Gary, lists, You've raised a question about what I meant in offering this remark: My assumption is the phenomenological categories of monad, dyad and triad (or first, second and third) are the formal features that we observe when we make any kind of skeleton diagram. That is, the formal relations of monad, dyad and triad are the "a priori" formal elements that are necessary for constructing and then reasoning about such skeleton diagrams.
The remark was designed to be a bit of a prod that was aimed at a claim made some time ago by Jon Awbrey to the effect that that triadic relations can be understood--first and foremost--as ordered triples. I tried to offer a bit of a challenge to this back in January, and Jon has been gracious in patiently developing a set of responses to some of my concerns. As I said earlier, my thoughts on the matter are not entirely clear. As such, I'm groping around a bit as I try to figure out what is causing me to feel unsettled by such a suggestion. For the last several months, I've been digging my way through the details of "The Logic of Mathematics," and the account he provides in that essay of the character of both degenerate and genuine dyads and triads. My aim is to use the account he provides in this essay in order to interpret the later essays on the nature of dyadic and triadic relations--especially those dealing with the nomenclature and division of such relations. Let me add that, in the remark copied above, I was simply applying what I've been trying to sort out in Peirce's account of monadic, dyadic and triadic relations to his remarks about the role of skeleton diagrams in perceiving and reasoning. The source of your puzzlement, as far as I can make it out, is that you want me to make a distinction between "the (abstract) categories as such" and the particular relations that are found in "the actual features we observe." It might help if I added the following clarification: these formal relations of the monad, dyad and triad--as they are studied in formal logic, phenomenology, the normative sciences--are embodied in token instances in diagrams and in our understanding of the rules that are used to interpret the meaning of such instances. As such, our understanding of these formal relations requires that we express them in both sinsigns and legisigns. I'm hoping that it is clear that my remark was centered on the phenomenological account--and what the role of these formal elements is when we make observations of the relations between the parts of skeleton diagrams. As far as I can tell, what I've said doesn't help much. Having said that, I'd be happy to carry on the conversation in the hopes of working together with the aim of making things clearer. --Jeff Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354 Here is the earlier email: ________________________________________ From: Gary Richmond [[email protected]] Sent: Thursday, April 23, 2015 10:20 AM To: [email protected] Cc: Peirce-L Subject: Re: [biosemiotics:8399] RE: [PEIRCE-L] Re: Natural Propositions, Ch. 10. Corollarial and Theorematic Experiments with Diagrams Jeff, Jon, lists, Jeff, I think your response to Jon's concerns about Ketner's comments in A Thief of Peirce makes good sense, while I'm uncertain exactly what you meant by your concluding comment. Regarding Jon's 1st concern that "icons are not the most general types of signs and so the leap to signs in general falls a bit short." You wrote: JD: if we agree that every kind of dicisign or argument involves iconic qualisigns, sinsigns and legisigns as component parts, then the leap to the generalization may not be problematic. Even in cases where we abstract from many of the iconic features of the component signs, iconic features remain nonetheless, or self-controlled reasoning about such signs would not be possible. In a word, abstraction from certain iconic features yet leaves some "iconic features" such that reasoning about dicisigns and arguments remains possible; so, generalizing does not necessarily do away with certain iconic features. Makes sense to me. As to Jon's 2nd concern having to do with " the many senses of the word "model" and not having read Ketner's "Thief" I don't know which of the multitude he has in mind." You wrote: JD: if we replace Ketner's use of the word "model" with "diagram," [. . .] much of the weight of what Peirce is claiming falls on the conception of a skeleton diagram. I think that's correct and, indeed, in the Ketner passage from Thief with which I conclude this post, Ketner explicitly equates 'model' and 'diagram' in remarking that mathematics is "the science that models (diagrams) relations in areas under study." This brings us back to Peirce's notion of "abstractive observation," which he says is familiar to and offers no problem for ordinary folk, but seems to become problematic for some theorists. CSP: [The ordinary person] makes in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what modifications the hypothetical state of things would require to be made in that picture, and then examines it, that is, observes what he has imagined [. . . ,] such a process, [being] at bottom very much like mathematical reasoning [allows us to] reach conclusions as to what would be true of signs in all cases, so long as the intelligence using them was scientific. And, again, by a "scientific intelligence" Peirce means one "capable of learning by experience." So, I'm a bit uncertain as to what your intended meaning is in writing: JD: My assumption is the phenomenological categories of monad, dyad and triad (or first, second and third) are the formal features that we observe when we make any kind of skeleton diagram. That is, the formal relations of monad, dyad and triad are the "a priori" formal elements that are necessary for constructing and then reasoning about such skeleton diagrams. I'm not sure if the (abstract) categories as such (as opposed to particular relations) are the actual features we observe. Perhaps I'm just missing something here, but if you'd further explicate your remarks it would be helpful. I think your remark may relate to what Ketner says as he continues his analysis of the passage we've been discussing . In the following passage he considers, especially, "visual diagrams" (although he's just made some brief remarks on auditory and other diagram types). KK: . . . Pierce thought sight was probably best adapted for detecting new features of relational patterns in diagrams that model triadic relations presently under study. People sometimes say, when they want an explanation, "Draw me a picture." To "Draw a picture," then, would be to proceed in the way that Peirce would have recommended in response to the question "How can we study phenomena rich in triadic relations if dyadic considerations alone cannot exclusively do the explanatory job?" If we add that Peirce recognized algebras and other arrays of symbols as visual diagrams, then we can state that mathematics, not in the narrow sense in which it is usually understood today, but as the science that models (diagrams) relations in areas under study, would be among the finer tools for "drawing pictures" that humankind has yet developed (Ketner, 278). Best, Gary [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 Wed, Apr 22, 2015 at 8:09 PM, Jeffrey Brian Downard <[email protected]<mailto:[email protected]>> wrote: Jon, Gary, Lists, Jon has raised two concerns about Ketner's statement in the "Thief". Here are some quick responses to the concerns: (1) A major problem is that icons are not the most general types of signs and so the leap to signs in general falls a bit short. Response: if we agree that every kind of dicisign or argument involves iconic qualisigns, sinsigns and legisigns as component parts, then the leap to the generalization may not be problematic. Even in cases where we abstract from many of the iconic features of the component signs, iconic features remain nonetheless, or self-controlled reasoning about such signs would not be possible. (2) A minor problem has to do with the many senses of the word "model" and not having read Ketner's "Thief" I don't know which of the multitude he has in mind. Response, if we replace Ketner's use of the word "model" with "diagram," I don't think anything is lost. We would then remain truer to what Peirce says in the passage. As far as I can see, much of the weight of what Peirce is claiming falls on the conception of a skeleton diagram. Peirce says: The faculty which I call abstractive observation is one which ordinary people perfectly recognize, but for which the theories of philosophers sometimes hardly leave room. It is a familiar experience to every human being to wish for something quite beyond his present means, and to follow that wish by the question, "Should I wish for that thing just the same, if I had ample means to gratify it?" To answer that question, he searches his heart, and in doing so makes what I term an abstractive observation. He makes in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what modifications the hypothetical state of things would require to be made in that picture, and then examines it, that is, observes what he has imagined, to see whether the same ardent desire is there to be discerned. By such a process, which is at bottom very much like mathematical reasoning, we can reach conclusions as to what would be true of signs in all cases, so long as the intelligence using them was scientific. My assumption is the phenomenological categories of monad, dyad and triad (or first, second and third) are the formal features that we observe when we make any kind of skeleton diagram. That is, the formal relations of monad, dyad and triad are the "a priori" formal elements that are necessary for constructing and then reasoning about such skeleton diagrams. Elsewhere, he calls the diagrams skeleton sets, or network figures, but I think he is talking about the same kind of thing. --Jeff Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354 ________________________________________ From: Jon Awbrey [[email protected]<mailto:[email protected]>] Sent: Wednesday, April 22, 2015 2:12 PM To: Gary Richmond; Peirce-L; [email protected]<mailto:[email protected]> Subject: [PEIRCE-L] Re: Natural Propositions, Ch. 10. Corollarial and Theorematic Experiments with Diagrams Re: Gary Richmond At: http://permalink.gmane.org/gmane.science.philosophy.peirce/16249 Gary, List, There are many problems here that I see right off. (1) A major problem is that icons are not the most general types of signs and so the leap to signs in general falls a bit short. (2) A minor problem has to do with the many senses of the word "model" and not having read Ketner's "Thief" I don't know which of the multitude he has in mind. But that's all I have time for now, so sufficient unto the day ... Jon On 4/22/2015 4:48 PM, Gary Richmond wrote: > Cathy, Jon, Frederik, Lists, > > I agree that CP 2.227 is a most extraordinary passage, one which Ken Ketner > has referred to as "one of the most remarkable theoretical passages ever > written" (Ketner, *A Thief of Peirce,* 276). > > Just before quoting it he remarks that in it "Peirce brought together the > concepts we need to make sense of diagrammatic thought as a nonreductive > technique for modeling, and for thereby gaining an understanding of triadic > phenomena." > > Ketner spends much of the rest of his essay discussing the importance of > the passage, perhaps getting a bit carried away with the 'power' of it.. > > *I ask you to note carefully several things about this remarkable > paragraph. First of all the sheer power of it will grow on you, so please > give it a chance to serenade you. One instance of its power is the > connection it makes between mathematics and novels! Second, by reading sign > as "triad," we get the result that semeiotic is the study of triadic > action, a study accomplished by constructing and observing models! *(op. > cit., 277) > > > What especially interests me is that Ketner describes 'abstractive > observation', a phrase used three times in the passage (and implied several > times moreh) in this way: > > *Abstractive observation is of course observation of relations in models. > Also, a sign or representation, this paragraph encourages one to infer, is > itself some kind of model of that which it represents (its object) to that > which interprets it (its interpretant). *(277) > > > Several thoughts came to mind in reading this, but the first one is this: > does Peirce use this expression, 'abstractive observation', elsewhere and > consistently? If so, can we agree with Ketner that 'abstractive > observation' is "*of course*" necessarily "observation of relations in > models"? If we can, than the expression could be an especially useful > shortcut for saying just that and, perhaps, be given greater currency. > > Best, > > Gary > -- 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 .
