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>
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