Gary R., List: GR: What are the implications of this 'correction' re: dimension for Peirce's model/diagram of the earliest Universe as interpreted by you?
It is actually consistent with my understanding that Peirce endorsed my option #2--continuous space-time has a definite number of discrete dimensions; it is "a figure of lower dimensionality" in the original continuum. It also prompted me to learn more about Mitchell and his concept of *logical* dimensions. For anyone interested, I recommend Randell R. Dipert's 1994 article in *Transactions of the Charles S. Peirce Society*, "The Life and Logical Contributions of O. H. Mitchell, Peirce's Gifted Student" (https://www.jstor.org/stable/40320486). Finally, some further exploration of Peirce's writings led me to one of his discussions about Existential Graphs in the 1903 Lowell Lectures, which includes some interesting remarks about continuity and dimensionality. CSP: But I ask you to imagine all the true propositions to have been formulated; and since facts blend into one another, it can only be in a continuum that we can conceive this to be done. This continuum must clearly have more dimensions than a surface or even than a solid; and we will suppose it to be plastic, so that it can be deformed in all sorts of ways without the continuity and connection of parts being ever ruptured. Of this continuum the blank sheet of assertion may be imagined to be a photograph. When we find out that a proposition is true, we can place it wherever we please on the sheet, because we can imagine the original continuum, which is plastic, to be so deformed as to bring any number of propositions to any places on the sheet we may choose. (CP 4.512) The continuum of true propositions has more than three dimensions, and the blank sheet of assertion is a two-dimensional representation of any selected portion of it. Peirce initially compared it to a photograph, but went on to suggest that "a map of such a photograph" (CP 4.513) is an even better analogy. CSP: By taking time enough I could develop this idea much further, and render it clearer; but it would not be worth while, for I only mention it to prepare you for the idea of quite different kinds of sheets in the gamma part of the system. These sheets represent altogether different universes with which our discourse has to do. (CP 4.514) Different sheets represent different universes of discourse. Peirce later introduced different *tinctures* as an alternative way of representing different modal universes on the *same* sheet (cf. CP 4.553-554; 1906). CSP (continued): In the Johns Hopkins *Studies in Logic*--I printed a note of several pages on the universe of qualities--*marks*, as I then called them. But I failed to see that I was then wandering quite beyond the bounds of the logic of relations proper. For the relations of which the so-called "logic of relatives" treats are *existential* relations, which the nonexistence of either relate or correlate reduces to nullity. Now, *qualities* are not, properly speaking, individuals. All the qualities you actually have ever thought of might, no doubt, be counted, since you have only been alive for a certain number of hundredths of seconds, and it requires more than a hundredth of a second actually to have any thought. But all the qualities, any one of which you readily can think of, are certainly innumerable; and all that might be thought of exceed, I am convinced, all multitude whatsoever. For they are mere logical possibilities, and possibilities are general, and no multitude can exhaust the narrowest kind of a general. Nevertheless, within limitations, which include most ordinary purposes, qualities may be treated as individuals. At any rate, however, they form an entirely different universe of existence. It is a universe of logical possibility. (CP 4.514) The blank (and untinctured) sheet of assertion represents the universe of *actuality*, and accordingly the relations depicted on it "are *existential* relations" between *individuals*. However, the continuum of qualities constitutes "a universe of logical possibility" that is "entirely different," because "*qualities* are not, properly speaking, individuals." Nevertheless, for "most ordinary purposes, qualities may be treated as individuals." As such, presumably the universe of qualities *could* likewise be represented by a two-dimensional sheet (or tincture). CSP (continued): As we have seen, although the universe of existential fact can only be conceived as mapped upon a surface by each point of the surface representing a vast expanse of fact, yet we can conceive the facts [as] sufficiently separated upon the map for all our purposes; and in the same sense the entire universe of logical possibilities might be conceived to be mapped upon a surface. Nevertheless, in order to represent to our minds the relation between the universe of possibilities and the universe of actual existent facts, if we are going to think of the latter as a surface, we must think of the former as three-dimensional space in which any surface would represent all the facts that might exist in one existential universe. (CP 4.514) If "the universe of existential fact" is represented by a two-dimensional surface, then its relation to "the entire universe of logical possibilities" is more accurately diagrammed by representing the latter as "a three-dimensional space" that encompasses *all* such surfaces. Hence the continuum of actuality is "a figure of lower dimensionality" in the continuum of possibility, like "an oval line on a spheroidal or anchor-ring surface" (CP 4.642; 1908 May 26). Since everything actual is *also* possible, "the universe of actual existent facts" must accordingly be understood as a topical singularity *within* "the universe of possibilities"; and since the continuum of true propositions has *more than* three dimensions, the universe of possibility must likewise be understood as a topical singularity within the universe of truth. In other words, this conceptualization serves as a parallel alternative to Peirce's 1898 cosmological diagram. The multi-dimensional continuum of truth (3ns) corresponds to the unlimited two-dimensional "clean blackboard" (CP 6.203); the three-dimensional continuum of possibility (1ns) corresponds to the limited two-dimensional "new curve" that I have called a whiteboard (CP 6.206); and the two-dimensional continuum of actuality (2ns) corresponds to the one-dimensional "discontinuous mark" (NEM 4:345 & CP 6.208). Hence from the standpoint of topical geometry, all three "levels" in the constitution of being are *continuous*, but with different *dimensionality*. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sat, Aug 31, 2019 at 7:37 PM Gary Richmond <[email protected]> wrote: > Jon, List, > > > JAS: . . . as Pietarinen comments, "Peirce also makes the observation that > the notion of dimension does not imply that the geometry of logical space > is metric. If we have dimension, we already have a topological space > (topical geometry, topology, topics) that is not subject to measurement" > (p. 209). This means that I was wrong to dismiss Peirce's statement in the > Century Dictionary definition of "dimension" that "it has become usual, > in mathematics, to express the number of ways of spread of a figure by > saying that it has two, three, or *n* dimensions, although the idea of > measurement is quite extraneous to the fact expressed." Apparently he was > there referring *specifically *to the concept as employed in topical > geometry, such that measurement is *not* intrinsic to the relevant sense > of the term after all. I thus stand corrected. > > > What are the implications of this 'correction' re: dimension for Peirce's > model/diagram of the earliest Universe as interpreted by you? > > Best, > > Gary R > > *Gary Richmond* > *Philosophy and Critical Thinking* > *Communication Studies* > *LaGuardia College of the City University of New York* > >>
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