Re: [PEIRCE-L] [EXTERNAL] Peirce on Dimensionality (was Connected Signs Theorem)

[Jon Alan Schmidt]

Jack, List:

I can offer a couple more thoughts related to dimensionality.

First, I also suggest reading my earlier paper, "Peirce's Topical
Continuum: A 'Thicker' Theory" (
https://doi.org/10.2979/trancharpeirsoc.56.1.04), which quotes and comments
on a previously unpublished manuscript by Peirce that includes the
following definitions.

CSP: [I]n order to make up a continuum, two continua must have something in
common, but their common part need not be like them in complexity of its
composition. By a *portion*, in the terminology of this memoir, is meant a
part of like complexity of composition of its whole. A *limit *between two
portions of a continuum having no common portion is the part of lower
complexity of composition. The *dimensionality *of a continuum is the
number which measures the complexity of its composition. If the limit
between two portions of a continuum having no common portion is not
continuous, that continuum is said to have its dimensionality equal to one,
or to have *one dimension*. If the limit between two portions of a
continuum that have no common portion is, at highest, of dimensionality, N,
that continuum is said to have its *dimensionality *equal to N+1, or to
have N+1 *dimensions*. (R 144:2, c. 1900)


The portions of a continuous one-dimensional line are also continuous
one-dimensional lines, while the limits between such portions are discrete
dimensionless points. The portions of a continuous two-dimensional surface
are also continuous two-dimensional surfaces, while the limits between such
portions are one-dimensional lines that meet at dimensionless points. The
portions of a continuous three-dimensional space are also continuous
three-dimensional spaces, while the limits between such portions are
two-dimensional surfaces that meet at one-dimensional lines, which meet at
dimensionless points. And so on.

Second, with that in mind, I suggest that we can *diagram *the entire
universe as a semiosic continuum of three dimensions. It is a vast argument
whose portions are likewise three-dimensional spaces that correspond to its
constituent argument types, whose limits are two-dimensional surfaces that
correspond to proposition types, whose limits in turn are one-dimensional
lines that correspond to name types. The dimensionless points where
different spaces, surfaces, and lines meet correspond to the *discrete *tokens
of all three classes of signs. This reflects the "top-down" nature of a
true continuum (3ns), such that its material parts are indefinite
possibilities (1ns), only some of which are actualized (2ns).

CSP: Experience is first forced upon us in the form of a flow of images.
Thereupon thought makes certain assertions. It professes to pick the image
into pieces and to detect in it certain characters. This is not literally
true. The image has no parts, least of all predicates. Thus predication
involves precisive abstraction. Precisive abstraction creates predicates.
Subjectal [or hypostatic] abstraction creates subjects. Both predicates and
subjects are creations of thought. But this is hardly more than a phrase;
for *creation *and *thought* have different meanings as applied to the two.
... That the abstract subject is an *ens rationis*, or creation of thought
does not mean that it is a fiction. (NEM 3:917-918, 1904)


CSP: [A]n Argument is no more built up of Propositions than a motion is
built up of positions. So to regard it is to neglect the very essence of
it. ... Just as it is strictly correct to say that nobody is ever in an
exact Position (except instantaneously, and an Instant is a fiction, or *ens
rationis*), but Positions are either vaguely described states of motion of
small range, or else (what is the better view), are *entia rationis* (i.e.
fictions recognized to be fictions, and thus no longer fictions) invented
for the purposes of closer descriptions of states of motion; so likewise,
Thought (I am not talking Psychology, but Logic, or the essence of
Semeiotics) cannot, from the nature of it, be at rest, or be anything but
inferential process; and propositions are either roughly described states
of Thought-motion, or are artificial creations intended to render the
description of Thought-motion possible; and Names are creations of a second
order serving to render the representation of propositions possible. (R
295:117-118[102-103], 1906)


Arguments are not built up from their constituent propositions, and
propositions are not built up from their constituent names, including
predicates and subjects. Instead, these are all artificial creations of
thought for the purpose of *describing *arguments, which in themselves are
continuous inferential processes.

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Fri, Oct 8, 2021 at 7:09 PM JACK ROBERT KELLY CODY <
jack.cody.2...@mumail.ie> wrote:

> Jon, List,
>
> Cheers, Jon, that's 

Re: [PEIRCE-L] Improving the quality of discussions (wasAbracadabra

[Gary Richmond]

Correction: The first quotation in my post today should have been labeled
JFS (John Sowa) not JAS (Jon Alan Schmidt). My apologies. GR

“Let everything happen to you
Beauty and terror
Just keep going
No feeling is final”
― Rainer Maria Rilke

*Gary Richmond*
*Philosophy and Critical Thinking*
*Communication Studies*
*LaGuardia College of the City University of New York*








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<#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>

On Sat, Oct 9, 2021 at 3:01 PM Gary Richmond 
wrote:

> John, List,
>
> JAS: It's important to recognize that we are all sinners,
> and to do our best to promote more constructive discussions.
>
>
> I agree. And in a philosophical forum such as this, to "do our best" is to
> be as reasonable as it is possible for each of us to be. After all,
> 'reasonableness' is Peirce's *summum bonum *of philosophical esthetics
> (his spelling), which principle accepted and followed can then ground
> philosophical ethics and, further, logic.
>
> The one thing whose admirableness is not due to an ulterior Reason is
> Reason itself comprehended in all its fullness, so far as we can comprehend
> it. Under this conception, *the ideal of conduct will be to execute our
> little function in the operation of the creation by giving a hand toward
> rendering the world more reasonable whenever, as the slang is, it is "up to
> us" to do so.* In logic, it will be observed that knowledge is
> reasonableness. . .. (CP 1.615, EP 2:255, 1903. emphasis)
>
>
> The 'sin' -- for philosophy, logic, and science more generally -- is being
> *un*reasonable. As you concluded:  "Occasional lapses may occur.  But we
> should do our best."
>
> Best,
>
> Gary R
>
> “Let everything happen to you
> Beauty and terror
> Just keep going
> No feeling is final”
> ― Rainer Maria Rilke
>
> *Gary Richmond*
> *Philosophy and Critical Thinking*
> *Communication Studies*
> *LaGuardia College of the City University of New York*
>
>
>
>
>
>
>
>
> 
>  Virus-free.
> www.avg.com
> 
> <#m_-2275995507394885958_DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
>
> On Thu, Oct 7, 2021 at 10:58 PM sowa @bestweb.net 
> wrote:
>
>> Gary R:  My entire concern in this exchange and as regards the recent
>> discussions in parallel threads is that, given all the recent good
>> ideas on improving List discussions, can we sincerely 'practice what
>> we preach'?
>>
>> We are all sinners.  It's important to recognize that we are all sinners,
>> and to do our best to promote more constructive discussions. Occasional
>> lapses may occur.  But we should do our best .
>>
>> John
>>
>
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Re: [PEIRCE-L] Improving the quality of discussions (wasAbracadabra

[Gary Richmond]

John, List,

JAS: It's important to recognize that we are all sinners,
and to do our best to promote more constructive discussions.


I agree. And in a philosophical forum such as this, to "do our best" is to
be as reasonable as it is possible for each of us to be. After all,
'reasonableness' is Peirce's *summum bonum *of philosophical esthetics (his
spelling), which principle accepted and followed can then ground
philosophical ethics and, further, logic.

The one thing whose admirableness is not due to an ulterior Reason is
Reason itself comprehended in all its fullness, so far as we can comprehend
it. Under this conception, *the ideal of conduct will be to execute our
little function in the operation of the creation by giving a hand toward
rendering the world more reasonable whenever, as the slang is, it is "up to
us" to do so.* In logic, it will be observed that knowledge is
reasonableness. . .. (CP 1.615, EP 2:255, 1903. emphasis)


The 'sin' -- for philosophy, logic, and science more generally -- is being
*un*reasonable. As you concluded:  "Occasional lapses may occur.  But we
should do our best."

Best,

Gary R

“Let everything happen to you
Beauty and terror
Just keep going
No feeling is final”
― Rainer Maria Rilke

*Gary Richmond*
*Philosophy and Critical Thinking*
*Communication Studies*
*LaGuardia College of the City University of New York*








Virus-free.
www.avg.com

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On Thu, Oct 7, 2021 at 10:58 PM sowa @bestweb.net  wrote:

> Gary R:  My entire concern in this exchange and as regards the recent
> discussions in parallel threads is that, given all the recent good
> ideas on improving List discussions, can we sincerely 'practice what
> we preach'?
>
> We are all sinners.  It's important to recognize that we are all sinners,
> and to do our best to promote more constructive discussions. Occasional
> lapses may occur.  But we should do our best .
>
> John
>
_ _ _ _ _ _ _ _ _ _
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