Hi Jerry, List, First off, if things are sounding mystical to your ears, I hope it is a by product of the richness of the ideas Peirce is examining--and not a by-product of the comments I'm offering.
To a large degree, the answers to the questions you are trying to raise are going to be found in the larger story that is articulated in the theory of semiotics. At this point, I am trying to offer some comments on some of Peirce's explanations and definitions as a kind of run up to the phenomenological categories--and especially the distinction between the formal and material aspects of those categories. The general suggestion I'm making is that Peirce is not providing two entirely separate lists of the categories, one formal and that other material. Rather, there is a close connection between the two even if they do not, in experience, match perfectly because our experience of the material categories of quality, brute fact and mediation is always so richly complex. My general suggestion may seem controversial because some interpreters seem to be offering a different reading of the relevant texts. Confining myself to the subject of the phenomenological categories and the role of mathematics in informing our understanding of the essential formal elements of the monad, dyad and triad, I do take Peirce to be offering an account of the elements needed for setting up the frameworks necessary for referring to grounds, objects and interpretants. One might call them three interrelated "frames of reference." What do the signs that we use in mathematics refer to? Much depends upon whether we are using the signs to seeks answer to questions in pure or applied mathematics. Let's consider the case of pure mathematics. What do the signs used in topology refer to? In the account he offers in the New Elements, the key operations for setting up a system of mathematical diagrams are those of generation and intersection. These are the operations used to generate a line by moving a particle from a point, or for determining the location of a point on a line by intersecting it with another line. As we try to understand the conditions that make it possible for the different representations to refer, we'll need to be clear in identifying the representations we're talking about. It is one thing to ask: what does that particle in the diagram that is being moved refer to? It is another thing to ask, what does the symbol "particle" refer to? I hope it is clear that the conditions under which the symbol "particle" refers is dependent, in many respects, on the conditions under which the iconic particle that is draw on the page is able to refer. As a hypo-icon, the particle we move as we draw the line is remarkably rich as a sign. At any time in the act of drawing the line on the paper, there are qualisigns, sinsigns and legisigns working together so that the particle can function as a rich sign complex in a larger process of interpretation. What is more, the particle embodies the idea of a generator. That is, it embodies a more general rule that determines how we might generate innumerable other possible lines from the point. This is a more general rule that enables us to interpret the larger mathematical space in which the line is being constructed. It enables us to understand how one line my be transformed continuously to give us a line that is homeomorphic with the first, or how various kinds of discontinuities might be introduced to give us another different line altogether. I hope you can see that I'm trying to bracket some of the questions you've raised about the role of real things (i.e., chemical compounds, protein or DNA molecules, and the like) in serving as the grounds or objects to which one or another kind of representation might refer. I'm bracketing those questions for a reason. I'd like to keep the phenomenological analysis of the conditions under which the signs used in pure mathematics refer free from big metaphysical assumptions about what is really the case as a positive matter of fact. There is a long line of philosophers who have tried to import such metaphysical assumptions into their accounts of the reference and meaning of the signs used in math and formal logic (e.g., Mill, Quine, etc.), but Peirce is resisting this move--at least until we're ready to address questions in metaphysics. Once we are ready and we're using the methods appropriate for answering questions in metaphysics, we'll need to think about the real nature of an ideal system of mathematical definitions, hypotheses, theorems, etc., and what it is for that system to be real as a rich and consistent network of possible formal relations. --Jeff Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354 ________________________________________ From: Jerry LR Chandler [[email protected]] Sent: Tuesday, August 19, 2014 9:28 PM To: Jeffrey Brian Downard Cc: Peirce List Subject: Re: [PEIRCE-L] Phaneroscopy, iconoscopy, and trichotomic category theory Jeffrey: Your posts become increasingly mystical. This is not a judgement, merely an observation from a philosophy of mathematics perspective. At issue is how to you assign meaning to mathematical symbols. In particular, in light of K.S. and his comments on the meaning of number in the context of his description of gold? More to the point, does the meaning of mathematical symbols reside in mathematics itself or do the meanings refer to the reference systems for the symbol system, that is the application to a particular material reality, such as the atomic numbers? Or the sequence numbers for a genetic sequence? Or protein sequence? In yet other terms, does the concept of order infer a universal meaning or a meaning dependent on the nouns of the copulative proposition? Perhaps you can address these vexing issue? Cheers Jerry On Aug 19, 2014, at 8:28 PM, Jeffrey Brian Downard <[email protected]> wrote: > Gary F., Gary R., List, > > In an effort to think a bit more about the form/matter distinction as it > applies to the phenomenological categories, let me add few comments about an > explanation that Peirce provides concerning the mathematical form of a state > of things. I'd like to add some remarks about this explanation because I > think it offers us a nice way of responding to a concern Gary F. raised. > Here is the concern: > > Gary F. says: "Jeff, I’m interested in your question, 'is there any kind of > formal relation between the parts of a figure, image, diagram (i.e., any > hypoicon) that does not have the form of a monad, dyad or triad?' . . . I > confess that I have no idea how we would go about investigating that > question." > > My initial response was: "The answer to the question involves the whole of > Peirce's semiotic--and not just his account of the iconic function of signs. > So Peirce is bringing quite a lot to bear on the question. For starters, > however, I think we should consider the examples he thinks are most important > in formulating an answer. What Peirce sees is that, in mathematics, the > examples we need are as 'plenty as blackberries' in the late summer. (CP > 5.483) What do you know, it is late August. Let's go picking." > > As a first stop on our way to the briar patch, let's consider the following > definition from "The Basis of Pragmaticism in the Normative Sciences." > > "A mathematical form of a state of things is such a representation of that > state of things as represents only the samenesses and diversities involved in > that state of things, without definitely qualifying the subjects of the > samenesses and diversities. It represents not necessarily all of these; but > if it does represent all, it is the complete mathematical form. Every > mathematical form of a state of things is the complete mathematical form of > some state of things. The complete mathematical form of any state of things, > real or fictitious, represents every ingredient of that state of things > except the qualities of feeling connected with it. It represents whatever > importance or significance those qualities may have; but the qualities > themselves it does not represent." (EP, vol. 2, 378) > > Peirce suggests that this explanation is "almost self-evident." At this > point in his discussion, however, he merely ventures the explanation as a > "private opinion." I cite this passage because it bears directly on the > question of how our understanding of the mathematical form of something such > as a figure or diagram is supposed to inform our understanding of the formal > categories of monad, dyad and triad (or, firstness, secondness, > thirdness)--and how we might use those categories in performing a > phenomenological analysis of something that has been observed. > > Peirce says that he has introduced this explanation in order to account for > the emphatic dualism we find in the normative sciences. The dualism is > especially marked in logic and ethics (e.g., true and false, valid and > invalid, right and wrong, good and bad), but it is also found in aesthetics. > As such, he is noticing a phenomena that has been widely observed to be a > part of our common experience in thinking about how we ought to act and > think, and he is getting ready to venture a hypothesis to explain what is > surprising about the phenomena. The explanation of the dualism that follows > might seem a bit hard to make out, but I think it is clear that this is what > he is trying to do. > > That might have seemed a bit opaque, so let me try to restate the point. I > think Peirce is drawing on an understanding of mathematical form for the sake > of performing an analysis of a particular phenomenon that calls out for > explanation. We need to see what it is in the phenomena (i.e., the dualism > in the normative sciences) that really calls out for explanation. Otherwise, > we will not have a clear sense of whether one or another hypothesis is > adequate or inadequate to explain what needs to be explained. > > He says the following about his account of the mathematical form of a state > of a things: "Should the reader become convinced that the importance of > everything resides entirely in its mathematical form, he too, will come to > regard this dualism as worthy of close attention?" > > Why does Peirce say that the importance of everything resides in its > mathematical form? On my reading of this passage and what follows in the > next several pages of the essay, I think he is developing the claim I > asserted above. That is, every kind of formal relation that might be found > between the parts of a figure, image, diagram and the space in which such > things are constructed must have the form of what we are calling, in our > phenomenological theory, a monad, dyad or triad. > > It might sound ridiculous to suggest that the dualism present in our > experience of what is valid or invalid as a reasoning or what is right or > wrong as an action can be clarified by using a mathematical diagram, such as > a drawing on a piece of paper of two dots that we might count by saying "one' > and "two," but he says that we shouldn't disregard such a suggestion. He has > argued elsewhere that every observation we might make must involve some kind > of figure or diagram--and the form of such a figure or diagram can be > understood in terms of having the structure of a skeleton set (CP, 7.420-32), > or a network figure (CP, 6.211), or some other kind of really basic > mathematical structure. I refer to those particular mathematical structures > because the first can be applied to things in our experience that are more > discrete in character, and the second can placed over things more continuous > in character. > > Do you buy his claim here? Does the "importance of everything reside in its > mathematical form?" The argument he offers in the rest of section B is worth > a look. > > --Jeff > > > Jeff Downard > Associate Professor > Department of Philosophy > NAU > (o) 523-8354 > ________________________________________ > From: Jeffrey Brian Downard > Sent: Saturday, August 16, 2014 4:09 PM > To: Gary Richmond; Peirce-L; Gary Fuhrman; André De Tienne > Subject: RE: [PEIRCE-L] Phaneroscopy, iconoscopy, and trichotomic category > theory > > Gary R., Gary F., André, List, > > Peirce makes two suggestions for doing phenomenology, and both are reflected > in the place he gives this kind of science in his architectonic. > > 1) We should ask: what formal categories must be in experience in order to > make valid synthetic inferences from the things we've observed? Or, putting > the question in a more particular form: what formal elements must be in the > observations we made of some surprising phenomenon in order to draw a valid > adductive inference to an explanatory hypothesis? The same kind of question > could be asked about inductive inferences from a set of data. > > 2) In order to answer this question, we should look to math and see what > kinds of mathematical conceptions and principles might be borrowed from this > science so as to give us insight into those formal features of the phenomena > we observe. > > These suggestions are reflected in Peirce's placement of phenomenology > between math and the normative theory of logic. > > In order to see why these suggestions might be helpful for understanding > Peirce's theory of phenomenology (i.e., phaneroscopy), I'd suggest that we > take up a sample problem. Here is a question that mattered much to Peirce. > What kinds of observations can we draw on in formulating hypotheses in the > theory of logic about the rules of valid inference? Peirce's answer to this > question is that we are able to make a distinction between valid and invalid > inferences in our ordinary reasoning, and that we can classify different > kinds of inferences as deductive, inductive and adductive. The process of > drawing on our logica utens in making arguments and reflecting on the > validity of those arguments supplies us with the observations that are needed > to get a theory of critical logic off the ground. > > As we all know, any kind of scientific observation we make might contain one > or another kind of observational error. As such, we have to ask the > following questions. Once we have a set of observations in hand, how should > we analyze them? What is more, how can we correct for the observational > errors we might have made? We could frame the same kinds of questions about > the study of speculative grammar as I've stated for a critical logic. For my > part, I'm working on the assumption that Peirce's analysis of the elements of > experience is designed to help us give better answers to these kinds of > questions than we are able to get from other philosophical methods--including > those of Kant, Hamilton, Mill, Boole, etc. > > The study of icons, I take it, is part of a general strategy of thinking more > carefully about question (1) listed above. Gary R., are you thinking about > "iconoscopy" or "imagoscopy" differently? I think that the careful study of > icons can be especially helpful in setting up a theory of logic because of > the essential role that icons have in the process of making of valid > inferences. > > With this much said, let me ask a question that I think is really basic for > understanding Peirce's phenomenology: is there any kind of formal relation > between the parts of a figure, image, diagram (i.e., any hypoicon) that does > not have the form of a monad, dyad or triad? That is, take the space in > which a diagram or other figure might be drawn, and take the relations > between the parts of any diagram (both actual and possible), and ask > yourself: how are the actual parts of the token diagram connected to each > other and to all of the possible transformations that might be made under the > rules that are used to construct and interpret the diagram? Is there any > formal relation between the parts of the diagram and the space in which it is > constructed that does not have the character of a monadic, dyadic or triadic > relation? > > We see that Peirce makes much of the role of icons in necessary reasoning, > including the necessary reasoning by which mathematicians deduce theorems > from the hypotheses that lie at the foundations of any given area of > mathematics. The suggestion I'm making is based on the idea that icons have > a similarly essential role in the framing of a hypothesis and the drawing of > an inductive inference. Do you know of a place where Peirce argues this kind > of point? One sort of place that comes to my mind is the discussions he > provides of the process of formulating hypotheses in mathematics. > > --Jeff > > Jeff Downard > Associate Professor > Department of Philosophy > NAU > (o) 523-8354 > ________________________________________ > From: Gary Richmond [[email protected]] > Sent: Saturday, August 16, 2014 11:15 AM > To: Peirce-L; Gary Fuhrman; André De Tienne > Subject: [PEIRCE-L] Phaneroscopy, iconoscopy, and trichotomic category theory > > Gary, list, > > I suppose I expected--or at least, hoped--that Gary F. would respond to my > post on some of the issues we'd been discussing recently regarding > phenomenology, a topic of some considerable interest to both of us and, > hopefully, to others on the list as well. So, in an off-list email to him I > expressed this hope, and Gary wrote back in a message he said I could > reproduce here. (I've interleaved my own comments within the substantive > parts of that message) > > I’ve already agreed that iconoscopy is probably the only way to make > phaneroscopy scientific, if its formulations themselves are scientific. > > I would concur, especially if your qualification is met. But, for now, > iconoscopy is the subject of but a single, as far as I can tell, unpublished > article by Andre de Tienne (who, as I earlier suggested, thought the term > 'iconoscopy' didn't exactly catch his meaning, that something like > 'imagoscopy' might come closer). There were also several discussions of de > Tienne's ideas in 2009 (as interest was shown in then by Martin Lefebvre, > myself, and others) and again in 2011 when both Gary F. and I discussed them > in the slow read of Joe's paper, "Is Peirce a Phenomenologist?" See: > https://www.mail-archive.com/[email protected]/msg00043.html > > Still, the idea of this second phenomenological science seems sound to me, > and even necessary. Continuing: > > But I don’t have a proper response to this: > So what exactly are "the elements of the phaneron" once one's stated the > obvious, that is, the three universal categories? > I don’t think that’s obvious at all, or maybe I don’t get what you mean by > “obvious” here. It’s not even obvious to many list members what it means that > the three “categories” are “universal”. So I’m stumped for an answer to that > question. > > Hm. I guess I'm stumped by your being stumped. It may be that some, perhaps > many, list members don't 'get' Peirce's categories at all, let alone see them > as 'universal'. But some people do observe "the elements of the phaneron" and > do see them as universal. I would even suggest, by way of personal example, > that I saw them before I was even exposed to Peirce's writings, and before I > could give them names (certainly not firstness, secondness, and thirdness, > but, perhaps, something vaguely approaching something, other, medium). This > is merely to say that, if Peirce is correct and that the elements of the > phaneron are truly universal, then there's no reason why anyone attuned to > that kind of observation shouldn't and couldn't have touched upon them before > having Peirce's precise and helpful names for them. > > Phenomenology is admittedly a difficult science to grasp and even more > difficult to 'do', so I can imagine that many folk, including many > philosophers, haven't developed, or fully developed, the kinds of > sensibilities and abilities which Peirce thought were essential in doing this > science--that is, they haven't developed them any more than, for example, > I've developed some of the mental skills necessary for taking up certain > maths. But, as to our interests and talents, vive la difference! > > Also it’s still not clear to me how “category theory” or “trichotomic” is > related to phaneroscopy and iconoscopy, or why it’s part of Peircean > “phenomenology” (rather than logic or semiotic, or even methodeutic). It > seems to take the results of phaneroscopy (as articulated by iconoscopy, I > suppose) and apply them to the analysis and classification of more complex > phenomena such as semiotic processes. If so, then it should be subordinate to > phenomenology in the classification of sciences, not part of it. > > Here I must completely disagree. While it is true that trichotomic can and > will be applied in principle to semiotic, it is my opinion--well, more > precisely, my experience--that trichotomies are discovered in > phenomenological observation. And I personally have no doubt that Peirce > observed them in this way. It may be that one needs a kind of logica utens to > sort out some of these structures after the fact of the observation of them, > but, for example, it is possible in observing many phenomena, to 'see' that > firstness, secondness, and thirdness form a necessary trichotomy within > them,so to speak; and that 'something', 'other', 'medium' requires a > vectorial progression from 1ns, through 2ns, to 3ns, and in precisely that > (categorial, in this case, dialectical) order.These are, of course, two of > the most basic expressions of (a) trichotomic and (b) vectorial progression. > At the moment I can see no other place for the observation of such > trichotomic structure and the establishing of this as a principle for the use > by sciences which follow phenomenology except at the end (the putative third > division) of it. > > In logic, of course, Peirce considers diagrams more essential than language; > but I don’t see how diagrams can be used in phenomenology to avoid language, > so I don’t have a useful suggestion for doing that either, although I > wouldn’t want to say that it can’t be done. I was hoping somebody else would > have a better response. > > But certainly very many, perhaps most, diagrams of considerable value to and > use in science necessarily require language, or use language as an adjunct. > This, for example, is the case for some of the trichotomic diagrams Peirce > offers in certain letters to Lady Welby. The diagrams I use in trikonic are > meant, first, to show the categorial associations of the terms of a genuine > trichotomic relationship (those icons/images identified in what might be > called an iconoscopic observation, then given names) and, second, to show the > possible vectors (or paths) that are possible--and, some times, evident-- in > some of them. A logica utens allows one to extrapolate rather far in this > vectorial direction, in my opinion. But such a use of logica utens is the > case in theoretical esthetics and ethics as well. Ordinary logic (logica > utens) need not and probably cannot be avoided in the pre-logical (i.e., > pre-semiotic, pre-logica docens) sciences. > > If any of the above is useful as a prompt for a further explanation of > “category theory”, feel free to quote it and reply with a correction! > Meanwhile, yes, I am busy with a number of things these days … > > Yes, your remarks have been at least personally useful, especially in seeing > that until the first two branches of phenomenology, phaneroscopy and, > especially, iconoscopy, are much further developed, trichotomic category > theory will lack a solid basis. Still, important science has been > accomplished in all the post-phenomenological sciences without this grounding > and I expect this to happen in trichotomic as well. > > Peirce clearly saw the categories as a kind of heuristic leading him to a > vast array of discoveries along the way. It is not surprising, then, that > late in life he settled on an essentially trichotomic classification of the > sciences. It seems to me that if one allows for a second phenomenological > science, iconoscopy, that it makes sense to at least look for yet a third > one--perhaps especially in this science which discovers three universes of > experience. > > And further, it seems to me that the first of the semiotic sciences, > theoretical or semiotic grammar, gets one of its most important principles, > namely, trichotomic structure (cf. object/sign/interpretent; > qualisign/sinsign/legisign; icon/index/symbol; rheme, dicent, argument; the > trichotomic structure of the 10-adic classification of signs; etc.) not out > of thin air, but from some science preceding it according to Comte's > principle of the ordering of the sciences, that those lower on the list drawn > principles from those above them. > > Suffice it to say for now that in my opinion trichotomic category theory > ought be placed in phenomenology, not further down in the classification of > the sciences (Gary, you suggested methodology, which makes no sense to me at > all), And, rather than being "subordinate to phenomenology," it seems to me > that, within phenomenology, and at the conclusion of it, that it provides > exactly the bridge leading to the normative sciences, but especially to > semiotic grammar. > > Best, > > Gary > > Gary Richmond > Philosophy and Critical Thinking > Communication Studies > LaGuardia College of the City University of New York > C 745 > 718 482-5690<tel:718%20482-5690> > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. 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