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From: "Jon Alan Schmidt" <jonalanschm...@gmail.com>
Sent: Saturday, October 9, 2021 5:09 PM
To: "Peirce-L" <peirce-l@list.iupui.edu>
Subject: Re: [PEIRCE-L] [EXTERNAL] Peirce on Dimensionality (was
ConnectedSigns Theorem)
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comments on a previously unpublished manuscript by Peirce that includes the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 helpful. I'm rereading your Temporal Synechism article
(https://doi.org/10.1007/s10516-020-09523-6) at present which also helps
clarify some of these issues.
Best
Jack
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