Re: [PEIRCE-L] Peirce's Ongoing Semiotic Project, was, Re: Interpretants, as analyzed and discussed by T. L. Short
Robert, I agree that lattices would make a good formal structure for classifying and organizing interpretants. If all the interpretants are derived by formal rules of inference according to some formal logic, then a lattice would be the appropriate mathematical structure for organizing and displaying them. Following is an article that I presented at a conference on formal ontology in 2006: A Dynamic Theory of Ontology, https://www.jfsowa.com/pubs/dynonto.htm . The basic idea is a dynamically growing lattice that has no limit on size. Whenever any word shifts its meaning in the slightest -- from one microsense to another, a new branch in the lattice is created. But I also realize that such a system could quickly grow beyond what people are capable of understanding. It's not likely to be the way that people normally use language. Peirce also recognized the vagueness and complexity and immense variability of the way language is normally used, Since Peirce had a very strong background in formal mathematics and logic, a very strong background in language and the linguistics and psychology of his day, and a very practical sense of how people reason about commonsense and the informal significs of Lady Welby, he was trying to find some way to relate and integrate all these methods. That led to his final decade of 2003 to 2013, when he was frantically trying to relate and integrate and synthesize everything -- with a few people like William James, Lady Welby, and some others as correspondents. It's amazing how far he got, but it's not surprising that there are many loose ends that don't quite fit. It's good to explore further developments of his ideas, but we have to be careful to distinguish his words from our extensions. Anything other than an exact quotation is the opinion of the author. Nobody can claim that his or her ideas are what Peirce intended, John From: "robert marty" John, List John, concerning Peirce's mathematical background, I can't find a note attached to your message, but perhaps I misread it? I want to point out, however, that I did some research to find out whether Peirce was aware of Lattice Theory since I think you are aware that over forty years ago, I showed that classes of signs were naturally organized in lattice structures (10, 28, 66 conditionally, depending on the respective number of constituents 3, 6 or 10). I argued that Peirce had intuited these structures as affinities (CP 2.264). Here's what I've found that answers the question positively. As you know, Garrett Birkhoff found Lattice Theory in purely algebraic terms in his eponymous 1940 book: Birkhoff, Garrett, 1940, Lattice Theory, Revised Edition (1948), Free Download, Borrow, and Streaming: Internet Archive. Peirce is cited several times as the precursor who formalized the foundations of Lattice Theory right from the first page of Chapter I, in which Birkhoff gives the mathematical definition of Partly (or Partially) Ordered Sets: -Page n18 1 From the German "teilweise geordnete Menge," Hausdorff [1], first ed., Ch, VI, §2. The assumptions go back to C. S. Peirce [1], and were also studied by Schroder [1]. They occur in a fragmentary way in Leibniz's works (circa 1690); see C. I. Lewis, A survey of symbolic Logic, Berkeley, U. S. A., 1918, pp. 373-87; for a fuller account, see L. Couturat, La logique de Leibniz d'aprés des documents inbditSy Paris, 1901, Ch. VIII. Thus PI is Leibniz's Property 7 (p. 3^), P2 his Property 17 (p. 382), and P3 his Property 15 (p. 382). He is also the author of fundamental definitions and notations: - Page n33 The definition of sums and products in terms of inclusion is due to C. S. Peirce [1, p. 33]; see also E. Schroder [1, p. 197], Th. Skolem [1]. H. Whitney has suggested the names "cap'' and "cup" for the symbols ... - Page n36 This notation is due to C. S. Peirce [2]. Birkhoff even cites a controversy concerning Peirce, who seems to have advanced on distributive lattices by being the victim of "severe influenza" if we are to believe the letter he sent to E. V. Huntington, which the latter reproduced. - Page n150 I Historical note: It is curious that C. S. Peirce [1] should have thought that every lattice was distributive. He even said L6', L6" are "easily proved, but the proof is too tedious to give"! His error was demonstrated by Schroder [1, p. 282], who showed that L6', L6'' were not implied by L1-L4, but (p. 286) implied each other and L6. A. Korselt (Math. Ann. 44 (1894), 156-167) gave another demonstration. Peirce at first [2] gave way before these authorities, but later (cf. E. V. Huntington [1, pp. 300-301]) boldly defended his original view. Peirce is quoted again in connection with more complex structures, such as Lattice-Ordered Semigroups, - Page n227 ** See C. S. Peirce, Mem. Am. Acad. Arts. Sci. 9 (1870), 317-78; E. Schroder [1, vol. Ill]; J. C. C.
[PEIRCE-L] OFF-LIST Re: Interpretants, Sign Classification, and 3ns (was Who, What, When, Where, How, and Why)
Gary: As always, I appreciate your positive feedback. I am starting to wonder if my recent flurry of List activity might finally result in a paper on speculative grammar. JFS already replied to my post (see below) but did so off-List, sending it to me only, without changing the subject line or otherwise saying so. Along with his questions at the end that are directed to "anybody else who may be interested," this suggests that it was unintentional, such that he might eventually send it to the List after all. JFS: Your comments confirm the fact that every example of Thirdness can be explained as the answer to a question that begins with word 'Why'. Obviously, my comments do no such thing, and hopefully, others would readily see that for themselves. JFS: Although Peirce hadn't mentioned that point, I think he would have been delighted if Lady Welby or some other correspondent had suggested it. JFS: I realize that Peirce did not mention the connection between the word 'why' and every instance of Thirdness. But if somebody had mentioned that connection to him, I believe that he would have been delighted to have that simple test. I honestly suspect that Peirce would have bluntly told JFS, Lady Welby, or anyone else making such a suggestion that it indicates a serious misunderstanding of both his categories and his semeiotic. So much for not putting words in his mouth, claiming to know what he intended, or (in this case) attributing specific sentiments to him without exact quotations. Just imagine how JFS would have reacted if I had said in my post, "I realize that Peirce did not specify the logical order of determination for all ten trichotomies in sign classification, but I think that he would have been delighted if Lady Welby or some other correspondent had suggested this solution." JAS: On the contrary, every answer to every question is an example of 3ns, because every sign is in the genuine triadic relation of mediating between its object and its interpretant. JFS: That point, although true, does not distinguish the three kinds of answers. Exactly--there is no distinction between the three kinds of answers that corresponds to Peirce's three categories. All signs, including every answer to every question, are examples of 3ns. Qualities and reactions are examples of 1ns and 2ns, respectively, not any answers to any questions. JFS: Can anybody find a genuine example of Thirdness that could not be the answer to a question that begins with the word "Why"? Conversely, can anybody find an example of Thirdness that could not be used as an answer to a question that begins with the word 'Why'? These are both the same question. Maybe he intended the second one to be, "Can anybody find an example of an answer to a question that begins with the word 'Why' but is not a genuine example of 3ns?" Of course, I already fulfilled both requests, but he dismissed my counterexamples with a bunch of hand-waving. Thanks, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Wed, Feb 14, 2024 at 6:29 PM John F Sowa wrote: > Jon, > > Your comments confirm the fact that every example of Thirdness can be > explained as the answer to a question that begins with word 'Why'. > Although Peirce hadn't mentioned that point, I think he would have been > delighted if Lady Welby or some other correspondent had suggested it. > > JFS: The monadic relations of 1ns express answers to the words Who, What, > When, or Where. The dyadic relations of 2ns express answers to the word > How. And the triadic relations of 3ns express answers to the word Why. In > particular, all examples of 3ns can be expressed as answers to > Why-questions. > > JAS> On the contrary, every answer to every question is an example of > 3ns, because every sign is in the genuine triadic relation of mediating > between its object and its interpretant. > > That point, although true, does not distinguish the three kinds of > answers. > > For the first four question words (who, what, when, where), the words in > parentheses in your answers are irrelevant, since the single word or phrase > is sufficient. > > JAS> Who retrieved the book? My dog (retrieved the book). What did the man > give his wife? (He gave her) a brooch. When did he give it to her? (He gave > it to her) on Valentine's Day. Where did the datestone hit the Jinnee? (It > hit him) in the eye. > > The next two sentences show that sentences given as answers may include > more or less than what was asked. The person who asked the question may > ask a follow-up question if more information is necessary. > > JAS> How did the woman obtain the brooch? Her husband gave it to her. > > The verb 'give' is triadic. It implies a dyadic physical transfer (answer > to How) plus the reason why: a gift includes the reason why the transfer > was made. The word 'lend' could have been used for the
Re: [PEIRCE-L] Entropy and the Universal Categories (was Re: The Proper Way in Logic)
As I wrote in reply to Jon, there is a cluster of words in English and other languages that express the goal, purpose, intention, desire, or Thirdness that explains why some agent does something. There was no single word in English that exactly expresses the reason until Peirce coined the word Thirdness. The biologist Lynn Margulis explained that all living things from bacteria on up exhibit goal-directed actions that non-living things never do. Her simplest example is a bacterium swimming upstream in a glucose gradient. No non-living things would ever do that. Some human for some purpose might design a robot to do that, The non-living robot would not have the intention, but the human who designed it had some goal or purpose or intention to design an artifact that would perform that action under those conditions. That is the most basic form of intentionality or goal-directed behavior or -- in essence -- Thirdness. Consciousness is not a requirement. My recommendation is to ask why. That's a simple test that corresponds to the common intersection of all those words. ET> Did the bus driver intentionally run over the pedestrian? Just ask the question "Why?" John From: "Edwina Taborsky" John, list I think it would help if you defined ‘intentionality’. Is it involved in all human actions? Did the bus driver intentionally run over the pedestrian? Edwina On Feb 13, 2024, at 3:26 PM, John F Sowa wrote: Edwina, Please see my response to Mike. I used the word 'intentionality' because it (or something like it) is involved in all human actions. For example, I can intentionally walk to the store. But what about each step in the walk? In effect, it is intentional, but it's only conscious when there is a puddle or a broken place in the sidewalk. Other animals at every level and even plants act upon principles that would be called intentional if they had been human. But consciousness is not necessary. And even for humans, all actions appear to have the some kind of intentionality, but the actors themselves will often say that they did it "absent mindedly". But absent minded actions are often done when people are "multitasking", such as talking on their cell phones while crossing the street and getting run over by a bus. They didn't intend to get run over by the bus, but they did intend to cross the street. The steps of walking were not conscious, but they were necessary parts of an intentional process. In effect, Thirdness is involved in every intentional action. And every instance of Thirdness by any living being could be called intentional if a human did it. Can anybody find an example of Thirdness in any of Peirce's writings that could not be considered intentional if it had been performed by a human? John _ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Interpretants, Sign Classification, and 3ns (was Who, What, When, Where, How, and Why)
List: JFS: And there are six kinds of reference that a sign my have to its interpretants. Although Peirce discusses "reference to an interpretant" in his groundbreaking early paper, "On a New List of Categories" (CP 1.553-559, EP 1:5-10, 1868), as far as I can tell, he *never *uses that phrase in any subsequent writings, including the extensive late texts about semeiotic. Instead, he consistently affirms that a sign *denotes *(refers to) its object and *signifies *its interpretant. There are indeed six classes of signs according to their dyadic relations with their two external interpretants (immediate is internal), but they have nothing to do with "the six basic question words." Instead, the division according to "the Nature of the Influence of the Sign"--i.e., its relation to its final interpretant (S-FI)--is rheme/dicent/argument, later generalized to seme/pheme/delome (CP 8.373, EP 2:490, 1908 Dec 25); and the one according to "the Manner of Appeal to the Dynamic Interpretant" (S-DI) is suggestive/imperative/indicative (CP 8.371, EP 2:490), based on whether the sign is presented/urged/submitted. CSP: According to my present view, a sign may appeal to its dynamic interpretant in three ways: 1st, an argument only may be *submitted *to its interpretant, as something the reasonableness of which will be acknowledged. 2nd, an argument or dicent may be *urged *upon the interpretant by an act of insistence. 3rd, argument or dicent may be, and a rheme can only be, presented to the interpretant for *contemplation*. (CP 8.338, 1904 Oct 12) In other words, the logical order of determination for these two trichotomies in sign classification is S-FI then S-DI, resulting in six classes--presented rheme (suggestive seme), presented dicent (suggestive pheme), presented argument (suggestive delome), urged dicent (imperative pheme), urged argument (imperative delome), and submitted argument (indicative delome). Incidentally, this is another reason why I argue that the logical (not temporal or causal) order of determination for the three interpretant trichotomies in sign classification (EP 2:481, 1908 Dec 23) is final (destinate), then dynamical (effective), then immediate (explicit)--since we know for sure that S-FI comes before S-DI, it makes sense that FI likewise comes before DI. I already made my case in another thread that DI must come before II ( https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00061.html), so the resulting sequence conforms to the principle that the genuine correlate (FI) logically determines the degenerate correlate (DI), which logically determines the doubly degenerate correlate (II). If we add the principle that trichotomies for relations always come *after *the trichotomies for the correlates that they involve, then we obtain the following logical order of determination for all ten trichotomies in Peirce's late taxonomies (CP 8.343-345, EP 2:482-483, 1908 Dec 24). 1. DO - Nature or Mode of Being of the Dynamical Object (abstractive/concretive/collective) 2. IO - Mode of Presentation of the Immediate Object (descriptive/desginative/copulative) 3. S - Mode of Apprehension or Presentation of the Sign (tone/token/type) 4. DO-S - Dyadic Relation of the Sign to its Dynamical Object (icon/index/symbol) 5. FI - Purpose of the Final Interpretant (gratific/actuous/temperative for producing feeling/action/self-control) 6. DI - Nature or Mode of Being of the Dynamical Interpretant (sympathetic/percussive/usual for feeling/exertion/sign) 7. II - Mode of Presentation of the Immediate Interpretant (hypothetic/categorical/relative) 8. S-FI - Nature of the Influence of the Sign (seme/pheme/delome generalizing rheme/dicent/argument) 9. S-DI - Manner of Appeal to the Dynamical Interpretant (suggestive/imperative/indicative for presented/urged/submitted) 10. DO-S-FI - Nature of the Assurance of the Utterance (abducent/inducent/deducent for instinct/experience/form) Note that none of these explicitly divides signs according to whether they denote monadic/dyadic/triadic relations. On the other hand, the paradigmatic cases of these are quality/reaction/mediation, and *all *the trichotomies are divisions into those three phaneroscopic categories (1ns/2ns/3ns), or rather the corresponding universes (possibles/existents/necessitants; EP 2:478-479, 1908 Dec 23). JFS: The monadic relations of 1ns express answers to the words Who, What, When, or Where. The dyadic relations of 2ns express answers to the word How. And the triadic relations of 3ns answer questions to the word Why. In summary, all examples of 3ns are answers to Why-questions. On the contrary, every answer to every question is an example of 3ns, because every sign is in the genuine triadic relation of mediating between its object and its interpretant. Moreover, any answer to a who/what/when/where question can be analyzed as an implied proposition that includes a dyadic or triadic
Re: [PEIRCE-L] Peirce's Ongoing Semiotic Project, was, Re: Interpretants, as analyzed and discussed by T. L. Short
John, List John, concerning Peirce's mathematical background, I can't find a note attached to your message, but perhaps I misread it? I want to point out, however, that I did some research to find out whether Peirce was aware of Lattice Theory since I think you are aware that over forty years ago, I showed that classes of signs were naturally organized in lattice structures (10, 28, 66 conditionally, depending on the respective number of constituents 3, 6 or 10). I argued that Peirce had intuited these structures as affinities (CP 2.264). Here's what I've found that answers the question positively. As you know, Garrett Birkhoff found Lattice Theory in purely algebraic terms in his eponymous 1940 book: Birkhoff, Garrett, 1940, Lattice Theory, Revised Edition (1948), Free Download, Borrow, and Streaming: Internet Archive. Peirce is cited several times as the precursor who formalized the foundations of Lattice Theory right from the first page of Chapter I, in which Birkhoff gives the mathematical definition of Partly (or Partially) Ordered Sets: * -Page n18* 1 From the German "teilweise geordnete Menge," Hausdorff [1], first ed., Ch, VI, §2. *The assumptions go back to C. S. Peirce [1]*, and were also studied by Schroder [1]. They occur in a fragmentary way in Leibniz's works (circa 1690); see C. I. Lewis, A survey of symbolic Logic, Berkeley, U. S. A., 1918, pp. 373-87; for a fuller account, see L. Couturat, La logique de Leibniz d'aprés des documents inbditSy Paris, 1901, Ch. VIII. Thus PI is Leibniz's Property 7 (p. 3^), P2 his Property 17 (p. 382), and P3 his Property 15 (p. 382). He is also the author of fundamental definitions and notations: - *Page n33* T*he definition of sums and products in terms of inclusion is due to C. S. Peirce [1, p. 33]*; see also E. Schroder [1, p. 197], Th. Skolem [1]. H. Whitney has suggested the names "cap'' and "cup" for the symbols ... - *Page n36* *This notation is due to C. S. Peirce [2]*. Birkhoff even cites a controversy concerning Peirce, who seems to have advanced on distributive lattices by being the victim of "severe influenza" if we are to believe the letter he sent to E. V. Huntington, which the latter reproduced. -* Page n150* I Historical note: *It is curious that C. S. Peirce [1]* should have thought that every lattice was distributive. He even said L6', L6" are "easily proved, but the proof is too tedious to give"! His error was demonstrated by Schroder [1, p. 282], who showed that L6', L6'' were not implied by L1-L4, but (p. 286) implied each other and L6. A. Korselt (Math. Ann. 44 (1894), 156-167) gave another demonstration. Peirce at first [2] gave way before these authorities, but later (cf. E. V. Huntington [1, pp. 300-301]) boldly defended his original view. Peirce is quoted again in connection with more complex structures, such as Lattice-Ordered Semigroups, -* Page n227* ** *See C. S. Peirce, Mem. Am. Acad. Arts. Sci. 9 (1870), 317-78*; E. Schroder [1, vol. Ill]; J. C. C. McKinsey, Jour. Symbolic Logic 6 (1940), 85-97; A. Tarski, ibid. 6 (1941), 73-89. The two Peirce articles mentioned are, of course, included in Birkhoff's bibliography. *- Page n290* C. S. Peirce, [1] On the algebra of Logic. Am. Jour. 3 (1880), 15-57; [2] On the algebra of Logic, ibid. 7 (1884), 180-202, It's clear, then, that by the 1870s-80s, Peirce had mastered the fundamentals of Lattice Theory. We may then ask why he failed to see that classes of signs with 3, 6, or 10 elements were organized in lattice structures. Nevertheless, the notion of affinity between triadic classes of signs and his evocation of the syntax of some of them are explicit expressions of this. The answer is not to be found in a possible limitation of his capacity as a mathematician to recognize in the universe of signs forms that were in his mind. The answer lies in the difficulty, if not the impossibility, of breaking out of the set-theoretic framework in which the most advanced mathematics of his time was embedded, a framework that Category Theory considerably expanded and formalized long after his death. I followed in Peirce's footsteps and made my way through Category Theory, a field with which I'm familiar, from 1977 and 1990 in French, and especially from 1982 in English. I quickly obtained the ten classes of triadic signs (naturally associated with the only ten possible functors between two elementary categories). The next step, the one that naturally enables us to understand the relationships between these classes, is that of the natural transformations of these functors, which define the immanent relationships that exist between these ten functors. The point of natural transformations is that they are transformations between functors (of the same source and target). The concept of natural transformation is specific to category theory. Categories can be seen as generalizations of structured sets and functors as generalizations of appropriate transformations for these
