Jon, List,
I think, the dimensionality of a line or of a surface is only then integer (1 or 2), if the line is straight, or the surface is even. Otherwise, the dimensionality of the line is between 1 and 2, or of the surface it is between 2 and 3.
Best, Helmut
09. Oktober 2021 um 23:08 Uhr
"Jon Alan Schmidt" <jonalanschm...@gmail.com>
wrote:
"Jon Alan Schmidt" <jonalanschm...@gmail.com>
wrote:
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A 'Thicker' Theory" (https://doi.org/10.2979/trancharpeirsoc.56.1.04), which quotes and comments on a previously unpublished manuscript by Peirce that includes the following definitions.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
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.BestJack
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