Jeff, lists, You wrote:
"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. " I too have spent many a month studying that difficult, but seemingly inexhaustible essay, "The Logic of Mathematics." I first got interested in it many years ago when Bernard Morand quoted a passage from it, one which led me to begin thinking almost compulsively about possible paths (or vectors) through categorial relations. So, for me this essay is essentially about something other than "ordered tuples." Here's the passage Bernard brought to my attention: [. . .T]his is only one of two sides of the shield, both of which must be examined, and which have to be synthesized in the really philosophical view. The reason of this is, that although the view which takes the triad first is necessary to the understanding of any given point, yet it cannot, from the very nature of the case, be carried out in an entirely thoroughgoing manner. How, for instance, would you begin? By taking the triad first. You thus do, in spite of yourself, introduce the monadic idea of "first" at the very outset. To get at the idea of a monad, and especially to make it an accurate and clear conception, it is necessary to begin with the idea of a triad and find the monad-idea involved in it. But this is only a scaffolding necessary during the process of constructing the conception. When the conception has been constructed, the scaffolding may be removed, and the monad-idea will be there in all its abstract perfection . . . (CP 1.490) In the course of this essay Peirce shows his method of logically deriving his three categories involutionally and yet on that Hegelian scaffold which he has so carefully and minutely analyzed. Thus, Peirce's involutional order for deriving/analyzing the categories, 3ns -> 2ns -> 1ns (or, more clearly, thirdness involves secondness and firstness; and secondness involves firstness) is the obverse of Hegel's dialectical order of 1ns -> 2ns -> 3ns (Peirce's something -> other -> medium). But continuing, you wrote: JD "[O]ur 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." I'm not certain that we mean the exact same thing in referring to "the phenomenological account" of the observation of diagrams. So, I too would be pleased to continue this discussion with you and others who may be interested in how such models (diagrams) function in diagram construction, observation, and manipulation followed by further observation, including in the light of Chapter 10. Best, Gary R [image: 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 Fri, Apr 24, 2015 at 3:48 PM, Jeffrey Brian Downard < jeffrey.down...@nau.edu> wrote: > 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 [gary.richm...@gmail.com] > Sent: Thursday, April 23, 2015 10:20 AM > To: biosemiot...@lists.ut.ee > 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 < > jeffrey.down...@nau.edu<mailto:jeffrey.down...@nau.edu>> 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 [jawb...@att.net<mailto:jawb...@att.net>] > Sent: Wednesday, April 22, 2015 2:12 PM > To: Gary Richmond; Peirce-L; biosemiot...@lists.ut.ee<mailto: > biosemiot...@lists.ut.ee> > 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 > 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 > . > > > > > >
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