Edwina, List,
One point I ways trying to make is that the various diagrams Peirce uses to characterize a branching line (e.g., branching trees, branch in a roadway) have a number of different sources--and Peirce explored the use of these different diagrams for more than a decade before he developed the EG. As such, I was agreeing with Gary F. that the particular use of the branching line in CP 1.343-9 should be interpreted in light of the rules for the beta system of the EG as Peirce was formulating them at the time of the Lowell Lectures of 1903. As the same time, I was point out that we have a considerable range of diagrams to consider as we try to understand what Peirce was doing (e.g., between 1886 and 1896) when he was developing the conception of a triadic relation prior to the formulation of the alpha and beta systems of the EG. In fact, we should consider a wide range of different sort of diagrams that involve branching lines as we try to understand what is involved in the notion of a triadic relation and what might be evolved from such a formal element of thought. These diagrams involving branching relations should be interpreted in light of his notes and responses to the works of Euler, Sylvester, Kempe, Listing, etc. For my part, I'm particularly interested in some of the objections he raises to Kempe's thesis in the Memoir that all mathematical relations can be "reduced" to dyadic relations between spots and lines. I'd like to interpret his response in light of his discussion of the categories and the topological notion of a furcation in a continuous line in MS 717. In response to your remark that loving is a dyadic relation, I'll start by saying that--in general--I agree. Having said that, your earlier rejoinder to Gary F. that genuine dyadic relations are, on Peirce's account, always reactions between two actual, discrete objects misses the mark. In "The Logic of Mathematics, an attempt to develop my categories from within," Peirce develops a rich classification of different sorts of dyadic relations. The dyadic relation A loves B is a materially and formally ordered dynamical dyad of diversity. A single actual, discrete object is also classified as a genuine dyad by Peirce (e.g., in comparison to a essential dyad or a inherential dyad). For instance, an individual object that has changed in some characteristic (e.g., the aspen leaf turned from green to yellow) can be classified as a qualitative dyad of diversity. With that much said, the reason I'm engaging with these questions about Peirce's account of triadic relations is that I'm particularly interested in exploring the differences between the classes of monadically degenerate triads, dyadically degenerate triads, genuine triadic relations and thoroughly genuine triadic relations. A number of the points made recently in various discussions on the Peirce-List seem to ignore the differences between the latter two classes. In saying that, I'm getting ahead of myself, so let me return to the example of "Every mother loves some child of hers." In focusing on the dyadic character of A loves B, you set to the side "Every", "some", and "of hers." The relations involved in putting those together in this proposition are not simple. We have two different quantifiers, and a fact with two parts. In my remarks, I was trying to draw attention to the fact that Peirce is focusing on the "possible space time continuity with several such phenomena to which it is related in the same way" (see Roberts, 20-6). Without yet worrying about how the space-time continuity might be represented in different sorts of diagrams, let me just ask how we might represent the references to "several such phenomena to which it is related in the same way." How does Peirce represent the reference to the range of phenomena that might be observed in this diagram in chapter 7 of the Grand Logic. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Edwina Taborsky <[email protected]> Sent: Friday, April 14, 2017 8:09 AM To: 'Peirce-L'; Jeffrey Brian Downard Subject: Re: Re: [PEIRCE-L] Laws of Nature as Signs Sorry, Jeffrey- but I don't see how your explanation below denies my view of the 'umbrella image' of the semiosic process. An 'existential graph with three tails' is a mere 'kinetic' description of a 2D diagram. It doesn't mean anything. The phrase: 'Mother loves child' - I'm removing the 'All' and 'Some' , or 'X loves Y' ..which seems to be, as noted a dyadic relation doesn't seem, to me, to fit the triad. It's a rhema with two blanks; a dyad. Roberts p 115. So- I'm confused about your point. Edwina -- This message is virus free, protected by Primus - Canada's largest alternative telecommunications provider. http://www.primus.ca On Fri 14/04/17 10:41 AM , Jeffrey Brian Downard [email protected] sent: Gary, F, Gary R. Edwina, John S., List, Gary F. has made a clear and interesting set of interpretative points about the “ 'umbrella image' of the triad. While I agree with much of what he says, let me insert some questions and offer some qualifications. I probably shouldn’t intervene in this discussion, but I have to say (one more time) that if we want to understand Peirce’s terms — especially what he means by a triadic relation — we need to read them in the context where Peirce uses them, not lift them out of their context and drop them into a scheme of our own invention. Or, to put the point in different terms, let's make our aims clear. If our goal is to interpret Peirce's texts, then we need to pay particular attention to the context of any given passage in a given essay, and the context of a given essay as part of a larger projected work or series of essays. What is more, we need to be clear about the aims that are guiding Peirce's inquiries and the methods he is using to answer the questions at hand. For these scholarly purposes, for instance, it probably makes sense to focus on the diagrams that Peirce actually used in his writings and refrain from developing our own. Having said that, if we are drawing on Peirce's ideas for our own purposes for the sake of using them to engage in our own lines of inquiry, then it may be productive to insert some of his ideas into different frameworks (some of our own making) or to draw on different diagrammatic systems or even to develop our own diagrams. If we don't really understand what Peirce was doing with those ideas, then we run the risk of misunderstanding them and using them poorly. As such, many of us who want to put the ideas to work in our own inquiries also want to ensure that we're doing a responsible job of trying to understand what Peirce is doing with those ideas. Edwina refers to an “'umbrella image' of the triad [1.347], which is something like a three spoked umbrella: -<.....but one can see even from this that there are THREE spokes or Relations in that image.” But in its context, that image is NOT a diagram of the S-O-I relation, the essential “sign relation.” That image is in fact an existential graph with three “tails.” The context, CP 1.343-9, is “From the “Lowell Lectures of 1903,” III, vol. 1, 3d Draught.” The larger context is the Lowell lectures (pieces of which are unfortunately scattered here and there in the CP) and the Syllabus which Peirce wrote to accompany them. The Syllabus of course includes the “Nomenclature and Divisions of Triadic Relations”, which ought to be the go-to text for Peirce’s explanation of the triadic relations involved in semiosis. It is helpful to point out the type of diagram Peirce is presenting in this passage is an example of an EG. With that crucial piece of information in hand, we know what rules to turn to for the sake of understanding the diagram and interpreting what is permissible in experimenting with it. Having said that, it is probably worth remembering that Peirce had specific sources he was drawing from in different stages of his career, and many of these external sources informed his use of similar sorts of diagrams independent of the EG, even if he later drew on some of those diagrammatic ideas later in the development of the existential graphs. Here are four such sources: (1) the graphical systems developed by Euler to solve problems in mathematics like the Seven Bridges of Königsberg problem and the later development of such diagrammatic systems in what has come to be know as graph theory; (2) the mathematical systems that were modeled by Sylvester, Clifford and Cayley on chemical graphs, (2) the diagrammatic systems that Kempe presents in his memoir on mathematical form (3) the topological conceptions of Riemann, Listing, Möbius, and others, and the wide range of diagrams that they and others developed illustrate the abstract conceptions. In fact, Peirce was explicitly drawing on a range of different sorts of diagrams in his work on logic and semiotics well before he developed the EG. For example, see the notes on Sylvester's work on algebraic invariants (MS 707), the notes on and responses to Kempe work (MS 708-16 and the many diagrams he used to explore both the formal categories and topological conceptions of continuity and discontinuity (e.g., MS 717, NEM 17) Consider the manner in which he draws on and explores these different diagrammatic approaches in, to take a couple of examples, chapter 7 of the Grand Logic, when he analyzes "Every mother loves some child of hers" and in "The Logic of Relatives," where he examines the analogy between chemical and logical diagrams. One thing that that stands out in his diagram of "Every mother loves some child of hers" is the manner in which he separates the persons involved in the assertion from the first and the second parts of the facts. Look at what Peirce says in his remarks about the diagram about the "possible space time continuity with several such phenomena to which it is related in the same way" (see Roberts, 20-6). How might this diagram inform our understanding of the different ways that a possible space time continuity might be represented diagrammatically? I'll stop there for now and take up your other remarks separately. --Jeff From: Gary Richmond [mailto:[email protected]] Sent: 12-Apr-17 16:45 To: Peirce-L Subject: Re: Re: Re: Re: Re: [PEIRCE-L] Laws of Nature as Signs Edwina, Jon S, List, First, I will have to disagree with you, Edwina, on one point since I think the three pronged spoke does exactly represent a triadic relation, not three relations (how do you figure that?) As I see it, the single node from which the three spokes protrude make it one relation, not three. But for a moment I'd like to refer to Peirce's notion of time--which I've discussed in the past as having some relationship to Bergson's flow and duration (durée)-- as a kind of analogy of the three 'moments' of semiosis. For Peirce there is a continuous melding of the past into the present anticipating the future. Andre de Tienne quotes Mihai Nadin on this in "Peirce's Logic of Information" <http://www.unav.es/gep/SeminariodeTienne.html> http://www.unav.es/gep/SeminariodeTienne.html (a paper, btw, which I find both intriguing, but have some reservations about--but not regarding the present point). De Tienne comments and then quotes Nadin, who here concentrates on 'anticipation' and Peirce's notion of 'final cause' (and teleology). In a remarkable programmatic paper titled "Anticipation: A Spooky Computation" Mihai Nadin has written that "every sign is in anticipation of its interpretation". He explains (NADIN 2000: §5.1.1): Signs are not constituted at the object level, but in an open-ended infinite sign process (semiosis). In sign processes, the arrow of time can run in both directions: from the past through the present to the future, or the other way around, from the future to the present. Signs carry the future (intentions, desires, needs, ideals, etc., all of a nature different from what is given, i.e., all in the range of a final cause) into the present and thus allow us to derive a coherent image of the universe. Actually […], a semiosis is constituted in both directions: from the past into the future, and from the future into the present, and forward into the past. […] The two directions of semiosis are in co-relation. In the first case, we constitute understandings based on previous semiotic processes. In the second, we actually make up the world as we constitute ourselves as part of it. This means that the notion of sign has to reflect the two arrows. De Tienne's comments just following this quotation relate directly to a consideration of the nature of the growth of symbols (" as having the nature of a law, symbols are partly general, partly vague enunciations of what could happen in the future given certain antecedent conditions that they spell out to some degree"), as I remarked in an earlier post. Thus they have this living quality--"symbols grow" Peirce says. Anticipation is a process through which the representation of a future state determines a present semiotic event, and this implies a teleological dimension, not of an Aristotelian, but of a Peircean kind. Put briefly, one simply needs to remember that for Peirce every symbol is teleological in the sense that, being preoccupied with its own development into new interpretants, some of which are dynamic and thus anchored in an experience they modify, it adopts a conditional (would-be) form that orients it toward the future. As legisigns, thus as having the nature of a law, symbols are partly general, partly vague enunciations of what could happen in the future given certain antecedent conditions that they spell out to some degree. Such an evolving, self-correcting outlook toward the likely future is structurally embedded within symbols and distinguishes them from other types of signs. In addition, all symbols are signs that seek to "replicate" themselves, since there is no law that governs no event. Replicated symbols are a special kind of sinsigns: they are rule-bound semiotic events whose instantiation occurs under the rule’s guidance. Each instantiation thus anticipates the rule that it replicates, and in doing so it anticipates the future: the instantiation takes it into account, and thus is determined by it, although that determination is, as Nadin says, in the range of a final cause rather than of an efficient cause. Semiotic events are vectorized, they happen not at random but within an inferential continuum that ensures that propositions that conclude arguments, especially ampliative ones, become themselves premises to new arguments, in the same way as any symbolic sign has first been an interpretant before serving as a sign solicitor of new signs. And recall that while Nadin is especially concerned with the symbol in the passage quoted above, he's written that " "every sign is in anticipation of its interpretation," or, better, its interpretant. Best, Gary R [Blocked image] Gary Richmond Philosophy and Critical Thinking Communication Studies LaGuardia College of the City University of New York C 745 718 482-5690 On Wed, Apr 12, 2017 at 4:02 PM, Edwina Taborsky <[email protected]> wrote: Yes, that's what I've been mulling over for years - where I think that there are three relations rather than one triadic relation. A large issue is the definition of 'sign'. Is it the representamen alone? Or is it the triad of the Immediate Object-Represntamen-Immediate Interpretant? Or is it even larger - and includes the Dynamic Object? My problem is that I can't figure out what ONE triadic Relation means. I can understand the 'umbrella image' of the triad [1.347], which is something like a three spoked umbrella: -<.....but one can see even from this that there are THREE spokes or Relations in that image. They may certainly interact and affect each other, but - this doesn't reduce them to ONE triadic Relation. I simply can't 'imagize' what 'one triadic Relation' would look like or how it would function. I can imagine ONE Sign SET [not a Relation], as an irreducible set, made up of three Relations. I can even imagine ONE Sign SET - made up of that image as outlined by JAS, made up of the Immediate Object-Representamen-Immediate Interpretant - and this triadic Sign would interact with the Dynamic Object - which is itself made up of a triad of an Immediate Object-Represntamen-Immediate Interpretant...and forms a Dynamic Interpretant, which is itself made up of an Immediate Object-Representamen-Immediate Interpretant. But- that's making me dizzy and I'll stop. Edwina
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