>>>>
>>>>>>>
>initiative.
>
>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>-It is recognizing that 'successful choosing' is logic to the
>>>>>>system; being did not always allow for our species as it is
>>>>>>
>>>>>>
>now.
>
>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>Being does not permit nor deny. Being is not a control
>>>>>
>>>>>
>mechanism
>
>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>as far
>>>>
>>>>
>>>>
>>>>
>>>>>as I can see or think. What system did you have in mind? What
>>>>>
>>>>>
>>>>>
>>>>>
>>>>logic?
>>>>
>>>>
>>>>
>>>>
>>>>>>>Let me be clear - these are not ordinary conceptions of
>>>>>>>mathematics. So they are questionable.
>>>>>>>b
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>-Popular conceptions are questionable because they are
>>>>>>
>>>>>>
>ordinary,
>
>
>>>>>>or perhaps i missed your point.
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>I was suggesting that your discussion of mathematicals was not
>>>>>
>>>>>
>>one
>>
>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>that
>>>>
>>>>
>>>>
>>>>
>>>>>would be understandable by the high school math student. So
>>>>>
>>>>>
>they
>
>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>tend to
>>>>
>>>>
>>>>
>>>>
>>>>>be strange and questionable.
>>>>>
>>>>>B
>>>>>
>>>>>
>
>
>

Worreller
Perhaps you could answer a question for me wrt something klein says
near the end of his introduction, a look ahead so to speak.
Klein says, "...we show that the revival and assimilation of greek
logistic in the sixteenth century are themslves prompted by an
already current symbolic understanding of number, and we attempt to
clarify the conceptual structure of the algebraic symbolism which is
its product..."
Does klein infer that- not only is our modern view (physics=math)
our expression of mind but it's structure is at our behest.
len


--- In klein@yahoogroups.com, "picard" <chofborg1@y...> wrote:
> Worreller
> Yes agreed; to 'have read' one must think the author's thoughts.
> Klein, in the introduction i think, wants us to appreciate that
> wrt our world and minds we and ancient thinkers are not that
> different. Maybe this is just my thought (but that's the point of
> discussion), mathematics has never really been simply about theory
> on one hand and application on the other, no, in and of itself it
> has always condensed to an examination of our individual conscious
> progress.
> len
>
>
> --- In klein@yahoogroups.com, worreller <worreller@c...> wrote:
> > Mr. Picard,
> >
> > I will tell you some points that Mr. Klein made in various
places.
> >
> > When reading the words of any thinker ( and there are not so
many
> > thinkers as we tend to believe) one's own habits of thought are
> > insufficient. This means that if one is going to read, as
opposed
> to
> > "that book is a good read," one must submit to the habits of
> thought of
> > the author. These days people are quick to attack this
suggestion
> as one
> > that undermines "critical thinking." But, of course, critical
> thinking
> > is impossible without judgment and judgment impossible without
> > discernment. If one has not thought the thought which affords
> > understanding of the text one has not finished reading it. And
> better
> > than critique, having submitted to the text long enough to think
> it one
> > is free to occupy the office which the composition is as well as
> > establish another such should it prove worthy to do so.
> >
> > picard wrote:
> >
> > >Bill
> > >My apologies, my thoughts, my obtuse language. Scientific, as a
> word
> > >and wrt social perspective, was meant to indicate that all of
us
> > >have (in some way) have been made physicists and questioners;
> even
> > >the most religious do not deny they share the 'stage' with
logic
> and
> > >reason. (Were things ever otherwise?, apperently there still
> remain
> > >corners of our world that are)
> > >
> > >
> > >In my understanding, thus far, mathematics was a gift of the
world
> > >to man. Mathematics and the world were one.
> > >
> > Yes, if you are indulging a certain way of speaking. There was a
> time
> > when everything they saw they could count. But than they saw the
> > continuous. With the theorem called Pythagorean comes the
> discovery that
> > there is no unit, no means, with which to count the side of a
> square
> > that will count its diagonal as well. Until than it looked to
> those who
> > liked counting so much that number and the world were one.
> >
> > But math had proved to these people that a thing could be
learned,
> that
> > is to say understood, which meant that a thing could be known.
> This
> > model for learning and knowledge was never betrayed by the
Greeks.
> It is
> > fair to point out that Plato, for instance, was not "the Greeks."
> >
> > >It is true today, but
> > >in the sense that the mathematics system sought is both logical
> and
> > >applicable (to the physical).
> > >
> > >
> > Yes. Although some argue that natural history (he peri phuseos
> historia)
> > was always a silent fifth art never far from the quadrivium
> (arithmetic,
> > geometry, music, astronomy) the inquiry into nature never did
> admit of
> > the kind of reflection which makes an art worthy of the name
> liberal.
> > Here liberal education is understood as the acquisition of the
> pursuits
> > that make it possible for a man to be a free one. As the
teachers
> began
> > to fear for their way they compensated with the addition of the
> trivial
> > supplments (logic, rhetoric and grammar). This trend drifted
from
> those
> > arts concerned with the mathema proper to the study  and
> generation of
> > -ologies.
> >
> > Skipping over a great deal I will conclude this confirming reply
> by
> > pointing out that today all four of the original liberal arts
> labor on
> > behalf of  physics and have probed so far into the nether
regions
> that
> > this mathematical physics affords no account apart from its
> symbolic
> > formula. Not only does submission to the rules of modern physics
> not
> > afford any human being a reflection which could be called
> liberating,
> > its results do not have sufficient semblance to anything anyone
> had ever
> > know to be knowledge to be worthy of the name.
> >
> > >There are many systems available for people to compare, combine
> and
> > >use, and these bring with them certain inherent problems such as
> > >contradiction and paradox.
> > >
> > The Greek cognate of system meant an ordered arrangement and was
> used of
> > many things, a row of columns, the unites in a number, the beams
> rowers
> > set on in the ships but it was never said of thought. It did not
> occur
> > to them to speak of systems of thought because they thought
about
> things
> > in the world, their thought was open to the world, their thought
> was the
> > world insofar as they had through thinking brought the world
with
> in.
> >
> > When you say this word "mind" what is it that you say? If you
> speak as
> > the moderns speak you mean some kind of a box which is by
> definition
> > (note what Bill said of definition) ever separate from any thing
> and
> > anything that could be called a world. Mind is a terrible word
to
> utter
> > on behalf of the Greeks but the only thing that could be vaguely
> > identified with this awful word was understood as that which was
> open to
> > the world, that by means of which one brought  the world within.
> It was
> > this alone and nothing else.
> >
> > In part two of this text Mr. Klein makes a suggestion concerning
> modern
> > conceptuality which  made the modern mind, the algebra, systems
of
> > thought and so much else follow.
> > Take care,
> >
> > J Keyser
> >
> > > At this point an individual might choose
> > >to ignore something(s) so as to say "this the world"
(definitions
> to
> > >masquerade as cause), when it is better asked "what is it that
> > >determines all else, here?"
> > >Wrt senses and thoughts: let a mind be a set M, in itself it is
a
> > >universal because it cannot deny any aspect of it's own
knowledge,
> > >physical or otherwise.
> > >len
> > >
> > >
> > >--- In klein@yahoogroups.com, "Bill Oates" <boates@e...> wrote:
> > >
> > >
> > >>Len
> > >>
> > >>Sorry but I am not following you. Perhaps you could expand on
> some
> > >>
> > >>
> > >this
> > >
> > >
> > >>or perhaps I am just obtuse.
> > >>
> > >>
> > >>
> > >>>-To the scientific.
> > >>>
> > >>>
> > >>Sorry still not understanding - in fact this only confuses
more.
> > >>
> > >>
> > >Maybe
> > >
> > >
> > >>you could start over and expand on this. What is scientific?
> > >>
> > >>
> > >>
> > >>>>How is mathematics given by the world different from a world
> > >>>>
> > >>>>
> > >that
> > >
> > >
> > >>>>is inseparable from the mathematics?
> > >>>>
> > >>>>
> > >>>-Fundamentally there is no difference, the exception being in
> > >>>
> > >>>
> > >those
> > >
> > >
> > >>>minds which tend now toward thinking of determination as
cause.
> > >>>
> > >>>
> > >>>
> > >>AS opposed to the Aristotle four fold?? What on earth is
> > >>
> > >>
> > >determination?
> > >
> > >
> > >>>>How do our eyes and thoughts tell us anything about goals?
> > >>>>
> > >>>>
> > >>>-Senses and thoughts are elements in the set.
> > >>>
> > >>>
> > >>>
> > >>Not as far as I can see....
> > >>
> > >>
> > >>
> > >>
> > >>
> > >>
> > >>
> > >>
> > >>>>How does mathematics (ancient or modern) act as an
initiative.
> > >>>>
> > >>>>
> > >>>-It is recognizing that 'successful choosing' is logic to the
> > >>>system; being did not always allow for our species as it is
now.
> > >>>
> > >>>
> > >>>
> > >>Being does not permit nor deny. Being is not a control
mechanism
> > >>
> > >>
> > >as far
> > >
> > >
> > >>as I can see or think. What system did you have in mind? What
> > >>
> > >>
> > >logic?
> > >
> > >
> > >>>>Let me be clear - these are not ordinary conceptions of
> > >>>>mathematics. So they are questionable.
> > >>>>b
> > >>>>
> > >>>>
> > >>>-Popular conceptions are questionable because they are
ordinary,
> > >>>or perhaps i missed your point.
> > >>>
> > >>>
> > >>I was suggesting that your discussion of mathematicals was not
> one
> > >>
> > >>
> > >that
> > >
> > >
> > >>would be understandable by the high school math student. So
they
> > >>
> > >>
> > >tend to
> > >
> > >
> > >>be strange and questionable.
> > >>
> > >>B
> > >>
> > >>
> > >
> > >
> > >
> > >
> > >
> > >This is one of the  lists sponsored by The Free Lance Academy,
> home of
> > >Slow Reading:  http://www.freelance-academy.org  To unsubscribe
by
> > >e-mail, mailto:klein-unsubscribe@onelist.com
> > >Yahoo! Groups Links
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> >
> >
> >
> > [Non-text portions of this message have been removed]

Worreller
Yes agreed; to 'have read' one must think the author's thoughts.
Klein, in the introduction i think, wants us to appreciate that
wrt our world and minds we and ancient thinkers are not that
different. Maybe this is just my thought (but that's the point of
discussion), mathematics has never really been simply about theory
on one hand and application on the other, no, in and of itself it
has always condensed to an examination of our individual conscious
progress.
len


--- In klein@yahoogroups.com, worreller <worreller@c...> wrote:
> Mr. Picard,
>
> I will tell you some points that Mr. Klein made in various places.
>
> When reading the words of any thinker ( and there are not so many
> thinkers as we tend to believe) one's own habits of thought are
> insufficient. This means that if one is going to read, as opposed
to
> "that book is a good read," one must submit to the habits of
thought of
> the author. These days people are quick to attack this suggestion
as one
> that undermines "critical thinking." But, of course, critical
thinking
> is impossible without judgment and judgment impossible without
> discernment. If one has not thought the thought which affords
> understanding of the text one has not finished reading it. And
better
> than critique, having submitted to the text long enough to think
it one
> is free to occupy the office which the composition is as well as
> establish another such should it prove worthy to do so.
>
> picard wrote:
>
> >Bill
> >My apologies, my thoughts, my obtuse language. Scientific, as a
word
> >and wrt social perspective, was meant to indicate that all of us
> >have (in some way) have been made physicists and questioners;
even
> >the most religious do not deny they share the 'stage' with logic
and
> >reason. (Were things ever otherwise?, apperently there still
remain
> >corners of our world that are)
> >
> >
> >In my understanding, thus far, mathematics was a gift of the world
> >to man. Mathematics and the world were one.
> >
> Yes, if you are indulging a certain way of speaking. There was a
time
> when everything they saw they could count. But than they saw the
> continuous. With the theorem called Pythagorean comes the
discovery that
> there is no unit, no means, with which to count the side of a
square
> that will count its diagonal as well. Until than it looked to
those who
> liked counting so much that number and the world were one.
>
> But math had proved to these people that a thing could be learned,
that
> is to say understood, which meant that a thing could be known.
This
> model for learning and knowledge was never betrayed by the Greeks.
It is
> fair to point out that Plato, for instance, was not "the Greeks."
>
> >It is true today, but
> >in the sense that the mathematics system sought is both logical
and
> >applicable (to the physical).
> >
> >
> Yes. Although some argue that natural history (he peri phuseos
historia)
> was always a silent fifth art never far from the quadrivium
(arithmetic,
> geometry, music, astronomy) the inquiry into nature never did
admit of
> the kind of reflection which makes an art worthy of the name
liberal.
> Here liberal education is understood as the acquisition of the
pursuits
> that make it possible for a man to be a free one. As the teachers
began
> to fear for their way they compensated with the addition of the
trivial
> supplments (logic, rhetoric and grammar). This trend drifted from
those
> arts concerned with the mathema proper to the study  and
generation of
> -ologies.
>
> Skipping over a great deal I will conclude this confirming reply
by
> pointing out that today all four of the original liberal arts
labor on
> behalf of  physics and have probed so far into the nether regions
that
> this mathematical physics affords no account apart from its
symbolic
> formula. Not only does submission to the rules of modern physics
not
> afford any human being a reflection which could be called
liberating,
> its results do not have sufficient semblance to anything anyone
had ever
> know to be knowledge to be worthy of the name.
>
> >There are many systems available for people to compare, combine
and
> >use, and these bring with them certain inherent problems such as
> >contradiction and paradox.
> >
> The Greek cognate of system meant an ordered arrangement and was
used of
> many things, a row of columns, the unites in a number, the beams
rowers
> set on in the ships but it was never said of thought. It did not
occur
> to them to speak of systems of thought because they thought about
things
> in the world, their thought was open to the world, their thought
was the
> world insofar as they had through thinking brought the world with
in.
>
> When you say this word "mind" what is it that you say? If you
speak as
> the moderns speak you mean some kind of a box which is by
definition
> (note what Bill said of definition) ever separate from any thing
and
> anything that could be called a world. Mind is a terrible word to
utter
> on behalf of the Greeks but the only thing that could be vaguely
> identified with this awful word was understood as that which was
open to
> the world, that by means of which one brought  the world within.
It was
> this alone and nothing else.
>
> In part two of this text Mr. Klein makes a suggestion concerning
modern
> conceptuality which  made the modern mind, the algebra, systems of
> thought and so much else follow.
> Take care,
>
> J Keyser
>
> > At this point an individual might choose
> >to ignore something(s) so as to say "this the world" (definitions
to
> >masquerade as cause), when it is better asked "what is it that
> >determines all else, here?"
> >Wrt senses and thoughts: let a mind be a set M, in itself it is a
> >universal because it cannot deny any aspect of it's own knowledge,
> >physical or otherwise.
> >len
> >
> >
> >--- In klein@yahoogroups.com, "Bill Oates" <boates@e...> wrote:
> >
> >
> >>Len
> >>
> >>Sorry but I am not following you. Perhaps you could expand on
some
> >>
> >>
> >this
> >
> >
> >>or perhaps I am just obtuse.
> >>
> >>
> >>
> >>>-To the scientific.
> >>>
> >>>
> >>Sorry still not understanding - in fact this only confuses more.
> >>
> >>
> >Maybe
> >
> >
> >>you could start over and expand on this. What is scientific?
> >>
> >>
> >>
> >>>>How is mathematics given by the world different from a world
> >>>>
> >>>>
> >that
> >
> >
> >>>>is inseparable from the mathematics?
> >>>>
> >>>>
> >>>-Fundamentally there is no difference, the exception being in
> >>>
> >>>
> >those
> >
> >
> >>>minds which tend now toward thinking of determination as cause.
> >>>
> >>>
> >>>
> >>AS opposed to the Aristotle four fold?? What on earth is
> >>
> >>
> >determination?
> >
> >
> >>>>How do our eyes and thoughts tell us anything about goals?
> >>>>
> >>>>
> >>>-Senses and thoughts are elements in the set.
> >>>
> >>>
> >>>
> >>Not as far as I can see....
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >>>>How does mathematics (ancient or modern) act as an initiative.
> >>>>
> >>>>
> >>>-It is recognizing that 'successful choosing' is logic to the
> >>>system; being did not always allow for our species as it is now.
> >>>
> >>>
> >>>
> >>Being does not permit nor deny. Being is not a control mechanism
> >>
> >>
> >as far
> >
> >
> >>as I can see or think. What system did you have in mind? What
> >>
> >>
> >logic?
> >
> >
> >>>>Let me be clear - these are not ordinary conceptions of
> >>>>mathematics. So they are questionable.
> >>>>b
> >>>>
> >>>>
> >>>-Popular conceptions are questionable because they are ordinary,
> >>>or perhaps i missed your point.
> >>>
> >>>
> >>I was suggesting that your discussion of mathematicals was not
one
> >>
> >>
> >that
> >
> >
> >>would be understandable by the high school math student. So they
> >>
> >>
> >tend to
> >
> >
> >>be strange and questionable.
> >>
> >>B
> >>
> >>
> >
> >
> >
> >
> >
> >This is one of the  lists sponsored by The Free Lance Academy,
home of
> >Slow Reading:  http://www.freelance-academy.org  To unsubscribe by
> >e-mail, mailto:klein-unsubscribe@onelist.com
> >Yahoo! Groups Links
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
>
>
>
> [Non-text portions of this message have been removed]

Mr. Picard,

I will tell you some points that Mr. Klein made in various places.

When reading the words of any thinker ( and there are not so many
thinkers as we tend to believe) one's own habits of thought are
insufficient. This means that if one is going to read, as opposed to
"that book is a good read," one must submit to the habits of thought of
the author. These days people are quick to attack this suggestion as one
that undermines "critical thinking." But, of course, critical thinking
is impossible without judgment and judgment impossible without
discernment. If one has not thought the thought which affords
understanding of the text one has not finished reading it. And better
than critique, having submitted to the text long enough to think it one
is free to occupy the office which the composition is as well as
establish another such should it prove worthy to do so.

picard wrote:

>Bill
>My apologies, my thoughts, my obtuse language. Scientific, as a word
>and wrt social perspective, was meant to indicate that all of us
>have (in some way) have been made physicists and questioners; even
>the most religious do not deny they share the 'stage' with logic and
>reason. (Were things ever otherwise?, apperently there still remain
>corners of our world that are)
>
>
>In my understanding, thus far, mathematics was a gift of the world
>to man. Mathematics and the world were one.
>
Yes, if you are indulging a certain way of speaking. There was a time
when everything they saw they could count. But than they saw the
continuous. With the theorem called Pythagorean comes the discovery that
there is no unit, no means, with which to count the side of a square
that will count its diagonal as well. Until than it looked to those who
liked counting so much that number and the world were one.

But math had proved to these people that a thing could be learned, that
is to say understood, which meant that a thing could be known. This
model for learning and knowledge was never betrayed by the Greeks. It is
fair to point out that Plato, for instance, was not "the Greeks."

>It is true today, but
>in the sense that the mathematics system sought is both logical and
>applicable (to the physical).
>
>
Yes. Although some argue that natural history (he peri phuseos historia)
was always a silent fifth art never far from the quadrivium (arithmetic,
geometry, music, astronomy) the inquiry into nature never did admit of
the kind of reflection which makes an art worthy of the name liberal.
Here liberal education is understood as the acquisition of the pursuits
that make it possible for a man to be a free one. As the teachers began
to fear for their way they compensated with the addition of the trivial
supplments (logic, rhetoric and grammar). This trend drifted from those
arts concerned with the mathema proper to the study  and generation of
-ologies.

Skipping over a great deal I will conclude this confirming reply by
pointing out that today all four of the original liberal arts labor on
behalf of  physics and have probed so far into the nether regions that
this mathematical physics affords no account apart from its symbolic
formula. Not only does submission to the rules of modern physics not
afford any human being a reflection which could be called liberating,
its results do not have sufficient semblance to anything anyone had ever
know to be knowledge to be worthy of the name.

>There are many systems available for people to compare, combine and
>use, and these bring with them certain inherent problems such as
>contradiction and paradox.
>
The Greek cognate of system meant an ordered arrangement and was used of
many things, a row of columns, the unites in a number, the beams rowers
set on in the ships but it was never said of thought. It did not occur
to them to speak of systems of thought because they thought about things
in the world, their thought was open to the world, their thought was the
world insofar as they had through thinking brought the world with in.

When you say this word "mind" what is it that you say? If you speak as
the moderns speak you mean some kind of a box which is by definition
(note what Bill said of definition) ever separate from any thing and
anything that could be called a world. Mind is a terrible word to utter
on behalf of the Greeks but the only thing that could be vaguely
identified with this awful word was understood as that which was open to
the world, that by means of which one brought  the world within. It was
this alone and nothing else.

In part two of this text Mr. Klein makes a suggestion concerning modern
conceptuality which  made the modern mind, the algebra, systems of
thought and so much else follow.
Take care,

J Keyser

> At this point an individual might choose
>to ignore something(s) so as to say "this the world" (definitions to
>masquerade as cause), when it is better asked "what is it that
>determines all else, here?"
>Wrt senses and thoughts: let a mind be a set M, in itself it is a
>universal because it cannot deny any aspect of it's own knowledge,
>physical or otherwise.
>len
>
>
>--- In klein@yahoogroups.com, "Bill Oates" <boates@e...> wrote:
>
>
>>Len
>>
>>Sorry but I am not following you. Perhaps you could expand on some
>>
>>
>this
>
>
>>or perhaps I am just obtuse.
>>
>>
>>
>>>-To the scientific.
>>>
>>>
>>Sorry still not understanding - in fact this only confuses more.
>>
>>
>Maybe
>
>
>>you could start over and expand on this. What is scientific?
>>
>>
>>
>>>>How is mathematics given by the world different from a world
>>>>
>>>>
>that
>
>
>>>>is inseparable from the mathematics?
>>>>
>>>>
>>>-Fundamentally there is no difference, the exception being in
>>>
>>>
>those
>
>
>>>minds which tend now toward thinking of determination as cause.
>>>
>>>
>>>
>>AS opposed to the Aristotle four fold?? What on earth is
>>
>>
>determination?
>
>
>>>>How do our eyes and thoughts tell us anything about goals?
>>>>
>>>>
>>>-Senses and thoughts are elements in the set.
>>>
>>>
>>>
>>Not as far as I can see....
>>
>>
>>
>>
>>
>>
>>
>>
>>>>How does mathematics (ancient or modern) act as an initiative.
>>>>
>>>>
>>>-It is recognizing that 'successful choosing' is logic to the
>>>system; being did not always allow for our species as it is now.
>>>
>>>
>>>
>>Being does not permit nor deny. Being is not a control mechanism
>>
>>
>as far
>
>
>>as I can see or think. What system did you have in mind? What
>>
>>
>logic?
>
>
>>>>Let me be clear - these are not ordinary conceptions of
>>>>mathematics. So they are questionable.
>>>>b
>>>>
>>>>
>>>-Popular conceptions are questionable because they are ordinary,
>>>or perhaps i missed your point.
>>>
>>>
>>I was suggesting that your discussion of mathematicals was not one
>>
>>
>that
>
>
>>would be understandable by the high school math student. So they
>>
>>
>tend to
>
>
>>be strange and questionable.
>>
>>B
>>
>>
>
>
>
>
>
>This is one of the  lists sponsored by The Free Lance Academy, home of
>Slow Reading:  http://www.freelance-academy.org  To unsubscribe by
>e-mail, mailto:klein-unsubscribe@onelist.com
>Yahoo! Groups Links
>
>
>
>
>
>
>
>
>
>



[Non-text portions of this message have been removed]

Len

Perhaps we have more of a communication.

That we have all been made physicists is something that seems to accord
with Klein's comment that mathematical physics is our underlying mode in
the modern world.
Having said that  - what does it mean - is it too late to be anything
else anyway?
The stage sharing reminds one of Klein's friend Strauss concern with
'jerusalem vs athens' - a bogus concern in the end. Once we decide that
the choice is reasonable we have chosen Athens. Our faith is reasonable.

AS to the corners of our world that are unreasonable - hm - are they
growing?

To say this is the world instead of asking - but that is the physicist
speaking is it not? But the mathematics of modern world begins with
definition. We will call a point ...

Let x be ...

Let mind be a set ...

Are we trapped in the definitions?

b


> My apologies, my thoughts, my obtuse language. Scientific, as a word
> and wrt social perspective, was meant to indicate that all of us
> have (in some way) have been made physicists and questioners; even
> the most religious do not deny they share the 'stage' with logic and
> reason. (Were things ever otherwise?, apperently there still remain
> corners of our world that are).
>
> In my understanding, thus far, mathematics was a gift of the world
> to man. Mathematics and the world were one. It is true today, but
> in the sense that the mathematics system sought is both logical and
> applicable (to the physical).
>
> There are many systems available for people to compare, combine and
> use, and these bring with them certain inherent problems such as
> contradiction and paradox. At this point an individual might choose
> to ignore something(s) so as to say "this the world" (definitions to
> masquerade as cause), when it is better asked "what is it that
> determines all else, here?".
>
> Wrt senses and thoughts: let a mind be a set M, in itself it is a
> universal because it cannot deny any aspect of it's own knowledge,
> physical or otherwise.
> len
>
>
> --- In klein@yahoogroups.com, "Bill Oates" <boates@e...> wrote:
> > Len
> >
> > Sorry but I am not following you. Perhaps you could expand on some
> this
> > or perhaps I am just obtuse.
> >
> > >
> > > -To the scientific.
> > Sorry still not understanding - in fact this only confuses more.
> Maybe
> > you could start over and expand on this. What is scientific?
> >
> > >
> > > > How is mathematics given by the world different from a world
> that
> > > > is inseparable from the mathematics?
> > >
> > > -Fundamentally there is no difference, the exception being in
> those
> > > minds which tend now toward thinking of determination as cause.
> > >
> > AS opposed to the Aristotle four fold?? What on earth is
> determination?
> >
> > >
> > > > How do our eyes and thoughts tell us anything about goals?
> > >
> > > -Senses and thoughts are elements in the set.
> > >
> > Not as far as I can see....
> >
> >
> >
> >
> >
> >
> > > > How does mathematics (ancient or modern) act as an initiative.
> > >
> > > -It is recognizing that 'successful choosing' is logic to the
> > > system; being did not always allow for our species as it is now.
> > >
> > Being does not permit nor deny. Being is not a control mechanism
> as far
> > as I can see or think. What system did you have in mind? What
> logic?
> >
> > > > Let me be clear - these are not ordinary conceptions of
> > > > mathematics. So they are questionable.
> > > > b
> > >
> > > -Popular conceptions are questionable because they are ordinary,
> > > or perhaps i missed your point.
> >
> > I was suggesting that your discussion of mathematicals was not one
> that
> > would be understandable by the high school math student. So they
> tend to
> > be strange and questionable.
> >
> > B
>
>
>
>
>
> This is one of the  lists sponsored by The Free Lance Academy, home of
> Slow Reading:  http://www.freelance-academy.org  To unsubscribe by
> e-mail, mailto:klein-unsubscribe@onelist.com
> Yahoo! Groups Links
>
>
>
>
>
>

To say the mind is a universal is misleading because a universal
does not exist irrespective of it. If a mind deems there to be
objects then they exist. Objects are 'of the consisderation of
such', this is an ever deepening cycle toward truth about mind.
len


--- In klein@yahoogroups.com, "picard" <chofborg1@y...> wrote:
> Bill
> My apologies, my thoughts, my obtuse language. Scientific, as a
word
> and wrt social perspective, was meant to indicate that all of us
> have (in some way) have been made physicists and questioners; even
> the most religious do not deny they share the 'stage' with logic
and
> reason. (Were things ever otherwise?, apperently there still
remain
> corners of our world that are).
>
> In my understanding, thus far, mathematics was a gift of the world
> to man. Mathematics and the world were one. It is true today, but
> in the sense that the mathematics system sought is both logical
and
> applicable (to the physical).
>
> There are many systems available for people to compare, combine
and
> use, and these bring with them certain inherent problems such as
> contradiction and paradox. At this point an individual might choose
> to ignore something(s) so as to say "this the world" (definitions
to
> masquerade as cause), when it is better asked "what is it that
> determines all else, here?".
>
> Wrt senses and thoughts: let a mind be a set M, in itself it is a
> universal because it cannot deny any aspect of it's own knowledge,
> physical or otherwise.
> len
>
>
> --- In klein@yahoogroups.com, "Bill Oates" <boates@e...> wrote:
> > Len
> >
> > Sorry but I am not following you. Perhaps you could expand on
some
> this
> > or perhaps I am just obtuse.
> >
> > >
> > > -To the scientific.
> > Sorry still not understanding - in fact this only confuses more.
> Maybe
> > you could start over and expand on this. What is scientific?
> >
> > >
> > > > How is mathematics given by the world different from a world
> that
> > > > is inseparable from the mathematics?
> > >
> > > -Fundamentally there is no difference, the exception being in
> those
> > > minds which tend now toward thinking of determination as cause.
> > >
> > AS opposed to the Aristotle four fold?? What on earth is
> determination?
> >
> > >
> > > > How do our eyes and thoughts tell us anything about goals?
> > >
> > > -Senses and thoughts are elements in the set.
> > >
> > Not as far as I can see....
> >
> >
> >
> >
> >
> >
> > > > How does mathematics (ancient or modern) act as an
initiative.
> > >
> > > -It is recognizing that 'successful choosing' is logic to the
> > > system; being did not always allow for our species as it is
now.
> > >
> > Being does not permit nor deny. Being is not a control mechanism
> as far
> > as I can see or think. What system did you have in mind? What
> logic?
> >
> > > > Let me be clear - these are not ordinary conceptions of
> > > > mathematics. So they are questionable.
> > > > b
> > >
> > > -Popular conceptions are questionable because they are
ordinary,
> > > or perhaps i missed your point.
> >
> > I was suggesting that your discussion of mathematicals was not
one
> that
> > would be understandable by the high school math student. So they
> tend to
> > be strange and questionable.
> >
> > B

Bill
My apologies, my thoughts, my obtuse language. Scientific, as a word
and wrt social perspective, was meant to indicate that all of us
have (in some way) have been made physicists and questioners; even
the most religious do not deny they share the 'stage' with logic and
reason. (Were things ever otherwise?, apperently there still remain
corners of our world that are).

In my understanding, thus far, mathematics was a gift of the world
to man. Mathematics and the world were one. It is true today, but
in the sense that the mathematics system sought is both logical and
applicable (to the physical).

There are many systems available for people to compare, combine and
use, and these bring with them certain inherent problems such as
contradiction and paradox. At this point an individual might choose
to ignore something(s) so as to say "this the world" (definitions to
masquerade as cause), when it is better asked "what is it that
determines all else, here?".

Wrt senses and thoughts: let a mind be a set M, in itself it is a
universal because it cannot deny any aspect of it's own knowledge,
physical or otherwise.
len


--- In klein@yahoogroups.com, "Bill Oates" <boates@e...> wrote:
> Len
>
> Sorry but I am not following you. Perhaps you could expand on some
this
> or perhaps I am just obtuse.
>
> >
> > -To the scientific.
> Sorry still not understanding - in fact this only confuses more.
Maybe
> you could start over and expand on this. What is scientific?
>
> >
> > > How is mathematics given by the world different from a world
that
> > > is inseparable from the mathematics?
> >
> > -Fundamentally there is no difference, the exception being in
those
> > minds which tend now toward thinking of determination as cause.
> >
> AS opposed to the Aristotle four fold?? What on earth is
determination?
>
> >
> > > How do our eyes and thoughts tell us anything about goals?
> >
> > -Senses and thoughts are elements in the set.
> >
> Not as far as I can see....
>
>
>
>
>
>
> > > How does mathematics (ancient or modern) act as an initiative.
> >
> > -It is recognizing that 'successful choosing' is logic to the
> > system; being did not always allow for our species as it is now.
> >
> Being does not permit nor deny. Being is not a control mechanism
as far
> as I can see or think. What system did you have in mind? What
logic?
>
> > > Let me be clear - these are not ordinary conceptions of
> > > mathematics. So they are questionable.
> > > b
> >
> > -Popular conceptions are questionable because they are ordinary,
> > or perhaps i missed your point.
>
> I was suggesting that your discussion of mathematicals was not one
that
> would be understandable by the high school math student. So they
tend to
> be strange and questionable.
>
> B

Len

Sorry but I am not following you. Perhaps you could expand on some this
or perhaps I am just obtuse.

>
> -To the scientific.
Sorry still not understanding - in fact this only confuses more. Maybe
you could start over and expand on this. What is scientific?

>
> > How is mathematics given by the world different from a world that
> > is inseparable from the mathematics?
>
> -Fundamentally there is no difference, the exception being in those
> minds which tend now toward thinking of determination as cause.
>
AS opposed to the Aristotle four fold?? What on earth is determination?

>
> > How do our eyes and thoughts tell us anything about goals?
>
> -Senses and thoughts are elements in the set.
>
Not as far as I can see....






> > How does mathematics (ancient or modern) act as an initiative.
>
> -It is recognizing that 'successful choosing' is logic to the
> system; being did not always allow for our species as it is now.
>
Being does not permit nor deny. Being is not a control mechanism as far
as I can see or think. What system did you have in mind? What logic?

> > Let me be clear - these are not ordinary conceptions of
> > mathematics. So they are questionable.
> > b
>
> -Popular conceptions are questionable because they are ordinary,
> or perhaps i missed your point.

I was suggesting that your discussion of mathematicals was not one that
would be understandable by the high school math student. So they tend to
be strange and questionable.

B

--- In klein@yahoogroups.com, "oatesguyca" <boates@e...> wrote:
> .....> But what is that shift?

-To the scientific.

> How is mathematics given by the world different from a world that
> is inseparable from the mathematics?

-Fundamentally there is no difference, the exception being in those
minds which tend now toward thinking of determination as cause.

> Were we always in a position of believing our eyes and thoughts?

-If we chose to.

> How do our eyes and thoughts tell us anything about goals?

-Senses and thoughts are elements in the set.

> How does mathematics (ancient or modern) act as an initiative.

-It is recognizing that 'successful choosing' is logic to the
system; being did not always allow for our species as it is now.

> Let me be clear - these are not ordinary conceptions of
> mathematics. So they are questionable.
> b

-Popular conceptions are questionable because they are ordinary,
or perhaps i missed your point.
len


>
> --- In klein@yahoogroups.com, "picard" <chofborg1@y...> wrote:
> > Hi Bill
> > Klein's introduction seems to say that ancient greek mathematics
> > fore-shadowed the birth of modern mathematics. Sixteenth century
> > input shifted the focus from greek arithmos (mathematics as given
> > by the world) to a (physical) world that is inseparable from the
> > mathematics.
> > We are in the position of believing our eyes and thoughts; so,
> > irrespective of what they may tell us our goal must be to
maintain
> > some defined level of system-emergent control, mathematics exists
> > as that initiative.
> > len
> >

Len

Well there are similarities and differences beteen ancient and modern
mathematics. Klein seems to place the shift in the sixteenth century.
But what is that shift?

How is mathematics given by the world different from a world that is
inseparable from the mathematics?

Were we always in a position of believing our eyes and thoughts? How
do our eyes and thoughts tell us anything about goals? How does
mathematics (ancient or modern) act as an initiative.

Let me be clear - these are not ordinary conceptions of mathematics.
So they are questionable.

b

--- In klein@yahoogroups.com, "picard" <chofborg1@y...> wrote:
> Hi Bill
> Klein's introduction seems to say that ancient greek mathematics
> fore-shadowed the birth of modern mathematics. Sixteenth century
> input shifted the focus from greek arithmos (mathematics as given
> by the world) to a (physical) world that is inseparable from the
> mathematics.
> We are in the position of believing our eyes and thoughts; so,
> irrespective of what they may tell us our goal must be to maintain
> some defined level of system-emergent control, mathematics exists
> as that initiative.
> len
>

Hi Bill
Klein's introduction seems to say that ancient greek mathematics
fore-shadowed the birth of modern mathematics. Sixteenth century
input shifted the focus from greek arithmos (mathematics as given
by the world) to a (physical) world that is inseparable from the
mathematics.
We are in the position of believing our eyes and thoughts; so,
irrespective of what they may tell us our goal must be to maintain
some defined level of system-emergent control, mathematics exists
as that initiative.
len


--- In klein@yahoogroups.com, "Bill Oates" <boates@e...> wrote:
> Welcome
> This list has been somewhat empty = ok no messages for quite a
while. Is
> there any life in the old girl?
> Your first impression does not connect with my remembrance of the
> introduction. Could you expand?
> I do not get any notion of control of new thoughts. An attempt to
revive
> old ones though.
> regards
> Bill


Newbie here, just finished a first reading of klein's introduction
to his book. By 'weight', my first impression is, klein's work takes
thought down to thee base level of thinking; there is only one
option-control the emergence of new thoughts in and by contour form.
len

Welcome

This list has been somewhat empty = ok no messages for quite a while. Is
there any life in the old girl?

Your first impression does not connect with my remembrance of the
introduction. Could you expand?

I do not get any notion of control of new thoughts. An attempt to revive
old ones though.

regards

Bill

Newbie here, just finished a first reading of klein's introduction
to his book. By 'weight', my first impression is, klein's work takes
thought down to thee base level of thinking; there is only one option-
control the emergence of new thoughts in and by contour form.
len

New member, my dover paperback copy of klein's book just arrived.

Reading the backcover notes i was struck by the words, "...klein
investigates the revival and assimilation of greek mathematics...
from the specific standpoint of the conceptual transformation which
occurred in the course of that assimilation".
Have we learned to think that ancient greek mathematicians somehow
thought their world in abstract was flat, or does the mind strike
some balance between complexity and form?
If it is conceptual transformation then investigation is appropriate
for abstract beings such as ourselves (so 'far removed' from mere
protoplasm) trying to learn integration of thought.
len

Mainly, Klein does the kind of writing I have the most
respect for, interpretive reading but respectful of
the text and what it offers, as opposed to what others
may suggest it has to offer. His book on mathematics
is extremly helpful in considering same and other.

thanks,
brandon



> Hi Brandon:
>
> This group has been dormant for some time. It's not
> that we're not interested in Klein or
> Greek mathematics in general; we've just gone off to
> other topics, e.g. Phaedo, Aristotle's
> Organon, etc., for a bit.
>
> I'm not sure where you're coming from or going to.
>
> You are a philosophy major looking for a graduate
> school with a strong classics program?
>
> If that's the case, you can search on Google for
> some crude pointers. One that I found is:
>

__________________________________________________
Do You Yahoo!?
Tired of spam?  Yahoo! Mail has the best spam protection around
http://mail.yahoo.com

Hi Brandon:

This group has been dormant for some time. It's not that we're not interested in
Klein or
Greek mathematics in general; we've just gone off to other topics, e.g. Phaedo,
Aristotle's
Organon, etc., for a bit.

I'm not sure where you're coming from or going to.

You are a philosophy major looking for a graduate school with a strong classics
program?

If that's the case, you can search on Google for some crude pointers. One that I
found is:
http://www.vanderbilt.edu/AnS/history/graham/Classic%20Data.htm

I was a math & computer science grad student with but a keen interest in
philosophy and
no professional training as a philosopher. I picked up on the ancients
relatively late.

My general advice would be to pick what you can afford financially. Then, pick a
program
that has some depth--more than a few professors in the area that interests you
the most.
When I went to grad school in math, I envisioned working with a professor that
was very
prominent, but had, in fact, become burned out. But it was a broad program, and
I was
able to find someone else that was actively recruiting students. That's
important--the
eventual choice of a research supervisor and the availability of backups! (The
same thing
happened later in comp sci.) Finally, pick a grad school that you like--for the
cultural
environment and for the intellectual bent. For example, you might like an east
coast
school but not the Univ of Arizona, even though Tucson has a good philosophy
program.

Why were  you searching on Jacob Klein?

--Ron


--- In klein@yahoogroups.com, "brandonspun" <brandonspun@y...> wrote:
>
> High, I just found this list searching Jacob Klein on the internet. I
> am intersted in doing graduate studies on dialogue, synthetic and
> analytic inquiry, and first principles. Does any one know what schools
> or people to look to for guidance?
>
> Brandon
> brandonspun@y...

High, I just found this list searching Jacob Klein on the internet. I
am intersted in doing graduate studies on dialogue, synthetic and
analytic inquiry, and first principles. Does any one know what schools
or people to look to for guidance?

Brandon
brandonspun@...

got it.

Lee Perlman

Hi Bill:

Just responding to your Klein test: gottit.

--Ron

oatesguyca wrote:

>
>Hello
>
>Is this list working - old messages seem to be missing.
>
>bill
>
>
>
>
>
>
>This is one of the  lists sponsored by The Free Lance Academy, home of
>Slow Reading:  http://www.freelance-academy.org  To unsubscribe by
>e-mail, mailto:klein-unsubscribe@onelist.com
>Yahoo! Groups Links
>
>
>
>
>
>
>
>

Hello

Is this list working - old messages seem to be missing.

bill

--- In plato-phaedo@yahoogroups.com, jkeyser <jk@a...> wrote:

> As for you and I Bill, I do extend the invitation that I once
offered my old
> friend Lee. http://groups.yahoo.com/group/klein/message/196?source=1
>

OK, you didn't address it to me, and I'm by no means a mathematical
heavyweight, but I think if you've been attending to the discussion in
the Phaedo list you may understand that I find what you're presenting
here very interesting, not just because of Klien's contributions as
Mr. Gregory quotes him, but by reason of the intriguing notion that
something of the pre-Socratic number theory has been lost that has
current relevance. I think the relevance goes beyond mathematics. So
I'm very intrigued.

APMW

This invitation pertains to two different groups. One is the
plato-phaedo list, the other is a list called philosophy2. Both are
groups that existed in the somewhat distant past (well, not in the
lifetime of Plato, to be honest) and were extinguished by Yahoo Groups
due to inactivity and had to be recreated.

PLATO-PHAEDO

The plato-phaedo list had a long discussion of that dialogue and, thanks
to Angela Cembrola and (I believe) Michael Kochin, we were able to
rescue and upload the archives of past discussions. For some reason,
however, the subscriber base was never restored and at present there are
only 8 subscribers to that list.

The Phaedo is a very interesting and important dialogue.  I think it
would be good to generate a new slow reading of it.  If you would like
to participate and are not already a subscriber, you can subscribe by
sending a message to plato-phaedo-subscribe@yahoogroups.com, or
(preferably) by going to
http://groups.yahoo.com/group/plato-phaedo/join.

REQUEST FOR DISCUSSION LEADER:  If you would be interested in serving as
a discussion leader, please contact me at lrf@....


PHILOSOPHY2

The philosophy2 list started out as philosophy@...
(or something like that) and then became philosophy@... and
then philosophy@.... At that time it was intended for
general discussion about the nature of philosophy and the philosophy
profession (if that is not an oxymoron). Some time before I moved all my
lists to onelist.com (which ultimately became yahoogroups.com) we
started what was intended to be a systematic survey of the history of
philosophy, so when I moved my lists I decided to rename this one
philosophy-history, as a name more indicative of its purpose.  The
original list remained in existence for a while, but was deleted by
Yahoo at some point, and I lost control over the name. That is the
reason why, when I decided to recreate the list, it had to be under a
new name, and I chose to call it: philosophy2.

Anyway, if you would like to participate in general discussions about
the nature of philosophy and of (perish the thought) the philosophy
profession, you are invited to subscribe to philosophy2 by either
sending a message to philosophy2-subscribe@yahoogroups.com or going to
http://groups.yahoo.com/group/philosophy2/join.

And if you would like to serve as a discussion leader for this group,
please contact me at lrf@....

Lancelot Fletcher, president
The Free Lance Academy



[Non-text portions of this message have been removed]

Hi Klein group:

Put away that book and turn on the tube!

If you get PBS on TV (maybe this only applies to Klein
list folks in the US) there is an upcoming program on
the erased manuscript of Archimedes:

http://www.pbs.org/wgbh/nova/archimedes/about.html

--Ron

--- Icastes <pehme@...> wrote:
--snip--

>
> Aargh. No, Klein is very clear. There are ten,
> because one is both one as a
> determined one and an indeterminate one. It is this
> very meeting of ones
> that enables the other eidetic numbers to be, and
> thus enables the human
>

Let me repeat something from my post #670:

Klein, "Plato's Trilogy: Theaetetus, the Sophist and
the Statesman",
Univ of Chicago Press, 1977 (p. 61) confirms: "It
seems that Plato did
not extend the 'eidetic assemblages' beyond the
'eidetic ten'. Within
this hierarchy of nine 'eidetic assemblages' the first
one, the 'eidetic
Two,' is the most important."

I'm just quoting Jacob Klein. He is very clear, yes.

--Ron

Ron Allen writes:

[snip]

> > Which ones? I've lost a bit of the past by having to
> > change computers in
> > midstream, with many thanks to Bill Gates. I also
> > noticed that the
> > bounce-back on my recent post to J Keyser took a
> > very long time to get back
> > to me, and I wonder what's going on.
>
> I haven't had any problems in replying directly to
> Klein messages sent to me from Yahoo. Are you on Mac
> or Linux now?

Just venting my frustration with Windows, no matter what version I use. I
was having such a horrible time with Windows in one machine (where I used to
be) that I simply changed grabbed another machine and started over again,
with the intent of fixing the old one sometime...

I have never used a Mac until recently when I started teaching at St. John's
University, where the entire network is on Macs. I must reserve judgment on
it, though. I have used Linux, but I am not proficient enough on it.
However, the main trouble is that I have all kinds of software that I use
regularly that are not available for anything but Windows. So I am wedded to
Bill Gates no matter what. If only someone would come up with a fool-proof
emulator...

[snip]


> > General comments:
> >
> > I don't think you have Klein correct here,
>
> Well, I guess I could just type out the text of his
> footnote....

I believe that Klein means the obvious, that the dyadic structure of the
whole itself is the foundation for the generation of numbers, not that Ross
is correct in the way he derives the numbers. I don't think anyone is going
to argue that numbers derive from anything else, as the whole of things is
the whole of all things, including numbers.

> and I
> > believe Klein is basically
> > wrong about Plato in his tipping the balance to a
> > favoring of Aristotle.
>
> OK. I think that Plato's philosophy might be amended
> to better defend itself against Aristotle's attack.
> One way to start is by getting rid of the arithmoi
> mathematikoi as assemblages of "identical" noetic
> units. Next thing is to shed the Pythagorean heritage,
> especially the numerology. Plato did an outstanding
> job, even as an old man, in the Sophist. Ostensibly an
> attack on Protagoras, et al., it's really a defense of
> his middle ground against Parmenides. The cost is
> adding some additional structure to the higher noeta.

No, I think the opposite. The problem is that Aristotle's entire
cosmological structure is wrong, and as such in the end his defense of the
inherent self-identity of things collapses in a way that Plato's Heraclitean
flux of things does not.

Klein clearly sees that there is something wrong with Plato's view that the
things of the world are fundamentally illusory (in a flux), and thus goes
along with Aristotle's view against Plato.

> If
> > Klein takes Ross's position, then he is wrong as
> > well. I have no problem
> > with Klein being wrong about anything. But one can
> > see that Ross's
> > speculation is clearly nonsensical as it presupposes
> > in an Aristotlean
> > framework a special purity of numbers, a special
> > beingness of numbers, that
> > they do not have in the scheme that I presented.
>
> There is also that same framework in the Parmenides,
> which Aristotle didn't write.

It may be Parmenidean, but it is not Plato's. As we have discovered, there
are a very limited number of eidetic numbers.

> >
> > Context: We are in a chapter on Aristotle, and we
> > have to come to terms with
> > what is the difference between Plato and Aristotle.
> > It is an argument over
> > the character of the whole and the character of the
> > parts (101; cf. n. 116).
>
> Wrong, as regards mathematics. It's an argument over
> the mode of being of mathematical objects: separate
> (Plato) or not (Aristotle).

No, wrong. The very problem of the mode is inherent in the way the whole is
structured. The whole of Aristotle, including a prime mover, thought
thinking itself, and separate intellects, with energeia, is missing in
Plato. It is Aristotle's structure of the whole that enables the numbers not
to be separate as they are in Plato.

> What we should reflect how Aristotle's account works
> and whether Klein got it right or not.

Klein's entire discussion is directed to this problem of the whole and how
it is structured. It is not about numbers alone, as it would be fruitless to
speak of numbers without the whole of which they are a part.

> > In effect, the argument is over the status of
> > whether parts have an identity
> > of their own within the whole. In Plato, they do
> > not, because the Good, that
> > is which is perfect and the cause of all perfection,
> > is beyond all being.
>
>
> > That means that in Plato no being, no thing, has the
> > good, but must reach
> > out to the Good to become something. This chorismos
> > thesis, Klein says, has
> > its strongest support in mathematics, as we found in
> > the preceeding chapter
> > on Plato's math, particularly about the whole being
> > apart from all things
> > and not identifiable with any part. The eidetic
> > numbers, of which there are
> > only ten,
>
> Just when I thought we were making progress...aargh.
>
> The eidetic numbers are 2, 3, 4, 5, 6, 7, 8, 9, and
> 10. There are nine (9), neuf, nueve, djevjat', kyu,
> and so on of them. They stop at 10, but they start at
> 2: 10-2+1 = 9.

Aargh. No, Klein is very clear. There are ten, because one is both one as a
determined one and an indeterminate one. It is this very meeting of ones
that enables the other eidetic numbers to be, and thus enables the human
construction of all other numbers. That is the indeterminate dyad, the one
and one, that we makes two the number. In your formulation, two somehow
exists separately from the whole of things and not generated out of the
whole. In Plato, no eidetic number has self-identity. Only in Aristotle does
two have a self-identity.

> Not that it matters a whole heck of a lot, but it's
> good to keep in mind that 1 was not clearly understood
> as a number until after Aristotle's impact was felt.
>
> There has been some argumentation lately that
> Aristotle also had a concept of zero, meden, but I
> think that's controversial.

Acutally, Plato and Aristotle both have a zero, but it is not a mathematical
zero in the way we use it. The zero technically speaking would be the
indeterminate, a kind of cosmic zero representing the partless whole itself.
The entire Aristotlean universe, eternal as it is, whose outside has not
outside but only an inside, is actually located nowhere, the zero.


> something which you (and I believe Mr.
> > Hopkins) initially denied
> > of the notion that all numbers are eidetic, arise
> > out the notion that the
> > eidetic numbers are "roots" out of which all other
> > numbers may be generated.
>
> I don't remember Burt Hopkins drawn into my dispute
> with Steve Sorensen. But anyway, I was pointing to
> what I thought was, on Klein's part, of failing to
> point out how scant are the references to mathematical
> number in the Platonic corpus, and that there are a
> lot of reasons to think that Plato thought these
> things to be of secondary importance. I think that
> Plato must accept them, however, based on Aristotle's
> authority that he did, and the fact that Plato didn't
> work out how arithmetic could work from monadic,
> eidetic numbers. The notion of assemblages of
> "identical units" is self-stultifying, as Aristotle
> argues. And it's an obvious argument. So it seems
> rather like Plato must have been trying to avoid this
> as his central account of arithmetic. Also, the
> Phaedo, which was written by Plato, not Aristotle,
> directly argues in favor of Twoness instead of adding
> one and one together to get from eight to ten.

I didn't go back to read the posts, so Mr. Hopkins happily may have enjoyed
staying out of the fray.

The problem of twoness, as I noted above, is the problem of the dyadic
structure of the whole. I am, of course, using the word "dyadic" and
applying it to Plato even though Plato himself does not. Twoness, then, is
generated out of the very fact that the whole, although a complete
indeterminate, nevertheless, has a "natural" determinateness as "one." And,
as we find in Godard's movie, 1 + 1...

> When I argued against arithmoi mathematikoi in Plato,
> it was from knowing what damage A. was going to do to
> P. for taking this stance. It might be possible, I
> thought, to put the a. mathematikoi aside, and
> buttress P.'s chorismos thesis by affirming a.
> eidetikoi. Maybe it's all just too speculative on my
> part.


I don't see what damage Aristotle has done at all, as it is Aristotle who is
crippled at this point, as he is wrong about the eternity of the world and
no one at this point can demonstrate or even articulate how the physical
cosmos is either coterminous or a reflection of the absolute circularity of
thought itself or the way that thought separates into separate
intelligences, etc.. While the Aristotlean view appears to be complete
sanity in comparison to Plato, it is Aristotle's merging of cosmology with
ontology that appears to have failed entirely ever since his cosmos has
proven to be a pretty image and nothing else.

> > Moreover, these roots act much more as principles,
> > so to speak, or a
> > reflection, of the very way all things hang
> > together, as their heirarchy
> > form higher and higher genera, and so on (92-93)
> > until we finally come to
> > the highest of all things, the Good, that is
> > completely separate from all
> > beings. If we go along with Plato, then all
> > individual things participate in
> > greater things that, strictly speaking, are noetic,
> > and all the rest are in
> > Heraclitean flux, a kind of illusion.
>
> Your train gets onto a new age track as soon as a
> switch isn't locked down somewhere.
>
> I think that Plato just wants to emphasize that there
> has to be a limit to ever increasing truthfulness, and
> our language is not adequate to the task of describing
> it. You can't articulate a lot about Plato's Good,
> just as you can't say a lot about Parmenides's One.

There is no New Age here. It is plain in Plato, e.g., Philebus 20d (and
elsewhere). Only the Good is perfect; only the good is sufficient and
differs from all the beings in sufficency; and it is logos choiceworthy. In
other words, only the good is one; only the good is the whole, and as such
all beings must come to be and are dependent upon other beings and thus
inherently defective; and it is only the good that motivates human desire.
The Good is beyond all the beings, and as such all beings, unlike in
Aristotle, do not contain the Good and must reach out to the Good to
complete themselves. Aristotlean energeia which is applied to all beings is
an attempt to refute that Aristotlean position. As I have noted previously,
the only thing that resembles energeia in Plato is Socrates, the only
Platonic being that can achieve its proper being by knowing the Good being
the philosopher. (Klein, by the way, very neatly outlines this Aristotlean
view in his "Aristotle, An Introduction.")

Best regards,

Kalev Pehme

Dear Klein group:

I've replied to Kalev Pehme's post, below:

--- Icastes <pehme@...> wrote:
> Ron Allen writes:
>
>
>   Ah, ha, ha, ha, ha! Kalev Pehme, it's good to see
>   you're back spamsophosizing us, and that the long
>   respite hasn't infected you with either lucidness
> or
>   forthright argumentation. Some things never
> change,
>   and I'm beginning to think that you are the One.
>
>   Hey, don't you have some unanswered questions from
>   Burt Hopkins to address?
>
>
> Which ones? I've lost a bit of the past by having to
> change computers in
> midstream, with many thanks to Bill Gates. I also
> noticed that the
> bounce-back on my recent post to J Keyser took a
> very long time to get back
> to me, and I wonder what's going on.

I haven't had any problems in replying directly to
Klein messages sent to me from Yahoo. Are you on Mac
or Linux now?

>
>   Well, anyway, hardy greetings, and let me comment
> on
>   your post. A few things are inserted down below.
>
>   --- Icastes <pehme@...> wrote:
>   > Ron Allen writes:
>   >
>   > > Hello furtive Klein groupies:
>   > >
>   > > Let me try posting this comment again;
> previous
>   > effort via another
>   > > browser/server seemed to fail. I have to
> retype it
>   > too. Apologies, if
>   > > there's a basically duplicate post that pops
> up
>   > someday.
>   > >
>   > > There is another way to approach Bill's
> question
>   > below. Instead of
>   > > invoking the Divided Line, as I like to do, we
>   > could try interpreting it
>   > > as deriving mathematicals from the One and the
>   > aoristos dyas
>   > > (indeterminate dyad).
>   > >
>   > > Klein covers this--very briefly--on p. 98:
> "Thus
>   > by a continual
>   > > 'duplication' of the eide--which the logs
> grasps
>   > in the 'division' of
>   > > the gene--it makes the 'genetic' order of the
>   > eidetic numbers possible."
>   > >
>   > > Footnote #110 contains a litte more on this
>   > generation of the eidetic
>   > > numbers. This would give us only the even
>   > eidetics. We get the odds via
>   > > some kind of delimitation through the One. He
>   > seems to agree with Ross,
>   > > who in his books on Aristotle's Metaphysics,
>   > explains the derivation as
>   > > follows:
>   > >
>   > > One => (aoristos dyas) => 2;
>   > > 2 => (aor dyas) => 4 => (a d) => 8;
>   > > 2 => (One) => 3; 4 => (One) => 5; 8 => 9;
>   > > 3 => (a d) => 6; 5 => 10;
>   > > 6 => (One) => 7.
>   > >
>   > > Ross says this is speculative, though.
>   > >
>   > > We can get all numbers in this way, too.
>   > >
>   > > Klein and Ross seem different on the role of
> the
>   > aoristos dyas. For
>   > > Ross, it's more of an infinitely duplicating
>   > thing, and he doesn't seem
>   > > to emphasize the imaging aspect of its
> generation
>   > of things. But for
>   > > Klein it's imaging aspect is important. So, is
> the
>   > eidetic 2 the image
>   > > of the One? Why is it that only arithmetic
> noeta
>   > seem to be generated?
>   > > Or is there a generation of Red and Barbarian
> from
>   > more fundamental
>   > > Forms? Or it could be that we want to deny
>   > Aristotle and Ross's report
>   > > on generation of eidetic numbers and carefully
>   > consider that Klein says
>   > > that it's the "genetic order" that is made
>   > possible. So, the eidetic
>   > > numbers always existed, then, and the order is
>   > what is created by the
>   > > One operating alternately with the aoristos
> dyas.
>   >
>   > Ross is incorrect,
>
>   Well, then Klein would be incorrect too, because
> he
>   clearly states in the footnote that eidetic
> numbers
>   derive from not only from the aorist dyad, but
> from
>   the delimitation of the One as well. You seem to
> have
>   an apoplexy as soon as your are about to assert
> Jacob
>   Klein is wrong. It's OK! He's not a saint. Instead
> you
>   strike out at Sir David Ross, who did say his
>   derivation was conjectural.
>
>
>
> General comments:
>
> I don't think you have Klein correct here,

Well, I guess I could just type out the text of his
footnote....

and I
> believe Klein is basically
> wrong about Plato in his tipping the balance to a
> favoring of Aristotle.

OK. I think that Plato's philosophy might be amended
to better defend itself against Aristotle's attack.
One way to start is by getting rid of the arithmoi
mathematikoi as assemblages of "identical" noetic
units. Next thing is to shed the Pythagorean heritage,
especially the numerology. Plato did an outstanding
job, even as an old man, in the Sophist. Ostensibly an
attack on Protagoras, et al., it's really a defense of
his middle ground against Parmenides. The cost is
adding some additional structure to the higher noeta.

If
> Klein takes Ross's position, then he is wrong as
> well. I have no problem
> with Klein being wrong about anything. But one can
> see that Ross's
> speculation is clearly nonsensical as it presupposes
> in an Aristotlean
> framework a special purity of numbers, a special
> beingness of numbers, that
> they do not have in the scheme that I presented.

There is also that same framework in the Parmenides,
which Aristotle didn't write.

>
> Context: We are in a chapter on Aristotle, and we
> have to come to terms with
> what is the difference between Plato and Aristotle.
> It is an argument over
> the character of the whole and the character of the
> parts (101; cf. n. 116).

Wrong, as regards mathematics. It's an argument over
the mode of being of mathematical objects: separate
(Plato) or not (Aristotle).

What we should reflect how Aristotle's account works
and whether Klein got it right or not.

> In effect, the argument is over the status of
> whether parts have an identity
> of their own within the whole. In Plato, they do
> not, because the Good, that
> is which is perfect and the cause of all perfection,
> is beyond all being.


> That means that in Plato no being, no thing, has the
> good, but must reach
> out to the Good to become something. This chorismos
> thesis, Klein says, has
> its strongest support in mathematics, as we found in
> the preceeding chapter
> on Plato's math, particularly about the whole being
> apart from all things
> and not identifiable with any part. The eidetic
> numbers, of which there are
> only ten,

Just when I thought we were making progress...aargh.

The eidetic numbers are 2, 3, 4, 5, 6, 7, 8, 9, and
10. There are nine (9), neuf, nueve, djevjat', kyu,
and so on of them. They stop at 10, but they start at
2: 10-2+1 = 9.

Not that it matters a whole heck of a lot, but it's
good to keep in mind that 1 was not clearly understood
as a number until after Aristotle's impact was felt.

There has been some argumentation lately that
Aristotle also had a concept of zero, meden, but I
think that's controversial.

something which you (and I believe Mr.
> Hopkins) initially denied
> of the notion that all numbers are eidetic, arise
> out the notion that the
> eidetic numbers are "roots" out of which all other
> numbers may be generated.

I don't remember Burt Hopkins drawn into my dispute
with Steve Sorensen. But anyway, I was pointing to
what I thought was, on Klein's part, of failing to
point out how scant are the references to mathematical
number in the Platonic corpus, and that there are a
lot of reasons to think that Plato thought these
things to be of secondary importance. I think that
Plato must accept them, however, based on Aristotle's
authority that he did, and the fact that Plato didn't
work out how arithmetic could work from monadic,
eidetic numbers. The notion of assemblages of
"identical units" is self-stultifying, as Aristotle
argues. And it's an obvious argument. So it seems
rather like Plato must have been trying to avoid this
as his central account of arithmetic. Also, the
Phaedo, which was written by Plato, not Aristotle,
directly argues in favor of Twoness instead of adding
one and one together to get from eight to ten.

When I argued against arithmoi mathematikoi in Plato,
it was from knowing what damage A. was going to do to
P. for taking this stance. It might be possible, I
thought, to put the a. mathematikoi aside, and
buttress P.'s chorismos thesis by affirming a.
eidetikoi. Maybe it's all just too speculative on my
part.

> Moreover, these roots act much more as principles,
> so to speak, or a
> reflection, of the very way all things hang
> together, as their heirarchy
> form higher and higher genera, and so on (92-93)
> until we finally come to
> the highest of all things, the Good, that is
> completely separate from all
> beings. If we go along with Plato, then all
> individual things participate in
> greater things that, strictly speaking, are noetic,
> and all the rest are in
> Heraclitean flux, a kind of illusion.

Your train gets onto a new age track as soon as a
switch isn't locked down somewhere.

I think that Plato just wants to emphasize that there
has to be a limit to ever increasing truthfulness, and
our language is not adequate to the task of describing
it. You can't articulate a lot about Plato's Good,
just as you can't say a lot about Parmenides's One.
--Ron

--snip--