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 ________________________________________ From: Jeffrey Brian Downard [jeffrey.down...@nau.edu] Sent: Saturday, November 5, 2016 10:03 PM Cc: Peirce-L Subject: RE: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology)) Jon, List, From a logical point of view, when we study some relation--such as the dyadic relation of A is brother of B--we are isolating the relate, the correlate, and the relation between them. We understand that the things standing in the position of relate and correlate will typically have many internal relations among the parts that make them up. We also understand that the things in the position of relate and correlate may stand in a variety of different external relations to other things. But, when we analyze this particular relation of being a brother, we ignore those other relations. That is, we ignore such things as the fact that one might be taller than another or that one might be more social than the other. We do the same thing, I take it, when we are engaged in a phenomenological analysis of something that has been observed. Phenomenological analysis works in manner that is analogous to logical analysis. Peirce explicitly says, for instance, that we do not attend to the parts of the spots. The fact that, in reality, the two spots on the page are arranged so that one is the left to the other brings in another kind of relation involving an observer. In relation to that observer, one is to the right and one is to the left really. But Peirce has isolated the relation of "being on the same surface." Let's consider a limiting kind of relation: C is similar to D. The relation of being on the same surface is a similarity, if I am not mistaken. Does such a relation of similarity involve some sort of order that holds between the relate and the correlate? There is a relation, but is it ordered? --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________________ From: Jon Alan Schmidt [jonalanschm...@gmail.com] Sent: Saturday, November 5, 2016 5:05 PM To: Jeffrey Brian Downard Cc: Peirce-L Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology)) Jeff, List: Just thinking out loud here ... Do two random spots on a page have a relation? If not, then this example is not pertinent; but if so, is it accurate to say that they have no order? Doesn't the fact that they occur on the same piece of paper--like, say, chalk marks on a blackboard--entail that there is order in some sense? Again, I see that they are not "ordered" in terms of having a hierarchy or sequence, but in fact one will be to the left of the other, one will be above the other, etc. If we rotate the page 180 degrees, then these relations will be reversed from our point of view, but the spots will still exhibit the same order because of the underlying paper. As long as they are potential spots, they "cannot be placed in any particularly regular way," as Pierce said; but once they are actual spots, they now have been placed in a particularly regular way, and are distinguishable only because of the order that is manifested in their relations. Regards, Jon On Sat, Nov 5, 2016 at 6:10 PM, Jeffrey Brian Downard <jeffrey.down...@nau.edu<mailto:jeffrey.down...@nau.edu>> wrote: Jon, Gary R, List, First, let me point out that my comments were meant as interpretation of how Peirce is coming at these questions about the character of dyadic and triadic relations from the side of math (including formal logic), phenomenology and semiotics. I am not making any metaphysical claims about what, really presupposes what. My aim was to hold off on those sorts of questions--at least for now. In response to your claim that all dyads are, in some way or another, organized, I tend to disagree. Let's take one of Peirce's examples from "The Logic of Mathematics" as a starting point. If you put two spots on a page, they are not ordered. As soon as you say that one is the left of the other, or that one is above the other, you are comparing them with respect to some third thing. Here is the passage: "Two phenomena, whose parts are not attended to, cannot display any law, or regularity. Three dots may be placed in a straight line, which is a kind of regularity; or they may be placed at the vertices of an equilateral triangle, which is another kind of regularity. But two dots cannot be placed in any particularly regular way, since there is but one way in which they can be placed, unless they were set together, when they would cease to be two. It is true that on the earth two dots may be placed antipodally." (CP 1.429) If you take a pair of things as a collection within the mathematical system of set theory, the pair can be treated as an unordered set, or as an ordered set. The character of the set as a whole is, itself, some third thing. As such, the character of the set may be characterized in terms of a general rule of order between the members--or a set may not impose such an ordered rule on its members. In the case of a dyad of identity, we have a dyad that consists of two instances of the same thing. Setting aside some temporal or spatial framework, the dyad of identity is unordered. Some mathematical collections allow multiple instances of the same thing (e.g., multiple instances of the number 1), but the postulates of most set theories do not allow multiple members that are identical. There is a short discussion within the context of formal logic of unordered collections of two or three things CP 4.345. He calls such relations doublets and triplets, whereas he calls the ordered collections dyads and triads. I must admit that this pretty thin evidence for my claim that some dyads (or doublets in the context of the system of logic he is developing at 4.345) may not involve an ordered relation, but it is what I have to offer at this point. I don't see textual evidence for the claim that every sort of relation--of any kind--always involves some kind of order or another. Having said that, Peirce is typically considering limiting kinds of cases in order to clarify some matter that is at hand. In order to get a better understanding of different sorts of order, considering relations that are unordered may be helpful. Looking ahead, preserving the conceptions of unordered relations may help us explain how things (e.g., some undifferentiated possibilities) which lack order might come to get ordered. After all, the presence of order--of any kind--is one of the things that needs to be explained. Given the fact that we're now looking at RLT, I think it makes sense to hold off on the Minute Logic--at least for now. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354<tel:928%20523-8354>
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
