Jeff, List: At first, I was not sure how helpful CP 6.395&397 could be, since they are from an article published in 1878, 20 years before RLT and 30 years before "A Neglected Argument." Leaving aside that concern, I read through the subsequent text and came to wonder if the "general characteristic of the universe" that Peirce said in CP 6.397 "would be of such singular assistance to us in all our future reasoning that it would deserve a place almost at the head of the principles of logic" is what he described a few paragraphs later.
CSP: ... while a certain amount of order exists in the world, it would seem that the world is not so orderly as it might be, and, for instance, not so much so as a world of pure chance would be. But we can never get to the bottom of this question until we take account of a highly-important logical principle which I now proceed to enounce. This principle is that any plurality or lot of objects whatever have some character in common (no matter how insignificant) which is peculiar to them and not shared by anything else. The word "character" here is taken in such a sense as to include negative characters ... (CP 6.401-402; 1878) He then proceeded to show that "any two things, *A* and *B*, have in common" the character of "un-*A*-*B*-lessness," and concluded, "It is obvious that what has thus been shown true of two things is *mutatis mutandis*, true of any number of things." It seems to me that having something in common is a form of similarity; i.e., it entails a *relation* between them. Since any two (or more) objects have some character in common, it is also the case that any two (or more) objects have a relation between them--including two random spots on a page--and thus are intelligible, and thus manifest what Peirce (much later) called super-order. This is my current hypothesis about Peirce's position on "What sort of a conception we ought to have of the universe, how to think of the *ensemble* of things," especially when we translate it into the notion of continuity. What you noticed in italics on page 259 of RLT is telling, I think. CSP: We can hardly but suppose that those sense-qualities that we now experience ... are but the relics of an ancient ruined continuum of qualities, like a few columns standing here and there in testimony that here some old-world forum with its basilica and temples had once made a magnificent *ensemble*. (RLT:258-259) The ensemble corresponds to the original, most general continuum of *potential *qualities, out of which are determined the individual sense-qualities that *actually *occur--like the discrete columns that remain from the ancient (continuous) forum. Regards, Jon On Sun, Nov 6, 2016 at 8:59 AM, Jon Alan Schmidt <[email protected]> wrote: > Jeff, List: > > I will try to take a closer look at this later. > > Thanks, > > Jon Alan Schmidt - Olathe, Kansas, USA > Professional Engineer, Amateur Philosopher, Lutheran Layman > www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt > > On Sun, Nov 6, 2016 at 3:36 AM, Jeffrey Brian Downard < > [email protected]> wrote: > >> Jon S, Gary R, List, >> >> Given our interest in providing a clearer meaning for the conceptions of >> order and Super-order, I think that these passages might be helpful. >> >> Any proposition whatever concerning the order of Nature must touch more >> or less upon religion. In our day, belief, even in these matters, depends >> more and more upon the observation of facts. If a remarkable and universal >> orderliness be found in the universe, there must be some cause for this >> regularity, and science has to consider what hypotheses might account for >> the phenomenon. One way of accounting for it, certainly, would be to >> suppose that the world is ordered by a superior power. But if there is >> nothing in the universal subjection of phenomena to laws, nor in the >> character of those laws themselves (as being benevolent, beautiful, >> economical, etc.), which goes to prove the existence of a governor of the >> universe, it is hardly to be anticipated that any other sort of evidence >> will be found to weigh very much with minds emancipated from the tyranny of >> tradition. (CP 6.395) >> >> And then, two paragraphs later: >> >> If we could find out any general characteristic of the universe, any >> mannerism in the ways of Nature, any law everywhere applicable and >> universally valid, such a discovery would be of such singular assistance to >> us in all our future reasoning that it would deserve a place almost at the >> head of the principles of logic. On the other hand, if it can be shown that >> there is nothing of the sort to find out, but that every discoverable >> regularity is of limited range, this again will be of logical importance. >> What sort of a conception we ought to have of the universe, how to think of >> the ensemble of things, is a fundamental problem in the theory of >> reasoning. (CP 6.397) >> >> So, how should we "think of the ensemble of things"? Peirce provides the >> definition for "ensemble" in the Century Dictionary. In the second >> definition of the term, he characterizes the mathematical use of the >> conception. In that definition, he makes a distinction between an ensemble >> of the first genus, the second genus, and a tout ensemble. It is clear, I >> think, that he is talking about a tout ensemble at 6.397. What is more, I >> believe that he is talking about a tout ensemble in RLT, when he puts the >> word in italics on page 259. How should we think of order and Super-order >> as they are applied to each of these three sorts of ensembles? >> >> He explicitly uses "tout ensemble" in the following passage: >> >> The division of modes of Being needs, for our purposes, to be carried a >> little further. A feeling so long as it remains a mere feeling is >> absolutely simple. For if it had parts, those parts would be something >> different from the whole, in the presence of which the being of the whole >> would consist. Consequently, the being of the feeling would consist of >> something beside itself, and in a relation. Thus it would violate the >> definition of feeling as that mode of consciousness whose being lies >> wholly in itself and not in any relation to anything else. In short, a >> pure feeling can be nothing but the total unanalyzed impression of the >> tout ensemble of consciousness. Such a mode of being may be called simple >> monadic Being. CP 6.345 >> >> Given the fact that Peirce draws this meaning of "tout ensemble" from >> mathematics, I'm wondering if some examples from topology, projective >> geometry or metrical geometry might help to clarify the differences between >> a tout ensemble and ensembles of the first and second genus. Peirce offers >> the example of Desargues' theory of Involution and its use in the 6 point >> theorem on page 245. How does the conception of an ensemble apply in this >> case where we are looking at the intersection of these rays as they are >> projected from their origins at Q and R? >> >> The upshot of this example is made clearer when he says that Cayley >> showed that the whole of geometrical metric is but a special problem in >> geometrical optic. The point Peirce is making is that the development of >> the conception of a projective absolute as a locus in space was central for >> thinking about the character of projective space as a whole--i.e., as a >> tout ensemble. Taken as a whole, the topological character of the space is >> something that we study by a process of decomposition. That is, we cut it >> up and see how the parts are connected. In this way, we come to see what >> Listing numbers are for the Chorisis, Cyclosis, Periphraxis and Immensity >> of such a space. The Periphraxis and Immensity, I take it, are especially >> important in understanding the character of the tout ensemble of a >> projective space. He says that the Periphraxis of perspective space is 1, >> and that the Immensity of any figure in our space is 0, except for the >> entirety of space itself, for which the Immensity is 1. >> >> These kinds of exercises in mathematics are essential, I believe, for >> understanding the points he is illustrating using the diagram involving >> blackboard on pages 261-3. How might we draw them out? >> >> --Jeff >> >> Jeffrey Downard >> Associate Professor >> Department of Philosophy >> Northern Arizona University >> (o) 928 523-8354 > >
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