Jon, List, In your response, I take you to be clarifying your earlier statement: "Some people like to think of these as "icons" of triadic sign relations, but they are less icons than mnemonic devices that just barely serve to jog our collateral knowledge of their referents, only if we do indeed have that knowledge, and only if we know the key, the stylistic conventions that were used to create them." I was trying to resist some implications that might follow from saying that they are just "mnemonic devices."
If my reading of the general tenor of what you are saying is on track, then I agree with what you say in the clarification (or, I think I do). Having said that, I do want to emphasize the distinction between the account of the categories as it is used in the semiotic theory, and the account of the categories as it is developed in the context of the phenomenological theory. I take Peirce at his word when he says in "The Logic of Mathematics: an Attempt to Develop my Categories from Within," that he is asking what is required in the way of an account of the categories for the purposes of refining his logical theory. My assumption is that Peirce is drawing on the logical theory to constrain the hypotheses he is formulating about the character of the formal categories as they are being articulated in the context of a phenomenological theory. He is asking: what assumptions must I make for the sake of the explanations I've already given in my theory of logic? As far as I can tell, the distinction between reference to a ground, reference to an object and reference to an interpretant supplies the core of the ideas needed for his account of the formal elements in all experience. At this point, I'm not able to make out how the phenomenological account of the categories fits into your reconstruction of the argument of the 1870 Logic of Relatives. At this point, I haven't yet seen all of the story you're wanting to tell. I made a comment in an earlier post on the interpretation of a largely unintelligible fragment of handwriting in one of Peirce's MS to the effect that he might mean something quite specific when he uses the term Appearance with a capital "A." My guess is that he is referring quite directly to Kant's claim that the formal character of the manifold of intuition is that it is a homogeneous manifold. At some point in the future, I'd like to take up some questions with you about the possible implications of this idea for our understanding of what Peirce means when he talks about the categories as being introduced for the sake of unifying the "manifold of experience." For now, I'll just wait until I see more of your reconstruction and explanation of the 1870 Logic of relatives before trying to dig further into these questions. --Jeff Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354 ________________________________________ From: Jon Awbrey [[email protected]] Sent: Monday, April 07, 2014 2:02 PM To: Jeffrey Brian Downard Cc: Sungchul Ji; Peirce List Subject: Re: de Waal Seminar : Chapter 5. Semeiotics, or the Doctrine of Signs Jeff, There's a rather long history of people borrowing Peirce's terminology while leaving his definitions and methods behind. I see that fine old tradition has now been extended to category theory, graph theory, and who knows what else. The full title of Peirce's 1870 Logic of relatives is “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic”. From the very beginning Peirce is clear about the distinction in semiotic roles between what plays the role of a "notation" (a calculus, a language, or any brand of syntactic system) and what plays the role of the object domain that is thereby denoted. Relative terms (rhemes or rhemata) are pieces of notation in the sign domain. As are logical graphs (entitative or existential). The structure of a syntactic expression does convey information about the structure of the relation it denotes, and maybe its okay to call the formula "iconic" on that account, so long as you don't forget the great differences between a single string of syntax and a whole collection of tuples that constitutes the extension of the relation in question. A good notation is a very handy thing, but only so long as you remember that it is notation. Otherwise nothing but confusion reigns ... Regards, Jon Jeffrey Brian Downard wrote: > Sung, Jerry, List, > > I understand that we are using somewhat different language and graph systems > as bases for understanding Peirce's arguments in his phenomenology and > semiotics. Jon has suggested that Peirce's different ways of diagramming > these relations are hardly more than hints of ideas, so we should be careful > about how much we derive from one or another manner of representing these > things graphically. I want to resist Jon's suggestion. As such, let me try > to restate the question. Given your way of putting things, let me ask the > following question: is there anything that is obscured if you assume that > there is an "internal node" at the heart of every elementary relation? I am > suggesting that any graphical system, including the one that you have > formulated or a bipartite system of graphs that allows nodes to be connected > to several lines (i.e. edges, relations, etc.) will run the risk of obscuring > things that Peirce wanted to analyze further. > > I recognize that you and Jerry seem to have different dispositions towards > the way Peirce is using graph theory to analyze these things. You are saying > that your system is equivalent to Peirce's and that it expresses the heart of > what he is really trying to say. Jerry, on the other hand, seems to suggest > that Peirce is hamstrung by limitations that have their source in outmoded > 19th century ways of thinking about and graphing chemical relations. > > So, let me try to state the question I've been trying to push as a challenge. > For those who think that the most elemental relations can be understood as a > node with one, two or three relations jutting out from it (such as you have > characterized them in your diagrams, and as the nodes and edges are > characterized in the example of the bipartite graph on the WikiPedia site I > referred to earlier), are you able to articulate the basic points Peirce is > making against Kempe's analysis of mathematical form in your terms? My hunch > is that Peirce's arguments are valid, that they can be used against alternate > analyses of the reasonings--and that these alternate analyses fail because > they tend to obscure points about the elemental character of a triadic > relation that Peirce wanted to make as clear as possible. > > --Jeff > > Jeff Downard > Associate Professor > Department of Philosophy > NAU > (o) 523-8354 -- academia: http://independent.academia.edu/JonAwbrey my word press blog: http://inquiryintoinquiry.com/ inquiry list: http://stderr.org/pipermail/inquiry/ isw: http://intersci.ss.uci.edu/wiki/index.php/JLA oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
