Gary R., List: GR: Are you suggesting that it is* only* in the aboriginal (from Latin <https://en.wikipedia.org/wiki/Latin> *ab <https://en.wiktionary.org/wiki/ab#Latin> origine <https://en.wiktionary.org/wiki/origine#Latin> --*“from the beginning”) continuum that there are *no discrete dimensions*?
In order to answer this question, I will begin by quoting a little-known passage that I have excerpted several times over the past few months, including just a few days ago in this thread. CSP: In the first place, then, I do not call a line, or a surface, or anything else, continuous unless every part of it that is homogeneous in dimensionality with the whole and is marked off in the simplest way is, in respect to the connexions of its parts, precisely like every other such part; although, if the whole has but a finite number of interruptions, I do call it "continuous in its uninterrupted portions." In the next place, I conceive that a Continuum has, IN ITSELF, no definite parts, although to endow it with definite parts of no matter what multitude, and even parts of lesser dimensionality down to absolute simplicity, it is only necessary that these should be marked off, and although even the operation of thought suffices to impart an approach to definiteness of parts of any multitude we please.* *This indubitably proves that the possession of parts by a continuum is not a real character of it. For the real is that whose being one way or another does not depend upon how individual persons may imagine it to be. (R S-30 [Copy T:5-6]; c. 1906) Although it has never appeared in the secondary literature--presumably because of the obscurity of the manuscript, which received a "supplementary" number from Robin--I consider it to be Peirce's clearest definition of his late topical conception of continuity, because I think that it elaborates helpfully on a subsequent one that is commonly cited. CSP: If in an otherwise unoccupied continuum a figure of lower dimensionality be constructed--such as an oval line on a spheroidal or anchor-ring surface--either that figure is a part of the continuum or it is not. If it is, it is a topical singularity, and according to my concept of continuity, is a breach of continuity. If it is not, it constitutes no objection to my view that all the parts of a perfect continuum have the same dimensionality as the whole. (Strictly, all the *material*, or *actual*, parts, but I cannot now take the space that minute accuracy would require, which would be many pages.) That being the case, my notion of the essential character of a perfect continuum is the absolute generality with which two rules hold good, first, that every part has parts; and second, that every sufficiently small part has the same mode of immediate connection with others as every other has. (CP 4.642; 1908 May 26) Every material part of a perfect continuum is *indefinite *and has "the same dimensionality as the whole," but any number of *definite *parts of the same or "lesser dimensionality, down to absolute simplicity"--i.e., dimensionless and indivisible points--can be "marked off" as "interruptions" or "breaches of continuity." Therefore, since the original continuum has "some indefinite multitude of dimensions," all of its material parts must likewise have "some indefinite multitude of dimensions"; and any subsidiary continuum that has a *definite *number of *discrete *dimensions is "a topical singularity," like "an oval line on a spheroidal or anchor-ring surface." What is the implication of this for our *physical *universe? I see two alternatives. 1. Continuous space-time has no discrete dimensions in itself; it is a material part of the original continuum. 2. Continuous space-time has a definite number of discrete dimensions; it is "a figure of lower dimensionality" in the original continuum. #1 leads to my previous statement that you quoted twice--*discrete *dimensions are arbitrary and artificial creations of thought for particular purposes, cognitive constructions that *represent *space-time. However, Peirce evidently endorsed #2 instead. CSP: The whole universe of true and real possibilities forms a continuum, upon which this Universe of Actual Existence is, by virtue of the essential Secondness of Existence, a discontinuous mark--like a line figure drawn on the area of the blackboard. (NEM 4:345, RLT 162; 1898) As you already observed in your latest reply to Jeff, this would seem to require an external "scriber" who *chooses *to draw the line figure on the blackboard--i.e., to "mark off" the *discrete *dimensions of the physical universe as *definite *parts of the original continuum. As Peirce wrote elsewhere ... CSP: In a continuum there really are no points except such as are marked; and such interrupt the continuum. It is true that the capability of being marked gives to the points the beginnings of *potential being*, but only the beginnings. It should be called a *conditional being*, since it depends upon some will's being exerted to complete it. (R 1041:13; 1906) Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Thu, Aug 29, 2019 at 3:25 PM Gary Richmond <[email protected]> wrote: > Jon, Jeff, List, > > This message is meant to solicit clarification on what seems to be the > thrust of Jon's argument in support of a dimensionless ur-continuity. My > question is: Am I clearly grasping what you're getting at, Jon? You wrote > near the end of your post: > > JAS: What I notice is that *measurement *is evidently intrinsic to the > definition of dimension, except for the particular mathematical usage > mentioned in the first one, where "the idea of measurement is quite > extraneous." > > > Again, I would tend to strongly with your suggestion that: > > > JAS: ". . . *discrete *dimensions are arbitrary and artificial creations > of thought for that purpose, rather than *real *characters of space-time > in itself." > > > You continued: > > > JAS: [. . .] The linked video [which Jeff earlier provided] about higher > numbers of dimensions employs the same "bottom-up" analytic approach, using > the real number line--what Peirce called a "pseudo-continuum"--as the basis > for *defining *each individual dimension. > > > I would take it, then, that "pseudo-continuua," are most certainly of > *analytical* value as long as one remembers, as you have been positing > recently (and I agree) that: > > JAS: . . .*discrete *dimensions are arbitrary and artificial creations of > thought for that [analytical] purpose, rather than *real *characters of > space-time in itself. > > > You then asked if dimensionality would even apply in a "top-down" approach > and suggested that it may not, offering a Peirce quotation in support of > your suggestion : > > JAS: What might it look like to adopt a "top-down" synthetic approach > instead? Would the familiar notion of dimensions even apply? Maybe not, > according to Peirce. > > CSP: A continuum may have any discrete multitude of dimensions > whatsoever. lf the multitude of dimensions surpasses all discrete > multitudes there cease to be any distinct dimensions. I have not as yet > obtained a logically distinct conception of such a continuum. > Provisionally, I identify it with the *uralt * [Ger., ancient], vague > generality of the most abstract potentiality. (NEM 3:111, RLT 253-254; 1898) > > > You then quoted Peirce on the 'blackboard' as a metaphor for the > original, or, ur-continuum: > > CSP: Let the clean blackboard be a sort of diagram of the original vague > potentiality, or at any rate of some early stage of its determination. This > is something more than a figure of speech; for after all continuity is > generality. This blackboard is a continuum of two dimensions, while that > which it stands for is a continuum of some indefinite multitude of > dimensions. This blackboard is a continuum of possible points; while that > is a continuum of possible dimensions of quality, or is a continuum of > possible dimensions of a continuum of possible dimensions of quality, or > something of that sort. There are no points on this blackboard. There are > no dimensions in that continuum. (CP 6.203, RLT 261; 1898) > > > JAS: Rather than "a vague infinity of dimensions," there are no > *distinct *dimensions-- no *defnite *dimensions--no *discrete *dimensions > at all in the original continuum that is fundamental to the constitution of > being. > > > So, finally getting back to my question: Are you suggesting that it is* > only* in the in the aboriginal (from Latin > <https://en.wikipedia.org/wiki/Latin> *ab > <https://en.wiktionary.org/wiki/ab#Latin> origine > <https://en.wiktionary.org/wiki/origine#Latin> --*“from the beginning”) > continuum that there are *no discrete dimensions*? That makes sense to > me; and, of course, it has significant implications for what you and I have > been arguing regarding Peirce's late view of the situation of the earliest > cosmos; namely, that ur-continuity is quasi-necessarily primal in the > constitution of reality, including, of course, existential being on "time > is." > > Best, > > Gary R > > *Gary Richmond* > *Philosophy and Critical Thinking* > *Communication Studies* > *LaGuardia College of the City University of New York* > >>
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