Hello Gary R., List, Let me point to a place where Peirce explicitly discusses the kinds of questions that are behind the point I'm trying to make about the priority of graph theoretic conceptions and figures for analyzing these sorts of relations. Here are two excerpts from a long footnote in the "Prolegomena to an Apology for Pragmaticism":
1. it may possibly be that a more nearly ultimate analysis of Concepts would show, as Kempe's "A Memoir on the theory of Mathematical Form" [Philosophical Transactions of the Royal Society, v. 177, pp. 1-70, 1886] seems to think, that the pegs of simple concepts are all alike. 2. it might easily be thought that the concept of a scalar as well as that of a vector (in quaternions) can equally result from putting together the concepts of a tensor and a versor in different ways, while at the same time the concept of a tensor and that of a versor can, in their turn, result from putting together those of a scalar and of a vector in different ways; so that no one of the four concepts is more or less composite than any of the others. Were such a view borne out by exact analysis, as it certainly is not, a radical disparateness between the composition of concepts and that of chemical species would be revealed. But this could scarcely fail to entail such a serious revolution in accepted doctrines of logic as it would be unwarrantable gratuitously to suppose that further investigation will bring about. It will be found that the available evidence is decidedly that Concepts can only be combined through definite "pegs." (CP 4.561, note 1) Peirce goes on to compare the iconicity of the line of identity to the iconicity of the Phemic Sheet. The initial point I wanted to make is that, for the purposes of better understanding the way he is using diagrammatic figures to represent the key relations (i.e., between existing individuals, or for the universe of discourse as whole, where that universe might range over possibilities and not just existing individuals), the figures and conceptions drawn from graph theory will be more helpful than those drawn from the mathematics of vectors. The latter conceptions bring a lot with them that isn't needed. As Peirce is keen to point out, all we need to model the central logical relations are topological sorts of connections and disconnections. Considerations that pertain to scalars, vectors, tensors and versors and the like are not needed--at least not yet. Those kinds of quantitative considerations can be introduced later as we move from a qualitative to a quantitative system of relational logic. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________________ From: Jeffrey Brian Downard Sent: Thursday, December 31, 2015 1:44 PM To: Peirce-L Subject: RE: [PEIRCE-L] The categorial "mirror image" of 'determination' and 'representation'. Hello Gary R., List, Would anything be lost if we substituted the language "directed graphs" for "categorial vectors"? One reason I ask is that Peirce spent a fair amount of time and effort sorting through and responding to A.B. Kempe's various works on mathematical form. One of the criticisms that Peirce makes of Kempe's account is that, for the purposes of a logical analysis of mathematical reasoning, directed graph relations are more basic and undirected graph relations. There are several advantages to drawing on the mathematical conceptions of graph theoretic relations. One advantage is the scholarly point that Peirce was clearly drawing on these graph theoretical conceptions in his work in phenomenology. I don't see textual evidence for thinking that the conception of vectors is foremost in his mind. Another advantage is that graph relations are topological and not metrical in character. As such, fewer assumptions are needed about the underlying "spaces" (e.g., about the categories of being and the universes of discourse) in which the graph relations are being embedded once we put these kinds of diagrammatic figures to work in phenomenology and semiotics. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________________ From: Gary Richmond [[email protected]] Sent: Thursday, December 31, 2015 1:13 PM To: Peirce-L Subject: Re: [PEIRCE-L] The categorial "mirror image" of 'determination' and 'representation'. Gary F. list, As I just wrote in the other thread we've been dialoguing in, I don't really see at the moment any way to make headway in this matter of the vectors. The kind of example which Parmentier and I offer aren't convincing to you, while you counter with alternatives which I simply don't 'get' in the context of categorial vectors. So, it seems to me that when there seems to be no way forward, it is probably best to take a breather and see if either one of us can break through to the other's thinking, or can find some way to correct his own (or the other's) thinking. Best, Gary R [Gary Richmond] Gary Richmond Philosophy and Critical Thinking Communication Studies LaGuardia College of the City University of New York C 745 718 482-5690 On Thu, Dec 31, 2015 at 8:42 AM, <[email protected]<mailto:[email protected]>> wrote: Gary R, Reverting to a post you made over a month ago … I had written something about genuine triadic relations, such as are embodied in the processes of representing and determining — which in my opinion are both genuine, partly because they are mirror images of each other. By that I meant that the process by which the Sign represents the Object to the Interpretant is the same as the process by which the dynamic Object determines the Sign to determine the Interpretant, but with the putative ‘agencies’ trading places, so that the one process is regarded as the reverse of the other. But as your explanation shows, what you mean be “representation” is completely different. GR: I agree. For me this "mirror image" is at the very least reinforced categorially. This was first pointed out to me by Mats Bergman (I believe in his doctoral dissertation) in referring to a paper by R. Palmentier "Signs' Place in Medias Res: Peirce's Concept of Semiotic Mediation." Semiotic Mediation: Sociocultural and Psychological Perspectives. Ed. Mertz, Elizabeth & Parmentier. 1985. and which mirror image I first discussed in a paper on Peirce's trichotomic theory,"Outline of trikonic: Diagrammatic Trichotomic" in Section 5 on trichotomic vectors (i.e., possible paths through the three categories, probably several vectors occuring together in any actual semiosis). http://www.iupui.edu/~arisbe/menu/library/aboutcsp/richmond/trikonic.htm So, while all would agree that, for Peirce, when there is semiosis that the object (2ns) determines the sign (1ns) for the interpretant sign (3ns), Parmentier objects to Peirce's not drawing sufficient attention to its mirror, representation. So, for example (and using the kind of example Parmentier's gives): An interpretant/interpreter (3ns) within a particular art form, say a brilliant and creative playwright, say Shakespeare, out the wealth of his imagination could create a great and influential art work, a play, say Hamlet (1ns: the entire play being a sign, the character Hamlet being a sign, every word, every punctuation mark, etc. of the work being a sign), bringing into quasi-existence a virtual world of imagined relations (2ns). In this sense, determination: 2ns/1ns/3ns categorially mirrors representation: 3ns/1ns/2ns. GF: Not having read Parmentier, I’ve been reluctant to comment on this, but I have to say that I can’t make sense of a scenario where the “interpretant creates a sign to represent an object.” The example you give identifies the interpretant with an interpreter, which is deeply problematic to me, and even granting that point, I don’t see how Shakespeare can be the interpretant of the sign that is Hamlet; nor is it clear to me what the object of that sign is. (Curiously enough, Hamlet himself seems to say that the object of a play is human nature, when he says that the purpose of playing is “to hold the mirror up to nature,” so that people (i.e. the audience) see themselves in it; but in that case, their self-recognition is the interpretant, and the reversal that you and I both metaphorize as mirror-imaging is not implied at all!) GR: While I perhaps see Parmentier's point as regards the neglect by Peirce of this categorial vector in art, I do not see that Peirce neglected it in his primary focus, namely, science. Thus, to offer a very different example: An interpretan/interpreter (3ns) within a particular field of science, say a brilliant and creative theoretical physicist, say Einstein, out of the tremendous storehouse of his scientific and mathematical knowledge and creativity could hypothesize a great and influential theory, say, the general theory of relativity (1ns: the entire theory being a sign, every mathematical symbol, etc. being a sign), bringing into our scientific understanding a model of the large-scale structure of our 'actual' universe (2ns). [I've added a very brief note on trichotomic vector analysis at '*' below my signature.] GF: In that case I’d say it’s the mathematical model that is doing the representing (of the physical universe) to the physicist, and the interpretant would be the next step in the inquiry. But Einstein would say (in fact does say, in Turning Signs Chapter 9) that the physical universe does not fully determine the model which the equations of the physicist represent; so in that case representation and determination would not mirror one another. Now I don't know whether you had this categorial mirroring in mind when you wrote what I just quoted above, Gary. In any case, I have given this post a new subject heading in the interest of emphasing the "mirror image" of 'determination' and 'representation'. I hope that this thread will clarify your vector analysis, which I’ve been hoping for years to understand better than I do (as it’s probably obvious from the above that I don’t really get it.) I guess what I’m looking for is a more exact definition of the six vectors, along the lines of Peirce’s definitions in NDTR of the nine “parameters” as you call them. Then we need to look at examples of their application and consider the ‘fit’ between definition and example. I’ll do my best to ask the right questions about both. Maybe this will also help with the problem of naming the vectors, which you mention in the appended note. Gary f. * [In my understanding, this "mirror" represents but two of six possible vectors (again, paths through the categories) Note: in my paper mentioned above, I first called the 'vector of 'involution', mentioned above, the 'vector of analysis', but I now call it the path or order or 'vector of involution' as closer to Peirce's meaning and usage. The other 5 names have stayed the same: determination (i.e., semiotic determination), process (which, btw, includes evolution and inquiry), representation, aspiration (of the individual or community), order (shorthand for Hegelian or dialectical order), and, of course, the 6th just mentioned, involution ( again, the analysis of categorial involution commencing at 3ns). For more on categorial vectors, see my paper linked to above. ----------------------------- 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]<mailto:[email protected]> . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected]<mailto:[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 .
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