Jeff, List: I see that Gary R. started a separate thread for this right after I did. He suggested that I re-post my cosmological analysis of CP 6.490, but that dives right into metaphysical matters, so I think that it would be better just to stick with the text itself initially.
In what I quoted, Peirce defined "super-order" as "a character that is a generalization of order ... something like uniformity ... that of which order and uniformity are particular varieties ... Any general state of things whatsoever would be a super-order and a super-habit." Early in the final RLT lecture, Peirce commented on what it means for something to be general. CSP: That which is possible is in so far *general *and, as general, it ceases to be individual. Hence, remembering that the word "potential" means *indeterminate yet capable of determination in any special case*, there may be a potential aggregate of all the possibilities that are consistent with certain general conditions ... But being a potential aggregate only, it does not contain any individuals at all. It only contains general conditions which *permit *the determination of individuals. (CP 6.185, RLT:247) A super-order is thus a *potential *aggregate of all *particular *varieties of order and uniformity; i.e., it contains the *general *conditions which permit the determination of *individual *cases of order and uniformity. Peirce went on to identify another property of a potential aggregate. CSP: A potential collection, more multitudinous than any collection of distinct individuals can be, cannot be entirely vague. For the potentiality supposes that the individuals are determinable in every multitude. That is, they are determinable as distinct. But there cannot be a distinctive quality for each individual; for these qualities would form a collection too multitudinous for them to remain distinct. It must therefore be by means of relations that the individuals are distinguishable from one another. (CP 6.188, RLT:248) Relations constitute a particular variety of order. Hence there can be no relations, and therefore no distinguishable individuals, without a super-order that contains the general conditions which permit their determination. After giving the cave illustration, Peirce observed "that nothing but a rigidly exact logic of relations can be your guide in such a field," and that "when continua of higher dimensionality than 3 are considered ... we begin to have systems of relations between the different dimensions." This is followed by a paragraph that Jeff quoted previously. CSP: A continuum may have any discrete multitude of dimensions whatsoever. If the multitude of dimensions surpasses all discrete multitudes there cease to be any distinct dimensions. I have not as yet obtained any logically distinct conception of such a continuum. Provisionally, I identify it with the *uralt *vague generality of the most abstract potentiality. (RLT 253-254) A continuum of "the multitude of dimensions that surpasses all discrete multitudes" would be the ultimate potential aggregate, and thus the ultimate super-order. What does Peirce later say that "the clean blackboard" (CP 6.203, RLT:261) represents? "The original vague potentiality ... a continuum of some indefinite multitude of dimensions ..." I am guessing that Gary R. characterized the blackboard as "*ur*-continuity" precisely because Peirce here referred to "the *uralt* vague generality of the most abstract potentiality." He was talking about the same thing in both passages, as well as in CP 6.490 when he discussed super-order. CSP: Now continuity is shown by the logic of relatives to be nothing but a higher type of that which we know as generality. It is relational generality ... we must suppose that as a rule the continuum has been derived from a more general continuum, a continuum of higher generality. (CP 6.190, RLT:258) The source of *all *other continua is the continuum of the *highest *generality, a generality that exceeds all multitudes of discrete levels of relational generality, a generalization of generality--in a word, a super-order. Before we move on to "the questions of theological metaphysics" ... does all of this seem to be on the right track? Again, great suggestion. Thanks, Jon On Fri, Nov 4, 2016 at 4:52 PM, Jon Alan Schmidt <jonalanschm...@gmail.com> wrote: > Jeff, List: > > Thank you for this very interesting suggestion. In order to facilitate > such a discussion (hopefully), here is the passage about "Super-order" from > CP 6.490. > > CSP: Order is simply thought embodied in arrangement; and thought > embodied in any other way appears objectively as a character that is a > generalization of order, and that, in the lack of any word for it, we may > call for the nonce, "Super-order." It is something like uniformity. The > idea may be caught if it is described as that of which order and uniformity > are particular varieties ... A state in which there should be absolutely no > super-order whatsoever would be such a state of nility. For all Being > involves some kind of super-order. For example, to suppose a thing to have > any particular character is to suppose a conditional proposition to be true > of it, which proposition would express some kind of super-order, as any > formulation of a general fact does. To suppose it to have elasticity of > volume is to suppose that if it were subjected to pressure its volume would > diminish until at a certain point the full pressure was attained within and > without its periphery. This is a super-order, a law expressible by a > differential equation. Any such super-order would be a super-habit. Any > general state of things whatsoever would be a super-order and a super-habit. > > > Obviously I have been focusing on the blackboard diagram recently, so I > will need to review the earlier portions of the lecture in RLT with this in > mind. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Professional Engineer, Amateur Philosopher, Lutheran Layman > www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt > > On Fri, Nov 4, 2016 at 4:39 PM, Jeffrey Brian Downard < > jeffrey.down...@nau.edu> wrote: > >> Gary R, Jon S, List, >> >> The pages you and Jon are examining (RLT 261-4) are quite challenging. >> The guiding aims of the lecture, he tells us on the first page, are (1) to >> work out the logical difficulties involved in the conception of continuity, >> and then (2) to address the metaphysical difficulties associated with the >> conception. What is needed, he says, is a better method of reasoning about >> continuity in philosophy generally. >> >> It looks to me like the mathematical survey of the relationships he notes >> between topology, projective geometry and metrical geometries are being >> used to set up the arguments. Likewise, the phenomenological thought >> experiment involving the cave of odors is also doing some work. >> >> The mathematical examples he offers are meant, I am supposing, to offer >> us with some nice case studies that we can use to study the methods that >> have been taking shape in the 19th century in order to handle mathematical >> questions about continuity in topology and projective geometry. One goal of >> this discussion, I assume, is to analyze these examples in order to see how >> those mathematical methods might be applied to the logical difficulties >> involved in working with the conception. >> >> Then, the phenomenological experiment is designed as an exercise that >> helps to limber us up for the challenges we face. The goal is to provide us >> with some exercises of the imagination in which we are being asked to >> explore arrangements of odors in spaces that are markedly different from >> our typical experience of how things that are spatially arranged. One of >> the key ideas, I believe, is that this imaginative exploration does not >> involve any kind of optical ray of light or any physical straight bar that >> might be used to apply projective or metrical standards to the spatial >> arrangements. >> >> The big conclusion he draws from both the mathematical and >> phenomenological investigations is logical in character: "A continuum may >> have any discrete multitude of dimensions whatsoever. If the multiude of >> dimensions surpasses all discrete multitudes there cease to be any distinct >> dimensions. I have not as yet obtained any logically distinct conception of >> such a continuum. Provisionally, I identify it with the uralt vague >> generality of the most abstract potentiality." (253-4) On page 257, he >> makes the transition from the attempt to draw on mathematics and >> phenomenology for the sake of addressing the logical difficulties >> associated with the concept of continuity, and the then takes up the >> metaphysical difficulties. >> >> Before turning to the questions of theological metaphysics that he takes >> up on 258-9 or the example of the diagrams on the blackboard shortly >> thereafter, let me ask a question. In the Additament to the Neglected >> Argument, he makes use of the conception of Super-order. I am wondering if >> there is anything in his discussion of mathematics and phenomenology in the >> first part of this last lecture in RLT that might help us to clarify this >> conception of Super-order? What I'd like to do is to work towards a more >> adequate understanding of that conception and then see if it could be used >> to shed some light on the points he is making on pages 258-64--or vice >> versa. >> >> --Jeff >> >> Jeffrey Downard >> Associate Professor >> Department of Philosophy >> Northern Arizona University >> (o) 928 523-8354 > >
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