Re: [PEIRCE-L] Scroll vs Nested Ovals (was Existential Graphs in 1911)
<<< text/html; name="untitled-[2]": Unrecognized >>> _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Scroll vs Nested Ovals (was Existential Graphs in 1911)
Jon AS, Thank you for emphasizing the fact that Peirce's only comments in favor of the scroll came before June 1911. In Peirce's writings after that date, the scroll is "equivalent" to a nest of two negations. In mathematics and logic, equivalence means freely interchangeable in all contexts without any change in meaning. Other people may choose to use a scroll for any purpose they please, but their choices have no effect on the logic or on anything Peirce wrote. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Scroll vs Nested Ovals (was Existential Graphs in 1911)
In R670, Peirce said that the scroll is equivalent to a nest of two negations. That means that any occurrence of one may be replaced by the other without causing any change in the meaning. In L231 and later MSS, he did not mention or draw a scroll. That doesn't mean you are forbidden to draw a scroll if you like it. But there is nothing more to say. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Inference as growth (was No subject
Edwina, Thanks for the URL of that article. I changed the subject line to the title of https://scholar.uwindsor.ca/cgi/viewcontent.cgi?article=1047&context=ossaarchive The full title is "Inference as growth: Peirces ecstatic logic of illation", and I want to emphasize that this article is talking about illation as a process, not as a particular sign for if-then, The Latin verb 'infero' is irregular. Its present participle 'inferens' is the source of the English word 'inference'. Its past participle 'illatus' is the source of the words 'illation' and 'illative'. When Peirce said that 'ergo' (therefore) is a sign of illation that signals the end of a process. Modern logicians use the term 'rule of inference' for what Peirce called 'permission'. The present participle suggests one step of a continuing process. The article makes some good points, but it should not be considered as an argument for the scroll as a logical primitive. Peirce's permissions (in every version of EGs from 1897 to the end) depend only insertions and deletions in negative or positive areas. A scroll is just one particular arrangement. As Peirce wrote in R670, a scroll is equivalent to a nest of two negations. In L231 and later, he raised his pen when he drew two ovals in order to avoid any suggestion that the scroll shape had any significance. There is, of course, more to say. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911
Robert, Thanks for finding that quotation: > Thought is a thread of melody running through the succession of our sensations (CP 5.395) Now that you mention it, I recall reading that some time ago. It must have been lurking somewhere in my mind, but well beneath the conscious level. In any case, it's very appropriate. The connection to sensations emphasizes the relation to Bill's term "embodied experience". It is also related to my point that the total context is more important than particular words. That doesn't mean that words are irrelevant, but they can be highly misleading when taken out of context. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911)
Bill, Your comment is very close to what I was trying to say. > I have been a musician for seventy years, and I was a serious mathematician until age twenty. (I graduated with a double degree.) I can assure you that I dont think only in terms of the patterns . . . In fact, in my most treasured musical experiencesand Id venture to say the same for mathematicsI barely think at all. Its an embodied understanding: I feel what I apprehendand only after the fact, with a great sense of loss, do I think about it. And when I do think I mostly struggle to find some faint simulacrum of my experience. Sometimes that might involve patterns; sometimes I might draw pictures or notes or words; sometimes I simply get up from the desk and pace, wave my arms, sing a little. (Except for the singing, the same definitely goes for mathematics.) The phrase "embodied experience" is excellent. Peirce, Einstein, Archimedes, Whitehead, and many others would agree. In fact, the way you describe your experience and the difficulty of putting it into words is very close to what Peirce said about his "left handed brain" (he was left handed). And he admitted that he had considerable difficulty in expressing himself in words -- that is one reason why he preferred diagrams. He also hoped to generalize his diagrams to "stereoscopic moving images" or even physical models. He would have loved to work with a virtual reality system. When I mentioned "structural patterns", I chose that term because I needed a noun phrase to insert in the sentence. Your description is very close to the way that most professional mathematicians describe their way of thinking. For examples, and references see the first ten slides in "Peirce, Polya, and Euclid: Integrating logic, heuristics, and geometry" http://jfsowa.com/talks/ppe.pdf . The reason why I used the analogy of math to music is that I wanted to emphasize the non-verbal way of thinking in those fields. Any description in words cannot capture the essence of what goes on when a mathematician or a musician is deep in the creative experience. I'm thinking of the musician who was asked what his composition meant. As an answer, he played it again. Fundamental principle: For mathematicians and musicians, words are not just secondary, they're almost irrelevant. To understand them, look at what they do, not at what they say. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911
Gary R, My remarks were ad rem, not ad hominem. Mathematics is like music. A mathematician or a musician thinks only in terms of the patterns, the operations on those patterns, and their relationship to whatever notation is used to represent them. The words used to describe those patterns are useful for communication among teachers, students, and critics. But those words are absent from the minds of the artists (musical or mathematical) who are imagining and creating novel patterns. Peirce was a great mathematical/logical artist. In June 1911, he had a new insight into the melodies of logic. Any logician can "hear" an exciting new melody in R670 and L231 that was not present in R669 or the Monist article of 1906. Peirce didn't have to write a "note to self" about the change. He just did it. And any logician can "hear" it. But I realize that many people can't feel or hear the difference. I plan to post the 1906 version and the 1911 version on my web site, and I'll point out exactly where the differences occur and their implications. I'll post that in the next two days. And I won't refer to any other person's comments or opinions on the subject. Meanwhile, I recommend the following slides and their quotations of mathematicians, logicians, and linguists about their subject: http://jfsowa.com/talks/ppe.pdf . The application of Peirce's EGs to Euclidean diagrams is easy with the 1911 EGs, but not with the earlier versions. That application is one of the strongest arguments in support of Peirce's claim that EGs represent "the action of the mind in thought." John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911
Auke, I agree with your observation, and the conclusion: "It is a line of thought I can see leading to what Jon wrote." Charles' father Benjamin Peirce gave him a thorough training in mathematics from early childhood, and Charles devoured Whateley's logic book in a week when he was 13. He insisted that metaphysics should be based on mathematics, not on Hegel-style verbiage. Jon's method of focusing on the words is a kind of literary criticism that would be more appropriate for analyzing Shakespeare than Peirce. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911
Auke> I was thinking in terms of goals, i.e. what is the object you try to understand, not credentials. I can connect Jon's answer to my question with his line of reasoning and I did like that. There might be differences in the goals and then it is always better to asses and value the differences, instead of fighting about who is right. I have been doing research and teaching in logic, computer science, computational linguistics, and artificial intelligence for many years. In 1976, I had published an article on Conceptual Graphs in the IBM Journal of Research and Development. Then in 1978, I came across Don Roberts' book on EGs, and it was exactly what I was looking for. Peirce's EGs were far more elegant and powerful than the AI research in the 1970s. (including my own). I immediatetly adopted it as the foundation for the book I published in 1984. I continued reading Peirce's other writings and various publications about Peirce since then. Then in 2001, I came across Michel Balat's transcription of a first draft of L231 (mistakenly classified as R514). I realized that it was an excellent introduction to EGs, and I posted a copy with commentary on my web site: http://jfsowa.com/peirce/ms514.htm . I also realized that this version was far superior to Peirce's earlier versions. In particular, I used it to solve a previously unsolved research problem from 1988. I published the solution in Semiotca in 2011: http://jfsowa.com/pubs/egtut.pdf . In April 2015, I presented a lecture on related issues at a Peirce Session at the APA conference in Vancouver. In December of 2015, I presented an extended version at a workshop that Zalamea sponsored in Bogota. And in 2018, I publishted a 76-page version that spelled out all the details. The following slides are minor revisions of the 2015 version: http://jfsowa.com/talks/ppe.pdf . Slide 2 has a link to the 2018 publication in the Journal of Applied Logics. The workshop in Bogota included leading experts in existential graphs. Nobody raised any objection or even any comment about my use of the 1911 version of EGs. For mathematicians and logicians, clarity and precision are essential. The formal structure is everything, and the words are of minor interest. The fewer, the better. As for Jon's comments about earlier versions, any quotations prior to June 1911 are irrelevant. But I found Jon's comments useful for pointing out issues that I decided to restate more clearly. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911
Auke> Since perspective is important, it might be a good idea to explicate the differences in purpose each of you entertain. That's a good question. I have been working on research and teaching in logic, computer science, artificial intelligence and related areas for many years. In the 1970s, I _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Scroll vs Nested Ovals (was Existential Graphs in 1911)
Jon, List, A few more points: 1. The quotations you cited are from a time when Peirce still thought that a sign of illation was important for deduction. Note that in R670, he says that the EGs have just three syntactic features: a line of identity, a spot for a rheme and a shaded area for negation. The scroll is "equivalent" to a nest of two negations. It is not a primitive feature. In L231 and the later MSS, he did not draw a scroll or use the word. 2. When I wrote (in slide 10) that an inference was required for negation, I meant a "process of inference", not a "special sign for inference". But I admit that I should have been more precise: A negation results from an observation of a difference or distinction between two perceptions or two aspects of a single perception. That observation may be expressed in the form "A is not B". That process is far more primitive than an application of modus ponens. 3. In R270, the word he actually used to compare a scroll to a nest of two negations is "equivalent". Equivalence implies that one can be substituted for the other in any context. Since I wasn't looking at the MS at the moment, I said that a scroll is "nothing but" a nest of two negations. Equivalence implies that point. It also implies that a nest of two negations is "nothing but" a scroll. In any case, he did not draw a scroll or mention the word in L231 or the later MSS. 4. The word 'analytical' means "pertaining to analysis". It's not at all obvious what the phrase "more analytical" would mean. Although Peirce stated his "permissions" in different ways over the years, every proof from 1897 to the end took exactly the same number of steps. 5. Notice the proof of the Praeclarum Theorema in egintro.pdf. That proof took exactly 7 steps from a blank to the conclusion. In the Principia Mathematica, Whitehead & Russell took 43 steps, starting from 5 non-obvious axioms. That length does not make their method "more analytical" . More appropriate adjectives would be inefficient, inelegant, awkward, clumsy, not recommended... (And by the way, one of the 5 axioms in the 1910 edition was redundant, But nobody noticed that fact until 1926. 6. The most efficient proof procedures used today, do not depend on a special sign of illation or the rule of modus ponens. In dumping the scroll, Peirce was, as usual, ahead of his time. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911
Jon AS, List, The *opinion* that the EG version of June 1911 is Peirce's best is Peirce's own, as he stated in December, after six months of further consideration. The fact that he stated it in a lengthy letter to a member of Lady Welby's significs group is further evidence of its importance. That opinion is further supported by the development of logic in the following century. Please read beyond slide 12 of http://jfsowa.com/talks/egintro.pdf . See also http://jfsowa.com/talks/ppe.pdf . Slide 2 of ppe.pdf has a link to a 76-page article published in the Journal of Applied Logics that goes into all the details. One of the most important features of the 1911 version is its ability to serve as a foundation for Gerhard Gentzen's two systems of natural deduction and clause form (published in 1934). Those two system have had immense influence on modern proof procedures -- including the development of modern methods of computational theorem proving. But in 1988, Larry Wos, one of the pioneers in theorem proving methods, published an unsolved problem about relating Gentzen's two systems. This problem is important for automatically relating two different proof procedures. In 2011, I published the solution in Semiotica. For a quick outline, see egintro.pdf or ppe.pdf. For the details, see the article in the J. of Applied Logics. That proof is clean and clear in terms of the 1911 EGs. It's possible in terms of the earlier versions, but it is more complex and harder to discover. Another important point: The 1911 EGs can be generalized beyond two dimensions for "stereoscopic moving images". It's not an accident that Peirce mentioned them in L231, but he had not yet decided how to proceed with the details. ppe.pdf (and the JAL article) present a generalization. Whether that is what Peirce was thinking is not clear, but it shows that the 1911 EGs are sufficient to support something along the lines that Peirce was contemplating. As for the point that negation must be inferred, please reread slides 11 and 12 of egintro.pdf. Note that observing if-then is impossible (for a lengthy discussion, see Hume and the lengthy debates that followed). But the inference required for negation is quite simple: If you expect something and don't observe it, you can use the word 'not'. Children learn to use the word 'not' sometime after their second birthday -- around the same time that they learn to use the words 'I' and 'you' correctly. But they don't learn to use 'if-then' and 'or' until much later. And the idea that children (or even adults) would learn 'not' from the derivation that Peirce presented in 1906 or the one in R669 is absurd. There is much more to say about all these issues, but please read at least to the end of egintro.pdf. It also has many references for further study. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911
Jon, List, Again, you have not cited any statements by Peirce after June 1911. Therefore, nothing in your note contradicts the evidence that the 1911 version of EGs is Peirce's best and last available version. Furthermore, Peirce's letters of Sept. and Dec. 1911 explicitly reject the version of 1906 on which R669 is based. That does not mean that every statement he wrote about EGs prior to 1911 is obsolete, but it means that everything he wrote prior to June 1911 must be evaluated in terms of his 1911 version. Finally, an enormous amount of research on, with, and about logic has been done during the century following Peirce. The claim that a "sign of illation" is important or even useful for inference is false. The most efficient theorem proving methods today do *not* depend on a sign for if-then. I suggested slides 11 and 12 of http://jfsowa.com/talks/egintro.pdf in my previous note. For further evidence why a sign for if-then can be an *impediment* to inference, please read the slides about Gentzen's method of natural deduction and Peirce's *improvement* on it. For more detail, see the various references, especially http://jfsowa.com/talks/ppe.pdf . By demoting the scroll to *nothing but* a nest of two negations, Peirce's methods are a major simplification and clarification of Gentzen's system. Also note that Frege's proof procedure, which is the basis for the Principia by Whitehead and Russell, puts the sign for if-then at the center. But that results in a horribly complex proof procedure: 43 steps to prove a theorem that takes 7 steps by Peirce's rules (which depend only on negations). There is much more to say about all these issues. But the main point is very clear: In June 1911, Peirce realized that all inferences depend on inserting or erasing graphs or parts of a graph in positive or negative areas. That's is the foundation for defining an open-ended variety of derived rules of inference -- modus ponens is just one of many. Aristotle's syllogisms are others. So are Gentzen's methods and many versions used in computer systems. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911
Jon AS, All your citations are prior to R670, which demotes the scroll to nothing but a way of drawing two ovals (negations) without raising the pen. In R670, Peirce states the three primitives: existence, conjunction, and negation. And in L231, he drops the adjective 'illative' in front of the three permissions (rules of inference). All three of them are stated in terms of negations, and none of them mention or depend on the scroll in any way. Furthermore, the meaning of any general is determined by its implications for the future. Please read the slides that introduce EGs to beginners (and advanced students who learned the algebraic notations for logic): http://jfsowa.com/talks/egintro.pdf . The first ten slides are a basic intro. But slides 11 and 12 state why the scroll (or any other symbol for if-then) is not a primitive or necessary for deduction. The remaining slides show how Peirce's 1911 EGs are a major *improvement* on the mainstream logics of the 20th century and why they are an important foundation for the future. As Peirce said explicitly in Sept. and Dec. 1911, the 1906 version was as bad as it could be. Unless you can find any quotation after June 1911 where he uses the words 'illation' or 'illative' or deviates from his 1911 EGs, I consider the case to be closed. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911
Jon AS, List, For anyone who is not familiar with Peirce's 1911 EGs, see my introduction to EGs, which is based on the 1911 version. The first 10 slides are sufficient for an overview. The remaining slides show features of the 1911 EGs that make a major advance over the logics of the 20th century: http://jfsowa.com/talks/egintro.pdf The following comment shows why Peirce rejected R669 and replaced it with R670 and L231: JAS> Peirce had a very good reason for not writing a third rule at the end of R 669, and it was not because "he suddenly realized" something at that moment in time and "abruptly" abandoned his previous train of thought. It was simply because he had already stated the third rule a few paragraphs earlier, and had explicitly pointed out that it is not an illative permission; i.e., it is not a rule of inference. After reading that comment, I realized that Peirce's insight on 2 June 1911 was that the adjective 'illative' is irrelevant and misleading for all three permissions (rules of inference). The rules depend only on negation. They do not depend on a "sign of illation", such as a scroll or other symbol for if-then. In L231, Peirce called all three rules permissions (without the adjective 'illative'). I believe that R669 is the *last* MS in which he wrote the words 'illative' or 'illation'. I have not read all his extant MSS, but I very strongly doubt that he would continue using a word he had rejected. See slides 11 and 12 of egintro.pdf for an explanation in terms of the 20th c logics. For the details about Peirce's five MSS that document his development of the 1911 EGs and his rejection R669, see the attached file eg1911x,pdf.JAS> The final sentences [of R669] note the inadequacy of automated reasoning to apply "the two illative permissions," since they require "a living intelligence" (R 669:23-24[21-22], LoF 1:584). No. Modern theorem provers can use Peirce's rules (and other rules derived from them) quite efficiently. For an overview of the issues, see the slides in http://jfsowa.com/talks/ppe.pdf . For more detail, slide2 of ppe.pdf has a link to a 76-page article in the Journal of Applied Logics, JAS> Unlike "Prolegomena" (CP 4.569), none of these manuscripts includes a "4th Permission" expressing "the strange rule" that Peirce deemed to be inconsistent with "the reality of some possibilities" as affirmed by his pragmatism (CP 4.580-581, 1906), such that he was ultimately "sceptical as to the universal validity of" it (RL 477:33[13], 1913). That gets into his modal logic, which he intended to replace with Delta graphs. Any comment about modal issues in 1913 should be evaluated in terms of the Delta graphs, for which we don't have any MSS. JAS> deriving negation from... a scroll with a blackened inner close... is more analytical because it preserves the fundamental asymmetry of reasoning and can thus be easily adapted for intuitionistic/triadic logic without excluded middle, which "is universally true" (R 339:515[344r]). No. In R670, negation is a primitive. The scroll is nothing but a way of drawing a nest of two negations without raising the pen. Since negation is a primitive in R670, it would be absurd to derive negation from a nest of two negations plus a pseudograph. In structure, motivation, and applications, intuitionistic and 3-valued logic are totally different from each other and from any version of Peirce's EGs. Oostra's choice of the scroll as a marker for intuitionistic rules has no similarity to Peirce's use for any version of EGs. There is much more to say about these issues, and I'll write another note about them. John eg1911x.pdf Description: Adobe PDF document _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Sign Relations, Triadic Relations, Relation Theory
Azamat, People observe the intension/extension distinction without learning the name for the distinction. AA>It implies that operational meanings or definitions could be more significant than an intension/extension or representation/reference or connotation/denotation dichotomy. Languages developed thousands (millions?) of years before writing, and writing was used for a few thousand years before anybody started to write definitions in any kind of language or logic. For that matter, every infant learns language from use, not from definitions. But whatever meaning is learned may begin as extensional (particular names for individual persons or things) but children very quickly generalize them to kinds of individuals. The intensional meanings are generalizations learned from patterns of usage. Summary: Intensional meanings are essential for generality. People use the intensional meanings in the same way that they speak prose without knowing the word for what they do. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: Aw: Re: [PEIRCE-L] Sign Relations, Triadic Relations, Relation Theory
Helmut, In every version of language and logic -- ancient or modern, informal or formal -- the intensional definition is fundamental. It corresponds to the definition you'll find in a typical dictionary of any natural language or in any formal specification in science, engineering, business, or the arts. The extensional definition is determined by using the intensional definition to check for instances. If you have the intensional definition, you have all the information necessary to do anything you wish. But if you only have the set of instances (extension), you have insufficient information to determine the intended meaning. For example, if you find a set of people, you have no idea what intensional criteria were used to select them: Human beings? Featherless bipeds? Visitors from Los Angeles? Visitors from Australia? Students on a spring break? Musicians taking a lunch break between rehearsals?John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: Aw: [PEIRCE-L] Sign Relations, Triadic Relations, Relation Theory
Helmut, The distinction between intesion and extension is important for every version of logic since antiquity. The oldest example is "rational animal" vs. "featherless biped" -- those are two terms with different intensions, but the same extension. Diogenes the Cynic plucked a chicken and threw it into Plato's Academy while shouting "Here is Plato's man." Alonzo Church, who wrote that excerpt I cited, had been the editor of the Journal of Symbolic Logic for many years. It's just as important for the latest work in computer science for both theory and applications. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
RE: [PEIRCE-L] Sign Relations, Triadic Relations, Relation Theory
Terry, I completely agree with what you wrote (copy below). But I emphasized database relations because they are the most commonly used examples of relations that are defined by extension. However, the meaning of the data is specified by the rules or axioms that state the intensions. Those specifications are what we have been calling ontology. John --The intension / extension distinction is also crucial in the epistemology of science, insofar as the aim, goal, objective, etc. of genuinely rational scientific inquiry is to identify and express causal laws. For those laws arent merely descriptive of what actually has or is occurring in a context of precipitating conditions (as observed), but also in a cosmically nomic sense prescriptive of what would happen (under those conditions) if those conditions were met whether they actually are ever fulfilled or not. Reference class membership criteria are intensional, for instance, while the actual membership inclusion under those criteria is extensional. That intensionality of scientific language is essential for expressing the subjunctive and counterfactual nature of causation, especially for purposes not only of description (which only requires the use of extensional language), but for explanation, prediction, and corroboration as aspects of truly rational scientific methodology in general. These considerations are fairly well-covered in philosophy of science, of course, and one source I recommend is Jim Fetzers 1981 Scientific Knowledge. Im sure Susan Haack has also done important work on this, though Im at a loss for the moment as to which of her works is best to cite here. Ill look into it and report back . _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Sign Relations, Triadic Relations, Relation Theory
Jon A, It's important to distinguish the intension and the extension of a function or relation. The *intension* is its definition by a rule or set of axioms. The *extension* is the set of instances in some domain or universe of discourse: JA> We can now define a relation L as a subset of a cartesian product. That is a purely extensional definition. If we're talking about a database, for example, the extension may be constantly changing, but the intension may be the same for all the variations in extension For the distinction between extensions and intensions, see the discussion by Alonzo Church: http://jfsowa.com/logic/alonzo.htm . John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
RE: [PEIRCE-L] multiple-valued logic
Dear Jacob, Let me express my condolences on your loss. We'll miss your father's contributions to this list and to the study of Peirce's writings and their relationship to linguistics. When I read your note, I checked your father's list of publications at https://umich.academia.edu/CharlesPyle His articles emphasize issues about "wild language" that many linguists "sweep under the rug" because they don't fits their elegant systems of logic. Although I have been working on logic for years, I appreciate the importance of those wild issues. They are the source of the thorny examples and counterexamples that any truly adequate theory of linguistics must address. I am sorry that we will no longer have a chance to discuss those issues with him. John Sowa _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Intuitionistic logic
Ben, I agree with your analysis, and I'd like to add a comment about modal logic. Consider the sentence "It might rain tomorrow, and it might not." That sentence cannot be falsified because neither side makes a firm promise. But if you replace 'might' with 'will', the following statement is guaranteed to be false: "It will rain tomorrow, and it won't." Since the two sides make firm but contrary commitments, one or the other must be false. Those are examples of ordinary language, which is rarely so precise that it rules out anything in the middle. Modal logic is precise, but possibilities allow options that don't violate either case. In effect, ordinary language is often sufficiently vague that sentences have a modal effect -- a high probability, but not certainty. Brouwer was a mathematician, and he understood what it means to be precise. But he was concerned about extreme cases, especially about infinite sets and structures, where warnings, such as "Here be dragons", can't be ruled out. That is why he insisted on constructive proofs, rather than proofs by contradiction. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Asymmetry of Logic and Time
Jon, List, I have a high regard for the work that Ahti and Francesco have been doing, and I read the article you cited (copy of the reference below). They have been doing meticulous scholarship on the development of Peirce's EGs up to 1911. But unfortunately, they overlooked the implications of those five MSS from 1911. While Peirce was writing the three EG rules of inference around 8 pm on 2 June 1911, he suddenly realized that the rules depend *only* on whether an area is positive or negative. There is nothing special about a scroll. To see the difference, do a detailed comparison of R669 and R670. After June 2, everything depends on whether an area is shaded or unshaded. In R670, the primitives are existence, conjunction, and negation, The scroll is just a convenient way to draw two ovals without raising the pen. There is much more to say, but I'm short on time. John --- JAS> I have been thinking about writing an article on this topic myself, but it turns out that Bellucci and Pietarinen already covered a lot of the relevant ground in a 2016 paper (https://www.researchgate.net/publication/275038453_Existential_Graphs_as_an_Instrument_of_Logical_Analysis_Part_1_Alpha). Here are a few especially pertinent excerpts, which are entirely consistent with what I have been advocating all along. _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Representing Abduction in the EG
JBD> Many systems of logic do not have the power to express premisses or conclusions that articulate questions or lines of investigation. General principle for any version of logic: Restate the questions as declarative sentences in English that are to be proved or disproved. For example, Euclid stated his propositions as imperative sentences about drawing particular kinds of structures. Those sentences can be rewritten as declarative sentences that say there exists a structure with certain properties. For some discussion of that issue, see the slides I presented at a Peirce session of an APA conference in 2015: http://jfsowa.com/talks/ppe.pdf . At the bottom of slide #2 is the URL of an article in the Journal of Applied Logics that goes into much more formal detail. JBD> What is more, they don't have the ability to express a conclusion of an abuctive argument as being plausible. That requires Gamma graphs for representing metalanguage about the logic. RLT has an example of a Gamma graph for "That you are a good girl is much to be wished." Peirce has some examples of metalanguage, but he didn't develop it in detail. I discuss some of those issues in a talk I presented at the European Semantic Web Conference. For the slides, see http://jfsowa.com/talks/eswc.pdf . JBD> I am particularly interested in the question of what the "toothbrush" icon represents and how that logical notion might be better expressed in later version of the EG. First step: State what you think it represents in English. Then see whether you can translate that to some version of logic. You might find some of the examples in eswc.pdf helpful John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Representing Abduction in the EG
Jeff, All versions of logic, by Peirce and by any logicians before or after Peirce, represent propositions. Induction, abduction, and deduction are operations that relate propositions to one another in various ways. Those operations can be performed in equivaent ways with any notation for logic -- or even with propositions stated in English or any other language. JBD> It is an interesting question: how might one represent abductive inferences in the EG? Short answer: Peirce stated rules of inference for deduction with EGs. He also wrote a great deal about induction and abduction with examples stated in English. To adapt those examples to EGs, translate the English to EGs and then perform the equivalent operations on the EGs. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Other subdivisions of signs
Robert and Edwina, I agree with both of you that the lattice is more than a taxonomy. It shows the direction of the development of the categories. It is active, not passive. And I also believe that Peirce's 1903 classification of the sciences is much more than a taxonomy. The most important aspect of that classification is the way that all the sciences inherit their reasoning methods from mathematics and their data from phaneroscopy. That is another example of an active system, not a passive classification. Unfortunately, most discussions emphasize the classification and minimize or even ignore the fundamental dependencies that determine the classificationJohn _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Peirce's Medieval Logic Sources?
Jon A> the question of Peirce's sources on Medieval and Scholastic Logic, especially with regard to 1st and 2nd and maybe 3rd intentions. Peirce's source for that distinction is Ockham's Summa totius logicae. His most important application is in the 1885 Algebra of Logic. He adopted the term 'first intentional logic' for quantified variables (later lines of identity) that refer to things in the subject matter. He then used the term 'second intentional logic' for variables or lines that refer to relations. Ernst Schroeder translated those two terms to 'erste Ordnung' and 'zweite Ordnung'. Then Bertrand Russell translated the German back to English as 'first order' and 'second order'. It would be possible to have infinitely many N-th order logics, which would refer to relations in (N-1)st logic. But the general term for anything more than FOL is 'higher-order logic'. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Re: [ontolog-forum] Problems In Philosophy
David and Jon, C. S. Peirce made a very clear and sharp distinction between formal or mathematical logic and logic as semiotic. Peirce's algebra of logic (1885) is the foundation for Peano's version of logic and the predicate calculus of Whitehead and Russell. The term Peano-Russell notation is a misnomer, since Russell didn't add anything to the notation Peano adopted from Peirce. For a historical summary, see the article by Hilary Putnam: http:///jfsowa.com/peirce/putnam.htm . By formal logic or mathematical logic, Peirce included everything that modern logicians call formal logic. That also includes Peirce's existential graphs. But Peirce included much more in what he called logic as semiotic. Peirce's broad use of the term logic is close to the traditional textbooks called 'Logic' in the 19th century. Those books did include a huge amount semiotic along the lines of Aristotle and the medieval Scholastics. De Morgan introduced the term 'formal logic' for the algebraic tradition started by Boole and developed by the 19th century pioneers. That logic did *not* include the semiotic inherited from Aristotle. Short summary: When Peirce uses the word 'logic' by itself, it's important to check the context to see whather he's talking about formal logic or logic as semiotic. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] The lattice of five paths
Robert, I thought that the following paragraph in your article was especially informative: >From the "Five paths" article": We now have a semiotic tool of greater scope than the lattice itself, since it does not only classify signs, but also "streams of signs", that is, interpretative habits that have been inscribed in these paths and, as a result, have become communal semiotic characteristics. The lattices of the five paths (Table 5) therefore also classify the social histories of the modes of interpretation of signs The words 'communal' and 'social' remind me of Peirce's discussion of the "collateral experience" that the reader, viewer or listener uses to interpret signs. Following is the definition from the Commens Dictionary: 1908 [c.] | Letters to Lady Welby | MS [R] L463:14: "A Sign may bring before the Mind, a new hypothesis, or a sentiment, a quality, a respect, a degree, a thing, an event, a law, etc. But it never can convey anything to a person who has not had a direct experience or at least original self-experience of the same object, collateral experience." Depending on their collateral experience, the person who interprets a sign may ffine a degenerate interpretation or an accretive interpretation. The five paths show the possible kinds of differences -- degenerate or accretive. Although there are just five kinds of paths, each kind may have very different accretions or deletions, depending on the collateral experience of the person who interprets the sign. In my case, I had collateral experience that suggested some rather distracting thoughts while I was reading your article. The words 'nicotine', 'stream', and 'French' reminded me of a class in fluid mechanics that I attended many years ago. The professor recommended Gaulois Cigarettes -- not for smoking, but for wind-tunnel experiments. The Gaulois smoke is so thick that it doesn't dissipate in a wind tunnel. It shows very clear streams in the flow. Locke and others talked about "association of ideas". Peirce said that those ideas roughly correspond to his "experiences in the phaneron". There is an enormous range of possible variations among different interpreters, John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Experimental phaneroscopy
Today, the TV program "60 Minutes" reran an interview with the neuroscientist Marcel Just at Carnegie-Mellon University. Title: "Scientists are using MRI scans to reveal the physical makeup of our thoughts and feelings" Abstract "Ten years ago, 60 Minutes met a team of scientists at Carnegie Mellon University who had begun to decode simple thoughts inside the brain. Now they've moved on to identifying complex thoughts from spirituality to suicide." URL: https://www.cbsnews.com/news/functional-magnetic-resonance-imaging-computer-analysis-read-thoughts-60-minutes-2019-11-24/ In effect, scientists are now doing something many philosophers had thought was impossible: make phenomenology (or as Peirce called it, phaneroscopy) an experimental science. In 2004, André De Tienne wrote "Peirce thought that, after mathematics, the most fundamental of all sciences was phenomenology, or phaneroscopy as he dubbed it to escape from Hegel... The fact that it hasnt become a major field of research raises the question of whether there is any actual need for it, whatever it is, and of whether it has any future, assuming it ever had a past. This paper attempts to address some of these questions candidly. It tries to determine what it is that Peirce held phaneroscopy to be, what type of discourse it is bound to produce, and whether its activity can be said to be scientific by Peirces own standards. It examines its place between mathematics and the normative sciences, especially semiotics, and takes stock of both the type and the method of analysis Peirce associated with it." See http://www.iupui.edu/~arisbe/menu/library/aboutcsp/detienne/isphanscience.pdf Peirce used existential graphs as a tool for doing phaneroscopy: "The Phaneron being itself far too elusive for direct observation, there can be no better method of studying it than through the Diagram of it which the System of Existential Graphs put at our disposition." (MS 293, NEM 4:320, 1906) "Let us call all that ever could be present to the mind in any way or any sense, when taken collectively, the Phaneron. Then every thought is a Constituent of the Phaneron, and much besides that would not ordinarily be called a Thought. And therefore there can be no better instrument for thinking about Constituents of the Phaneron -- which is itself too evanescent for definite comprehension -- than to think about Existential Graphs... The greatest lesson of the Logic of Relatives and of that which is merely its expression, Existential Graphs, is that the Simple Concepts, Indecomposable or Constituent or Elements of the Phaneron do not, as the old Logic taught, differ from one other only in their matter, but also in their form." (MS 499, 1906) I presented some slides that discuss work by Marcel Just and colleagues and its relationship to Peirce's logic and semiotic. See Section 6, slides 34 to 53, of http://jfsowa.com/talks/eswc.pdf . The footnote to slide 40 has the URL of a paper by Mason & Just (2015). Summary: This is one of many examples where Peirce's insights in logic, semiotic, and diagrammatic reasoning are at the forefront of the latest research in science, engineering, and computer applications. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)
Auke, I apologize for my previous note. I accidentally hit SEND before I wrote anything. JFS> Formal EGs are the foundation. As Peirce himself said, logic as semiotic is much broader. It includes the methodeutic for analyzing and developing the immense variety of the empirical sciences. AvB> We have discussed this point before. It seems to me that you forget about speculative grammar and only recognize critic and speculative rhetoric... When I wrote "logic as semiotic", I implied all three branches. Then I emphasized methodeutic because I cited some slides and articles that discussed methods for using EGs in applications to various subjects. Among other things, those applications showed how the eg1911 version enabled a rather simple solution to an unsolved research problem from 1988. For over 20 years, some very good logicians were unable to find a solution by using the algebraic notations for first-order logic. But the symmetric rules of inference (permissions) of eg1911 indicated a direct path to the solution. See slides 65 ff of http://jfsowa.com/talks/ppe.pdf . After that solution was found, it could be translated to any other notation for FOL, including any algebraic version. Moral of the story: The iconic structure of EGs and their rules of inference do not increase the expressive power of FOL. But they enable people to "see" or "imagine" reasoning steps that may be obscured by the algebraic notation. In this case, the scroll would be "anti-iconic" because it is asymmetric, and the proof depends on the symmetry of the rules of inference. In any case, the original topic of this thread was very narrow: Peirce's EGs of 1911 and their relationship to his earlier EGs. For other issues, it's better to start a new thread. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)
> John, > > >> Op 30 augustus 2020 om 20:55 schreef "John F. Sowa" : >> >> >> Auke, I agree with you about the issues and priorities. >> >> AvB> Peirce is multi facetted. Each of us looks from a particular >> angle... I am not interested in what might be the final version >> Peirce wrote on the negation vs scroll issue... I can agree with >> you if we are discussing EG as a formal system. >> >> Yes. Formal EGs are the foundation. As Peirce himself said, logic >> as semiotic is much broader. It includes the methodeutic for >> analyzing and developing the immense variey empirical sciences. >> > > We have discussed this point before. It seems to me that you forget about > speculative grammar and only recognize critic and speculative rethoric. > But if we abstract from the apprehension of the sign as an object when we > look with the detached eye of the logician (the realm of critic), we must > take care when going to speculative rethoric to again direct our attention > to the role the apprehension of the sign as an object plays in our > processes of interpretation. We must acknowledge that each interpreter has > its own verso sheet. And, that this sheet determines as what sign a > representamen gets interpreted. > > Auke > > > > >> >> AvB> In a sense when we interpret we look at the input from all >> logical perspectives. Box-X running from to , or from >> doubt to belief. >> >> Yes. All versions of classical first-order logic are sufficiently >> expressive to define all the patterns of mathematics. But the >> eg1911 version (as stated in L231) has a simplicity and symmetry >> that makes the definitions easier to state and the proofs easier to >> discover. >> >> For examples, see the slides I presented at an APA conference in >> 2015 and extended with more examples for another workshop: "Peirce, >> Polya, and Euclid: Integrating logic, heuristics, and geometry," >> http://jfsowa.com/talks/ppe.pdf . >> >> Note that the two-dimensional shaded areas of eg1911 can be >> generalized to 3-D shaded regions for proofs in solid geometry. >> They could even be generalized to 4-D regions for "stereoscopic >> moving images", which Peirce mentioned in L231. Those >> generalizations are not possible with the 1903 scrolls or the 1906 >> recto/verso sides of a 2-D sheet. >> >> Another important example is an unsolved research problem that was >> stated in 1988 and remained unsolved until 2010. Good logicians >> failed to find the proof because they made the same mistake that >> Peirce stated in 1893 (CP 4.76): "For [the reader] cannot reason at >> all without a monstrative sign of illation." See the proof with EG >> rules in slide 65 ff of ppe.pdf. >> >> Examples of signs of illation (or inference) include Peirce's claw >> symbol for if-then in Boolean algebra or his scroll in EGs. Those >> symbols are asymmetric, but the critical step for solving the >> problem of >> 1988 is easier to discover with the symmetric EG "permissions". >> >> As for the time and date when Peirce discovered the simplicity and >> generality of the eg1911 rules, compare R669, which ends abruptly >> shortly after 7:40 pm on 2 June 1911, to the completely rewritten >> R670, >> which begins on June 7. On June 22, he began L231, which contains a >> complete and polished version of the logic in R670. >> >> The date of the discovery is interesting for Peirce scholars. But >> the >> power and generality of eg1911 is demonstrated by the applications. >> For >> more examples, see "Diagrammatic reasoning with EGs and EGIF", >> http://jfsowa.com/pubs/diagrams.pdf ; "Reasoning with diagrams and >> images", >> http://www.collegepublications.co.uk/downloads/ifcolog00025.pdf >> >> John >> >> _ _ _ _ _ _ _ _ _ _ >> ⺠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 . >> ⺠To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to >> l...@list.iupui.edu with no subject, and with the sole line >> "UNSubscribe PEIRCE-L" in the BODY of the message. More at >> http://www.cspeirce.com/peirce-l/peirce-l.htm . >> ⺠PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary >> Richmond; and co-managed by him and Ben Udell. >> > _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)
Auke, I agree with you about the issues and priorities. AvB> Peirce is multi facetted. Each of us looks from a particular angle... I am not interested in what might be the final version Peirce wrote on the negation vs scroll issue... I can agree with you if we are discussing EG as a formal system. Yes. Formal EGs are the foundation. As Peirce himself said, logic as semiotic is much broader. It includes the methodeutic for analyzing and developing the immense variey empirical sciences. AvB> In a sense when we interpret we look at the input from all logical perspectives. Box-X running from to , or from doubt to belief. Yes. All versions of classical first-order logic are sufficiently expressive to define all the patterns of mathematics. But the eg1911 version (as stated in L231) has a simplicity and symmetry that makes the definitions easier to state and the proofs easier to discover. For examples, see the slides I presented at an APA conference in 2015 and extended with more examples for another workshop: "Peirce, Polya, and Euclid: Integrating logic, heuristics, and geometry," http://jfsowa.com/talks/ppe.pdf . Note that the two-dimensional shaded areas of eg1911 can be generalized to 3-D shaded regions for proofs in solid geometry. They could even be generalized to 4-D regions for "stereoscopic moving images", which Peirce mentioned in L231. Those generalizations are not possible with the 1903 scrolls or the 1906 recto/verso sides of a 2-D sheet. Another important example is an unsolved research problem that was stated in 1988 and remained unsolved until 2010. Good logicians failed to find the proof because they made the same mistake that Peirce stated in 1893 (CP 4.76): "For [the reader] cannot reason at all without a monstrative sign of illation." See the proof with EG rules in slide 65 ff of ppe.pdf. Examples of signs of illation (or inference) include Peirce's claw symbol for if-then in Boolean algebra or his scroll in EGs. Those symbols are asymmetric, but the critical step for solving the problem of 1988 is easier to discover with the symmetric EG "permissions". As for the time and date when Peirce discovered the simplicity and generality of the eg1911 rules, compare R669, which ends abruptly shortly after 7:40 pm on 2 June 1911, to the completely rewritten R670, which begins on June 7. On June 22, he began L231, which contains a complete and polished version of the logic in R670. The date of the discovery is interesting for Peirce scholars. But the power and generality of eg1911 is demonstrated by the applications. For more examples, see "Diagrammatic reasoning with EGs and EGIF", http://jfsowa.com/pubs/diagrams.pdf ; "Reasoning with diagrams and images", http://www.collegepublications.co.uk/downloads/ifcolog00025.pdf John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Peirce's discovery of 2 June 1911 (was Philosophy of EGs
Auke, On that point, there is no disagreement whatsoever: AvB> The decision of what is obsolete or not must be based on a reality check and the context of his thought and experiences. Not on what is written last. On 2 June 1911, Peirce used a reality check to recognize that his presentation of EGs in 1906 was based on a mistake. On June 7, he began the development of a cleaner and more elegant version of EGs, which he presented in L231 (June 22). See http://jfsowa.com/peirce/eg1911.pdf . By every reality check with the development of logic in the 20th and 21st c, the version of eg1911.pdf has stood the test of time. But the version of 1906 received terrible reviews by Quine, Martin Gardner, and many others -- including Peirce himself, who called it "as bad as it could be" (L376, December 1911). The primary criterion for EGs is not "what was written last", but what Peirce himself wrote about his earlier versions of EGs. R670 (June 7), which led to L231 (June 22), is Peirce's own reality check on the version of 1906 (and R669, which he began to write as a rehash of the version of 1906). John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Peirce's discovery of 2 June 1911 (was Philosophy of EGs
Jon AS, List This thread began with my note of August 2nd, which I include below in the file 2aug20.txt. All the points in that note are based on the citations included in it. But I changed the subject line of this note to emphasize Peirce's fundamental insight of 2 June 1911 shortly after 7:40 pm. That was when Peirce finished writing two of his three "Illative Permissions" in R669. He then wrote a short paragraph with a few lines at the top of a new page. And he stopped. He did not write the third permission (about double negations), he left most of the sheet blank, and he never resumed R669. Three questions: Why did he stop when he had enough paper to write the third permission? Why did he begin a completely new version of EGs in R670 with different notation and terminology? And what did he do in the time between June 2 and June 7? My guess: He reviewed his earlier writings on EGs, especially the ones from 1903 and 1906. The content of R670 and L231 shows what he rejected. His comments in L378 and L376 show that he considered the presentation in 1906 "as bad as it could be". But his comments in R670 show that he considered some combination of shading with tinctured areas as possible. That would be an option for Delta graphs, as I mentioned in an earlier note. JAS> understanding the entire system of EGs requires familiarity with all his different writings about them. Familiarity does not imply agreement. The writings prior to June 1911 have some useful insights mixed with some obsolete material. It's necessary to evaluate them in terms of L231. JFS> There is no need to derive negation from anything else. JAS> Peirce repeatedly says otherwise, as I have repeatedly demonstrated.. All those quotations are prior to June 1911. They're irrelevant and obsolete. JAS> In R 669 (May 1911), he notes--just three weeks before composing RL 231--that necessary reasoning is possible without the concept of falsity No, for several reasons: (1) That is not an exact quotation, since Peirce knew that affirmation and negation are fundamental to every version of logic from Aristotle onward. (2) Peirce had forgotten his 1884 point that all reasoning can be done with just insertions and deletions (W 5:107). And Peirce's discovery of 2 June 1911 makes the earlier quotations irrelevant. JAS> This (R 466:18-19, 1903) comes from one of Peirce's notebooks for the Lowell Lectures, which in RL 376 (December 1911) he calls "the better exposition" of EGs than "Prolegomena to an Apology for Pragmaticism" (1906). The three primitives are thus consequence (scroll), coexistence (blank), and identity (line) Although Peirce said that the version of 1903 was better than the version of 1906, it still has obsolete passages, such as the comments about the scroll. In R670, he writes "There are but three peculiar signs that the Syntax of Existential Graphs absolutely requires." The first is the line of identity. The, the second is the spot, which may be a medad or it may have one or more pegs. "The third is one that shall deny a Graph instance, or scribed assertion." With that explanation and further confirmation in L231, every previous comment about scrolls is obsolete and irrelevant. At this point, I rest my case. I stand by the attached 2aug20.txt and the additional comments above. Any relevant evidence to the contrary would have to come from documents later than June 1911. John To: ahti-veikko.pietari...@ttu.ee, francesco.belluc...@unibo.it, jonalanschm...@gmail.com> `` cc: "De Waal, Cornelis" , Martin Irvine Dear Ahti, Francesco, and Jon, I have long maintained that Peirce's best and final version of the syntax, semantics (endoporeutic), rules of inference, and terminology for EGs is in L231 and NEM 3.162-169. But Jon quoted some comments by Ahti that seem to contradict that claim. Instead of debating them on Peirce-L, I'd like to discuss the issues with this smaller group. First, I'll summarize my reasons for claiming that the copy in http://jfsowa.com/peirce/eg1911.pdf should be considered the most definitive: 1. By 1911, Peirce had abandoned hope of publishing a final version, but he knew that Lady Welby and her correspondents circulated letters among a group of well-respected philosophers and logicians. He considered the letter L231 to be as significant as a formal publication. 2. EG1911 is the clearest, shortest, and most elegant summary of Alpha + Beta. The shaded areas can be generalized to 3-D regions or to 4-D for stereoscopic moving images. Aspects of Gamma or Delta graphs could be added without changing the Alpha + Beta foundation. And eg1911 has a short, but complete selection of technical terms that could be adapted to a wide range of notations in any number of dimensions. 3. In L231, Peirce replaced the term 'illative transformation' with the term 'permission'. Perhaps he realized that the words 'illative' and 'illation' had become archaic. More
Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)
Jeff BD, Terry R, Jon AS, List I endorse Jeff's comments about the need to relate any author's work to his or her predecessors, contemporaries, and successors. I copied an excerpt from his note after my signature below. A major reason why Peirce's logic and semiotic were so advanced is that he had mastered all the major works from antiquity to the end of the 19th c -- especially the Scholastic logic, which was far more advanced than the typical textbooks of the 19th c. TR> [human]logic is essentially sensate and intuitive -- based on imminent pre-analytic experiential iconicity but equally vulnerable to error, mistake, and dissonance: e.g., it looks exactly like guacamole... I agree. The metaphor I use is "knowledge soup". William James called it the "blooming buzzing confusion". That's the content of the phaneron. The iconic structure of EGs makes them ideal for selecting lumps" from the soup and reasoning about them. TR> As far as possible-world semantics and models beyond FOL are concerned, two of the most helpful seminal works... _Essential Formal Semantics_ and _Topics in Conditional Logic_ [by Donald Nute]. I checked the Amazon previews of those two books. I agree that they provide good background for relating Peirce's writings to developments in the 20th c. Since Peirce was thinking "ahead of his time", texts from his future can help us understand some cryptic comments he had not fully developed. TR> Not convinced this is true: "JFS: And the syntax and semantics of any other versions of logic can be specified by mathematical theories expressed in FOL." Please note: I am *NOT* claiming that it's possible to translate other versions of logic to FOL. But every known version of mathematics can be specified by axioms stated in FOL. For examples, look at tools such as Mathematica or MathLab. The semantics of modal logic (every version, including Peirce's) can be specfied by a purely first-order theory of possible worlds. You don't have to believe me, you can look at references I cite (in http://jfsowa.com/pubs/5qelogic.pdf ) or at the references cited by Donald Nute or anybody else. JAS> RL 231 (June 1911) includes Peirce's simplest and clearest explanation of Beta EGs (NEM 3:162-169), which are equivalent to classical first-order logic. It is also his last thorough explanation of EGs in the extant manuscripts other than RL 378 (September 1911 in French), which is fully consistent with it. With this point of agreement, we can end that debate. I'll add the following observations, which I believe are not controversial: 1. The explanation of semantics (endoporeutic) is clearer than Peirce's earlier comments, and it is consistent with Risto Hilpinen's observation that endoporeutic is a version of Hintikka's game-theoretical semantics (GTS). 2. The rules of inference (permissions) are stated as three symmetric pairs instead of five separate rules. This symmetry is a major advance over other proof procedures, such as Frege's or Gentzen's. Among other important results, it enables a simple solution to an unsolved research problem from 1988. 3. The formalization in terms of shaded/unshaded areas permits a direct generalization to regions in higher-dimenions. Peirce had previously said that a limitation to a 2-D sheet required selectives or bridges that would not be required in 3-D graphs. And later in L231, he discussed reasoning in "stereoscopic moving images". That thought was probably in the back of his mind while he was writing the earlier pages. 4. Finally, the smaller number of technical terms reduces the time and effort for teaching and learning EGs. The absence of the word 'scroll' also avoids any questions about a possible difference in meaning. JAS> Peirce's multiple derivations of negation from the primitive logical relation of consequence are not "horribly contorted" at all. There is no need to derive negation from anything else. Affirmation and negation are the foundation for every logic from Aristotle to the present. For Peirce (L376, December 1911), "A denial is logically the simpler, because it implies merely that the utterer recognizes, however vaguely, some discrepancy between the fact and the speech, while an affirmation implies that he has examined all the implications of the latter and finds no discrepancy with the fact." The so-called "derivation" of negation from consequence is just a simple theorem of Boolean algebra: "not p" is equivalent to "if p then 0", where 0 represents Falsum. Boole's original algebra had 'not' as a primitive, but it didn't have 'if' until Peirce introduced his "claw" symbol. The exaggerated claim that Peirce made for "illation" results from one of his rare blunders: "For [the reader] cannot reason at all without a monstrative sign of illation" (CP 4.76, 1893). That claim is refuted by Peirce's 1884 discovery (R506, W 5:107): "Professor O. H. Mitchell's important paper "On a New Algebra of Logic" has led me to think that the p
Re: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)
Jon A, Helmut R, Terry R, Jon AS, List, JA> I can't imagine why anyone would bother with Peirce's logic if it's just Frege and Russell in another syntax, which has been the opinion I usually get from FOL fans. That is true. But the EG structure and rules of inference are elegant, and the algebraic structure is klutzy. For a mathematician, that is a huge difference.. What makes EGs elegant is the simplicity of the structure, minimum of primitives, and symmetry of the rules. As a result of that structure, note how eg1911 generalizes and relates Gentzen's two systems of natural deduction and sequent calculus. As a result, an unsolved research problem from 1988 is almost trivial in terms of the EG rules. See http://jfsowa.com/talks/ppe.pdf . JA> Peirce's 1870 Logic of Relatives is already far in advance of anything we'd see again for a century, in principle in most places, in practice in many others, chock full of revolutionary ideas... I agree. But those ideas are part of the ontology rather than the logic. HR> I think that "implication, imagination, or belief" mostly do not sit in the symbols of notation such as cuts, but in the variables I agree that variables are problematical. Three-dimensional graphs show direct connections. But 2-D graphs are forced to use klutzy features like selectives or bridges. The word 'cut' by itself is not bad. But it is a reminder of the recto/verso terminology, which Peirce said was "as bad as it could be". In eg191, Peirce talks about 'shading'. Although that word takes six letters, the people who the read and write EGs should forget the words and think directly in terms of the diagrams. When doing subtraction, for example, nobody thinks of the words 'minuend' and 'subtrahend'. The words are useful for talking about math, but they should never intrude on the structure of the math. TR> FOL doesnt accommodate possible-world semantics, which is necessary (and sufficient) to resolve the paradoxes of material conditionality that persist in FOL. Moreover, possible-world semantics for modalities (necessity, possibility) and intensional (vs. extensional) conditionality are prerequisites for expressing causal laws. That's true. For the semantics of modal logic, an ontology about possible worlds or something like Peirce's three universes (possibilities, actualities, and the necessitated) must be added. Work on modal semantics during the century after Peirce shows that FOL can be used to define such theories. See http://jfsowa.com/pubs/5qelogic.pdf and http://jfsowa.com/pubs/worlds.pdf . Peirce was not happy with the earlier versions of his modal EGs. What he intended for Delta graphs is unknown, but any version of FOL (including eg1911) could be used to state a theory of possible worlds that is sufficent to specify a semantics for Delta graphs.whatever that might be. JAS> As Peirce explains in R 490... "if A then B" is not logically equivalent to "not (A and not-B)". No. Don Roberts (1973:154) defined a scroll as "Two cuts, one within the other". That makes it exactly equivalent to "not (A and not-B)". That is the way Jay Zeman, Ahti, and many others have defined it, and every EG proof that Peirce wrote is based on that definition. Any ambiguous comments about scrolls are irrelevant. It's true that in some MSS, Peirce used a horribly contorted definition of negation in terms of a scroll. But in June 1911 (R670), he remembered that his permissions (rules of inference) depend only on whether an area is shaded or unshaded. Since a scroll is limited to two levels, it's just a special case. In R670, he wrote that Figure 10 with scrolls is identical to Figure 11 with nested areas. In L231 and later, he never mentioned the word 'scroll'. The word 'scroll' is just a redundant term for a nest of two ovals, and the way of drawing it cannot be generalized to 3-D. JFS> Unless any MSS later than December 1911 are found which say anything to the contrary, the version in L231 must be considered definitive. JAS> No one has the unilateral authority to declare that anything Peirce wrote "must be considered definitive," The only authority is Peirce's available MSS. The semantics of first-order EGs in June 1911 is consistent with earlier versions, and it's simpler, more precise, and more complete (full classical FOL with a structure that could be extended to metalanguage, second-order logic, and modal logic by borrowing fatures from earlier versions). Peirce continued to use that version until December 1911, and no later version has bee found. JAS> Peirce begins his December 1911 letter to Risteen (RL 376) by stating, "I mentioned to you, while you were [here] last year, that I have a diagrammatic syntax which analyzes the syllogism into no less than six inferential steps. I now describe its latest state of development for the first time." Exactly! Note that L231 shows the six steps of the syllogism from the starting Figure 11 to the concluding Figure
RE: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)
Gary F, To answer your questions: Classical first-order logic, usually abbreviated FOL, has pride of place among the open-ended variety of logics that have been specified during the past century. Primary reason: FOL is sufficient to specify 99.99% of all versions of mathematics from ancient times to the present. FOL can be used to specify every digital computer ever built and every program that runs on any digital computer. And the syntax and semantics of any other versions of logic can be specified by mathematical theories expressed in FOL. When I say that people in ancient times used FOL to specify mathematics, I mean that they used the equivalent of the words AND, OR, NOT, IF, SOME, EVERY, and EQUALS (=) in a way that could be translated to any modern notation for FOL, including eg1911. (http://jfsowa.com/peirce/eg1911.pdf ) Re Peirce's many versions of logic: Peirce made some extensions to Boolean logic in the 1860s, but his major extension beyond Boolean logic was his logic of 1870, which went beyond monadic predicates to n-adic predicates for any n>1. De Morgan called that work the greatest advance in logic since Aristotle. And he was right. The discovery of complete notations for FOL by Frege (1879) and Peirce (1885) presented mathematicians with a logic that was sufficient to specify all of mathematics. That was a revolutionary advance. Peirce (1885) also specified a version of second-order logic. That was an important advance beyoind Frege (1879). (See http://jfsowa.com/peirce/putnam.htm ) Peirce also used logic as a metalanguage in his 1898 example of an existential graph that stated "That you are a good girl is much to be wished". These two additions (second-order logic and metalanguage) could be added to the eg1911 notation with the same or similar additions he used with the earlier versions of EGs. The semantics of those additions could be specified along the same lines as modern extensions to the algebraic notations. One version I have been using is called Common Logic (CL). For references and discussion, see the slides I presented at a conference in June: http://jfsowa.com/talks/eswc.pdf Re modal logic: Any of the notations for modal logic that Peirce introduced before 1911 could be added to the notation of eg1911. But Peirce himself was unsatisfied with them. He mentioned a replacement, which he called Delta graphs. But so far, nobody has found any MSS that specify any detail. But any extensions during the past century could be added to the notation of eg1911. For some discussion, see http://jfsowa.com/pubs/5qelogic.pdf . Re three-valued logic: Peirce specified truth tables for three-valued logics in some MSS. Those could be used with the notation of eg1911. But the fact that he presented eg1911 at the beginning of a long letter on probabilty suggests that he may have been thinking of probabilty as the way to handle uncertain information. If so, classical FOL, as expressed in any notation including eg1911, could be used to reason about probabilities. Unless and until any MSS after 1911 are discovered, nobody knows exactly how Peirce would have extended EGs to handle any of the above issues. But eg1911 is a *better* foundation for adding such extensions than any previous version: 1. The use of shading instead of cuts or scrolls supports a simple extension beyond a two dimensional sheet: just use shaded regions in N-dimensional space. In one of his MSS, Peirce explicitly said that selectives are necessary only for a 2-D sheet, and that EGs on a plane should be considered *projections* from 3-D graphs. 2. The drastic reduction in technical terms in eg1911 clears the way for further extensions. In L231, he mentioned "stereoscopic moving images" and regretted that he could not afford the technology. Today's virtual reality would be ideal for allowing anyone to wander through a moving 3-D graph and make dynamic changes to it. 3. With today's technology, it's also possible to include arbitrary images and even 3-d virtual reality inside any region of an EG. In a talk I presented at an APA conference in 2015 and later at an EG workshop in Bogota, I proposed two new rules of inference -- observation and imagination -- which could be added to multi-dimensional EGs. Those two rules would be special cases of the rules of iteration and deiteration. For the slides, see http://jfsowa.com/talks/ppe.pdf . Slide 2 of ppe.pdf includes the URL of a 78-page article that was published in the Journal of Applied Logics, John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by G
Re: [PEIRCE-L] Re: Philosophy of Existential Graphs (was Peirce's best and final version of EGs)
Jon AS, In NEM 3:140, Peirce made a clear distinction between the vague words of ordinary language, and the precise terminology of science: CSP> The language and symbols of ordinary life are short, defective and figurative. As little as possible is spoken, as much as possible is left to implication, imagination and belief. But scientific symbols and methods should be complete. As little as possible should be left to implication, imagination and belief. By these criteria, eg1911, as specified in L231, is complete. It is logically equivalent to every version of classical first-order logic from Frege (1879) and Peirce (1885) to the present. Nothing is left to implication, imagination, or belief. As Peirce showed in R670, a scroll is logically equivalent to a nest of two ovals. AS Peirce said in NEM 3:140, a scientific notation should leave as little as possible to implication, imagination, or belief. That implies that there is no room for any residual meaning for a scroll that is in any way different from the meaning of a nest of two ovals. If you have any further questions, please study the progression from R669 to R670, L231, L378, and L376 and my commentary about them. Unless any MSS later than December 1911 are found which say anything to the contrary, the version in L231 must be considered definitive. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Re: Philosophy of Existential Graphs (was Peirce's best and final version of EGs)
Gary R, The primary claim of this thread is that Peirce's 1911 version of EGs, which he sent in the letter L231 to Mr. Kehler (a member of LadyWelby's significs group) is the one which he intended as a definitive statement of EGs. For Peirce's text and some commentary, see http://jfsowa.com/peirce/eg1911.pdf The issues copied after my signature below were discussed and shown to be irrelevant. Since you weren't involved in the earlier stages of the discussion, I'll summarize them briefly: 1. Nearly all words, when taken out of context, have a wide range of senses. The primary way to pin down their meaning in any particular application is to cite specific examples. 2. The phrase "as analytical as possible" without any examples is hopelessly vague. Taking it from one context in 1902 and applying it to another context in 1906 is dubious at best. 3. Peirce's 1906 version of EGs is the one he rejected in the strongest possible terms in the months following L231: CSP L378, Sept. 1911: "I use a diagrammatic syntax, which I described very badly and at an intolerable length in the Monist of October 1906." CSP L376, Dec. 1911: "in the Monist of Oct. 1906... The description was, on the whole, as bad as it well could be." To take a vague term from 1902 and apply it to a version of 1906, which Peirce rejected, is not a convincing argument. It does not deserve a QED. I consider this summary to be the end of the thread. Every objection to the original claim has been analyzed and shown to be irrelevant. John __JAS: [Peirce's] primary objective in developing both his logical algebras and EGs is not "making a calculus which would turn out conclusions by a regular routine." It is "simply and solely the investigation of the theory of logic," which requires "that the system devised for the investigation of logic should be as analytical as possible" (CP 4.373, 1902).JAS: EGs with shading, rather than cuts, satisfy this criterion as long as the derivation of negation from the primitive of consequence, reflecting the fundamental asymmetry of all semeiosis, is kept firmly in mind. Accordingly, I agree with Peirce's "confession" that it is an "error" to assume that "because the blackened Inner Close can be made indefinitely small, therefore it can be struck out entirely like an infinitesimal" (CP 4.564n, c. 1906). Instead, when a shaded area is intended to represent negation--not the antecedent of a consequence--it should have a darkened circle within it, "however small, to represent iconically, the blackened Inner Close" (ibid).[emphasis added by GR]QED (more or less), _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Re: Peirce's methodology
Robert M, Gary F, List, Before saying anything else, I'll remind everybody of two points: (1) theorematic reasoning is a special case of diagrammatic reasoning. (2) In Peirce's classification of the sciences, there is a two-way flow of information: every science (including every branch of philosophy) depends on mathematics for its methods of reasoning, and mathematical discovery is inspired by patterns found in all the special sciences. I strongly agree with Robert about the following quotation: CSP> "mathematics meddles with every other science without exception. There is no science whatever to which is not attached an application of mathematics..." (CP 1.245) GF> The relevance to John's original post, as i see it, is this: if theorematic reasoning is only a mathematical procedure, it leaves out the experiential element of Peirce's methodology and his pragmatism. I want to include everything. I cited Eisele's article because she was emphasizing the same points as Robert. And she would certainly agree with CP 1.245. Re imaginary vs actual: Diagrammatic reasoning applies to all experiences in the phaneron in exactly the same way. The past is known only by memory, which is notoriously error prone. The future is imaginary until the instant it becomes actual. And the present is fleeting. Therefore, any kind of planning for the future (including the very next step anyone is about to perform) involves a mixture of memory, perception, and imagination. Any diagrammatic reasoning about causality would relate perception (actual) and memory (past) to an action (imaginary future). As Peirce said many times, the meaning of any general is a would-be -- in the imaginary future. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)
Jeff, To be iconic, a notation must have some resemblance to the structure or image of which it is an icon. Any claim that some notation is iconic must be justified by showing the original which it resembles. JBD> As far as I can see, the scroll is a special kind of iconic sign because it expresses the continuity in the relationship between antecedent and consequent of the conditional, and this mirrors the continuity in the relationship between premisses and conclusions in an argument. During the month of June 1911, Peirce was reviewing and reorganizing his logical, philosophical, and semiotic foundations for EGs. He had several goals, one of which was a clear and precise summary for his most receptive audience, Lady Welby and her significs group. On May 25 (R669), Peirce began with a summary of his writings since 1896. For that purpose, the scroll was significant, since it was his inspiration for switching from entitative to existential graphs.. But in June 7 to 17 (R670), he remembered that the rules of inference depended only on whether an area was positive or negative. "It is only the color of the area itself which has the force of affirming, if it be white or evenly enclosed... or of denying if it be shaded or oddly enclosed." He said that a cut was just the boundary of an area, and it had no more meaning than punctuation. He also showed a scroll in Fig 10 as an alternate way of representing the shading in Fig 11. In fact, he did not use the word 'scroll' to describe Fig 10. He just wrote "the lines that represent the cuts". Apparently, he considered the word 'scroll' to be so meaningless that it was not worth mentioning. In L231 (June22), he adopted pencil shading, which was easy to draw. Therefore, he had no need to draw or mention cuts or scrolls. The words would be useless verbiage that could only cause confusion. But L231 also mentioned steroscopic moving images. Shaded areas could easily be generalized to shaded regions in 3D. Cuts might be represented as closed regions, but there is no convenient way to represent a 3-D analog of a scroll. Shaded and unshaded regions are iconic notations, but there is no way to represent a 3-D scroll. Therefore, he did not mention cuts or scrolls in L231. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: Fw: [PEIRCE-L] Philosophy of Existential Graphs (was Peirce's best and final version of EGs)
Jeff, In the note I just sent, I was talking about the version of EGs in L231. For that version of logic, there can be no difference in semantics between a scroll and a nest of two ovals. JBD> In the case of inductive and abductive inferences, the conditionals may take a variety of forms: epistemic, alethetic, deontic, etc. In each of these cases, the topological character of the relations may vary. I agree. People who adopt EGs for classical FOL may need to extend the notation for other kinds of logic. Since Peirce dropped the scroll in 1911, anyone might choose to adopt it for some new purpose. But it's important to emphasize that the new purpose would not be identical to anything Peirce had previously written -- unless (and this is a big UNLESS) they could prove that it was indeed identical to what Peirce had previously intended. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Re: Philosophy of Existential Graphs (was Peirce's best and final version of EGs)
Jon AS, This is yet another case where the mathematical structures are precise, but the words that describe them leave enough ambiguity to cause confusion. The beauty of eg1911, as specified in L231, is its brevity, simplicity, precision, and bare minimum of verbiage. Every EG that conforms to the syntax of eg1911 has a precise translation to and from a logically equivalent statement in Peirce's algebra of 1885. It also has a precise translation to and from a logically equivalent statement in every version of classical FOL from Frege's Begriffsschrift (1879) to any notation for classical FOL that anyone may publish in the future. Any EG drawn with a scroll would either be semantically identical to one with two ovals or it would be meaningless. There is no other option. End of story.John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Peirce's methodology
Auke, Jon A, List, AvB> I did like this ms fragment very much: "It is not so much the history of science as it is the history of sound scientific thinking which I am considering" [Peirce MS 12801]. JA> Exactly! We interpret texts in relation to the object in view. Yes. Words are highly ambiguous, and the "object in view" is an essential part of the context or "collateral experience" in terms of which the words are interpreted. That is the essence of Peirce's diagrammatic reasoning: always interpret the words (or other symbols) in terms of some diagram (or image or icon) of the subject matter. As Eisele said in the PDF: "Some iconic or symbolic form is adopted to represent the given premises." Note that she wrote "symbolic form". where the word 'form' is a diagram that relates the symbols -- as in an existential graph or a drawing by Euclid. In summary, words by themselves are just the starting point. The "collateral experience" for interpreting the words is a diagram, image, or form that is necessary to determine the relevant word senses in any given context. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Why if-then is not an essential primitive (was Peirce's best and final...
Jon AS, List, As I mentioned in my reply to Jeff, Peirce's ideas were often far ahead of his time, and it's important to see which of them not only stood the test of time, but even improved on later developments. I changed the subject line to emphasize a critical issue that famous logicians (Frege, Whitehead, Russell, Gentzen...) overlooked. For his version of first-order logic, Frege (1879) chose negation, if-then, and the universal quantifier as his three primitives. That was an unfortunate choice, which Whitehead and Russell adopted for their _Principia_. That book had the worst theorem-proving procedure ever inflicted on innocent students. In the 1930s, Gentzen presented two much better procedures: natural deduction and the sequent calculus. But Gentzen also made the mistake of making if-then a primitive. After a bit of digging, I found the passage where Peirce discovered what was essential: Vol 5:107 of _Writings_, MS R506. summer of 1884: CSP: The first chapter of [1880 Algebra of Logic] develops the reasons for choosing the copula of inclusion, exhibits its formulae, and attempts by means of it to consolidate syllogistic with Boolian algebra. But the study of Professor O. H. Mitchell's important paper "On a New Algebra of Logic" has led me to think that the passage from premiss to conclusion ought not to be considered as the essential and elementary type of logical movement. We have rather two elementary modes of modifying assertions and two corresponding modes of transforming them. The two modes of changing assertions are 1st to drop part of what has been asserted and assert less, and 2nd to add to what has been asserted and assert more. Those two "modes of changing assertions" are the basis for his "permissions" (AKA rules of inference) for existential graphs. Each rule inserts or erases an EG or part of an EG in some area. No rule mentions or requires a scroll (if-then statement). Peirce discovered that principle a dozen years before he invented EGs (December 1896). JAS: Peirce explained on multiple occasions--including R 669, written just a couple of weeks before R 670 and L 231--negation is not a primitive. It is derived from the fundamental logical relation of illation or (less archaically) implication. No. There are many different relationships among the 16 binary Boolean operators and the two constants v (verum) and f (falsum). Peirce wrote about them many times from different points of view. But there is no reason to consider any of those operators more fundamental than negation. Children learn the word 'no' long before they learn implication. Even your pet dog or cat learns the word 'no'. The following historical comment occurs only in R669, and Peirce deleted it in the revised version, R670: CSP: In the order of the actual mental evolution of the syntax of existential graphs, the Scroll was first adopted as a sign required before all others because it represented a necessary Reasoning... (R669:18-20[16-18], 1911 May 31) The syntax of the scroll may have influenced Peirce's choice of notation in 1896. But his EG rules of inference refer only to areas -- positive (unshaded) or negative (shaded). They don't refer to scrolls. JAS: As [Ahti] said in his introduction accompanying R 669-670 ... AVP: These last two manuscripts concerning "Assurance through Reasoning" present what may be Peirces most successful attempt to explain the logic of existential graphs, and the philosophy concerning the notation of diagrammatic syntax in particular. The notions of identity, teridentity, composition of graphs, plurality, conditional, scroll, and the derivation of the idea of negation as a consequence of the scroll, all get their fair shares of exposition. In this comment, Ahti did not explain why the scroll, which was considered important in R669, was demoted to "punctuation" in R670, and was not mentioned at all in L231. The most likely reason is that Peirce was not thinking about the EG rules of inference when he wrote R669. But he wrote his best and simplest statement of the rules in L231. Since he wrote R670 in the short time between those two MSS, he was starting to think about those rules. They depend only on the areas of EGs, not on the cuts or the scrolls. Even more important, L231 mentions reasoning about "stereoscopic moving images" . The 2-D areas can be generalized to 3-D or even 4-D regions for space + time. But scrolls are limited to 2-D. For the EG excerpts from L231, see http://jfsowa.com/peirce/eg1911.pdf . JAS: Since my personal interest in EGs is primarily philosophical rather than pedagogical, I am inclined to agree with Pietarinen's assessment. This is a matter of the most profound logical and philosophical issues. In the 1930s, Gerhard Gentzen published a highly respected book on logical deduction. Unfortunately, he was misled to think that the if-then statement (whatever it may be called) was essential. For my 2010 article in _S
Re: [PEIRCE-L] Peirce's Topical Continuum
Jeff, I agree with your points and concerns. The following issue is critical: JBD> The future of mathematics is hard to see--even for the best of mathematicians. Yes. And Peirce was far ahead of his time in many aspects of mathematics, logic, psychology, and philosophy. Therefore, it's essential to consider developments during the century *after* Peirce in order to understand Peirce's early versions of those ideas. For continuity and infinitesimals, Abraham Robinson in the 1960s vindicated Peirce's insights and restated them in a form that meets today's standards of rigor. Zalamea is a mathematcian who understands both Peirce's mathematics and modern mathematics. His insights are essential for understanding and clarifying Peirce's insights. Since Zalamea was writing for a 21st c. audience, he was using modern terminology. That practice is consistent with Peirce's ethics of terminology. Peirce's primary goal was to improve communication by developing a standardized terminology. Peirce himself abandoned some of his early terminology when he found that his contemporaries had adopted new terms. He would not obligate us to resuscitate any of his terms for which the world had established other standards. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Peirce's best and final version of EGs
Jon AS, JAS: I continue to agree that NEM 3:162-169 is Peirce's simplest and clearest explanation of existential graphs. That'a good. But the reason why it appears so clear and simple is that Peirce discovered a simple, universal, notation-independent mathematical structure that underlies all reasoning. That includes formal (mathematcal) reasoning and the informal common sense in ordinary thought and language. The version summarized in L231 has the expressive power of first-order logic, but it can be extended to the same subset of higher-order logic as Peirce's algebraic logic of 1885: 1. Three primitives: existence, negation, and predication (first, second, or third). 2. Two operations: insertion and deletion of any primitive or combination of primitives in any area. 3. Three symmetric pairs of permissions (AKA rules of inference) that state the conditions for performing either of the two operations. Each member of any pair is the exact inverse of the other. For this logic, Peirce continued his practice of writing diagrams on a two-dimensional sheet. But he stated the rules with such generality that they could be applied to any notation in a space of any number of dimensions -- linear, 2-D sheet, 3-D region, or 4-D region of space + time. With this flexibility, eg1911 becomes a universal, notation-independent system of deduction. The followig point from 1908 is just a special case: CSP: [The] purpose of the System of Existential Graphs ... [is] to afford a method (1) as simple as possible (that is to say, with as small a number of arbitrary conventions as possible), for representing propositions (2) as iconically, or diagrammatically and (3) as analytically as possible. (CP 4.561n, 1908) Peirce knew that graphs on a two-dimensional sheet would need ad hoc methods (selectives or bridges) for lines that cross. But 2-D shaded areas could be generalized to 3-D shaded regions to represent graphs without crossovers. For evidence that Peirce was thinking about 3-D or even 4-D logic in 1911, see L231 (or NEM 3.191), where he mentioned reasoning with "stereoscopic moving images". Peirce also knew that Euclid's diagrams were far more iconic than EGs for reasoning about geometry. NEM 3.191 is a hint that he may have considered some way of applying his 1911 rules directly to 2-D or 3-D Euclidean diagrams. In fact, it's quite easy to apply Peirce's 1911 rules of inference to Euclid's diagrams and proofs. For an example, see the slides http://jfsowa.com/talks/ppe.pdf . Slide 6 shows a diagram for Euclid's Proposition 1 and Euclid's proof, as translated to English by Heath. For a proof of Proposition 1 by Peirce's rules, see slides 30 to 43. In that proof, Euclid's diagrams are used to state propositions; Euclid's letters are used as selectives to show lines of identity; Euclid's diagrams may be enclosed in shaded areas for negations and implications; and diagrams or parts of diagrams may be inserted or erased according to Peirce's rules. Since Peirce stated his rules near the beginning of L231 and he talked about reasoning with images later in the same MS, it's quite likely that he may have been thinking of something along these lines. He may have written something about that possibility in some MS that was lost. It's even possible that some such MS might someday be found. JAS: Technically a scroll is not "just a way of drawing two cuts." These are indeed equivalent in classical logic, such that "if A then B" entails "not (A and not-B)" and vice-versa. No. In mathematics and mathematical logic, two equivalent notations (one-to-one mappings and identical entailments) have identical semantics. A choice between one or the other is just a matter of convenience in reading or writing. In R670 (1911), Peirce showed semantically identical EGs with cuts in Fig. 9, scrolls in Fig. 10, and shaded areas in Fig 11. Immediately after Fig. 11, he wrote "the cuts in themselves have no meaning whatever, but are, at most, pure punctuation-marks". JAS: However, Peirce recognized that "there is but one primary and fundamental logical relation, that of illation" (CP 3.440, 1896), which is what the scroll signifies when drawn as a single continuous cut that crosses itself so that the inner close touches the outer close at a node (CP 4.435-436, 1903; CP 4.564, 1906; R 669:16, 1911). The word 'illation' is an archaic synonym for 'inference', and 1896 was the time of Peirce's first thoughts about EGs. After he defined his more elegant system of 1911, he explicitly wrote that the cuts are "pure punctuation marks". As Figures 9 to 11 of R670 show, the scrolls are convenient punctuation marks for indicating the more fundamental shading. JAS: when adapting existential graphs to intuitionistic logic as Arnold Oostra has outlined. here a scroll is not equivalent to nested cuts; "if A then B" still entails "not (A and not-B)," but "not (A and not-B)" does not entail "if A then B." Intuitionistic logi
Re: [PEIRCE-L] Re: The Logic of Interpretation
Jon AS, Comparing Peirce's texts to the instructions on a 5th grade exam is like comparing quantum mechanics to 2+2=4. William James was Peirce's closest friend. He had spent years talking with CSP and reading his writings. But he described Peirce's lectures as flashes of brilliant light relieved against Cimmerian darkness! James wasn't a mathematician or a logician, but Christine Ladd Franklin was. Yet she was never able to appreciate Peirce's existential graphs. Quine was a brilliant logician, but he couldn't understand EGs The only way to understaand Peirce's writings it to skim, work, read, work, read more, work... and repeat. And by work, I mean do the kind of detailed work that Peirce did. For examples, see Photometric Researches. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Re: The Logic of Interpretation
Jon, Peirce's writings are a "How-to manual" about thinking and reasoning. If you have a how-to manual about cooking, skiing, or growing flowers, it's impossible to understand the manual without doing the work. If it's a manual on cooking, you have to buy the ingredients and follow the recipes. If it's about skiing, you have to buy the equipment, go out on the slopes, and practice. If it's about growig flowers, you have to buy the seeds, plant them (indoors or outdoors), and follow the instructions. What Jeff wrote (copy below) is advice about following Peirce's how-to manual about thinking and reasoning. Reading a manual about thinking is not sufficient. You have to get the ingredients (food for thought), get the utensils (paper, ink, computers, or whatever), and follow the recipes for analyzing and solving some significant problems. JAS> Observation - What does [Peirce's] text say? Interpretation - What does the text mean? Application - How does the text work? No. You can't learn cooking, skiing, or growing flowers by analyzing the texts. You have to do the much harder work of cooking food, skiing down a mountain, or growing actual flowers. After doing the actual work, you can understand the manual at a much deeper level, and you can then discover fine points that you missed on the first reading. It also helps to watch expert cooks, skiers, and gardners in action. That is why I recommended Peirce's _Photometric Researches_ as an example of Peirce applying his methods of analysis to a significant problem. John _ On Sat, Jul 18, 2020 at 8:31 PM Jeffrey Brian Downard wrote: Jon Schmidt, John Sowa, List, Jeff D: If you substitute "texts" for "facts", as you have suggested, how does that constrain the inquiries? Jon Schmidt: Again, I suggest that it constrains the inquiries to discerning the author's intended meaning as expressed in the texts themselves. At this stage, we are only seeking to ascertain what Peirce's actual views were as communicated by his writings, not assessing whether they are correct. JD: Readers need to carry out the inquiries themselves and then check to see if they arrive at the same result. Carrying out these inquiries seems to involve facts that go beyond the words written on the pages. Jon S: I agree, but I see it as a subsequent step. First we test our interpretative hypotheses against "the words written on the pages" in a good-faith effort to make sure that we have properly understood them. Then we test them against reality by conducting our own inquiries along the same lines. Jeff D: I disagree with the suggestion that it should be a two-step process. Let me distinguish the following questions we can ask as readers of Peirce's writings: How should we interpret a given text? How should we understand the methods Peirce is employing in his inquiries? For my part, I think that we should try to understand and employ Peirce's methods at the same time we are reading the texts. That is, (1) and (2) go hand in hand. You really can't make much headway on (1) without considering how Peirce is using experimental methods to push inquiry forward. Often, the arguments he offers in the texts are really just signposts that he is offering readers in the hope that we will be able to follow his lines of inquiry. In many cases, I find that Peirce is moving so fast and covering so much ground that the only way to fill in the gaps is to carry out the inquiries myself--drawing on his instructions and suggestions offered in other texts. If I am not inquiring myself about the same questions he is asking using the same methods he is employing, I often entirely fail to follow the directions contained in those signposts. In such cases, I have to start again in order to figure out where I lost the thread. In your response, you seem to have fastened on the following question, which I think is quite different from (2) above: Are the results that Peirce arrived at using those methods correct, or do we arrive at different results when using the same methods to address the same questions? Even here, we can ask this question in a modest fashion by using this approach as a check on our use of his methods. If I arrive at a different result, then I take it as an indication that I've misunderstood or misapplied his methods. Having said that, I do take myself to be capable of engaging in my own inquiries using these methods, and I find it interesting when I arrive at a different result. What is more, one can ask if Peirce is using the right methods. Where we have doubts about his methods or results that persist, it is only natural to ask how might we improve on those methods in a manner that is consonant with the aim of seeking the truth about what is really the case. Whenever I head down this track on the List, I try to clarify what I'm doing by spelling out where my methods or results differ from Peirce's. _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L
Re: [PEIRCE-L] Re: The Logic of Interpretation
Jeff D> What is more, one can ask if Peirce is using the right methods. Where we have doubts about his methods or results that persist, it is only natural to ask how might we improve on those methods in a manner that is consonant with the aim of seeking the truth about what is really the case. Whenever I head down this track on the List, I try to clarify what I'm doing by spelling out where my methods or results differ from Peirce's. I strongly agree. What Peirce wrote is just the tip of a huge iceberg of all the ideas he read, imagined, and anticipated. We have seen many examples where Peirce not only anticipated but improved on the innovations by his successors. I summarized some of them in "Peirce's contributions to the 21st century", http://jfsowa.com/pubs/csp21st.pdf . That paper was published in 2006, but I have since found even more examples where Peirce's ideas were *major* improvements. There's much more to say. Fundamental principle: When we read Peirce's writings (or writings by anybody else), we must always evaluate them in terms of everything we know. Since Peirce was so far ahead of his time, his contemporaries couldn't understand them, and he had no examples that he could cite. We now have a full century of ideas that we can and must use to understand and evaluate what Peirce wrote. As just one example, nobody understood Peirce's cryptic remarks about endoporeutic. But Risto Hilpinen recognized it as a version of Hintikka's Game Theoretical Semantics (GTS). Without that knowledge from the future, nobody could interpret what Peirce meant. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Two missing files (for Peirce's best and final version of EGs
Robert Marty noticed that I forgot to upload two files that I cited in my previous note: http://jfsowa.com/peirce/r670.pdf http://jfsowa.com/peirce/L378.htm I thank Robert, and I apologize for any inconvenience. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Peirce's best and final version of EGs
I have often said that the excerpt of L231 published in NEM 3:162-169 is Peirce's best and final version of existential graphs. For a copy and some brief comments, see http://jfsowa.com/peirce/eg1911.pdf Following are some objections to the claim that eg1911 is definitive: 1. In his 1973 book, Don Roberts cited L231, but he did not mention its notation (shaded ovals for negation instead of cuts) or its rules of inference (three symmetric pairs). He also cited R514, which contains a version that is almost identical to the version in L231. But he did not discuss the notation or terminology in either one. Apparently, he did not consider them important. 2. During the years between R514 (estimated date 1909) and L231 (1911), Peirce continued to use the notation and terminology of his earlier writings on EGs. Therefore, he didn't consider the R514-L231 version a replacement for the earlier versions. 3. The text of L231 ignores a large amount of Peirce's terminology and writings about EGs. It says nothing about Gamma graphs or the many complex issues they represent. The 1911 version seems to be a brief summary rather than a definitive presentation. I recently discussed these issues with Martin Irvine (on cc list above). He mentioned some related MSS from 1911 and said that the date of 1909 for R514 was wrong. It is a highly marked-up draft of L231, and it is now grouped with L231. He also mentioned other MSS, also from 1911, which use the same notation. He said that no later MSS with examples or discussion of EGs have been found. About a month before L231 (dated 1911 June 22), Peirce wrote R669 (May 25 to June 2) and a revised version R670 (June 7 to 17). For negation, Peirce used a black area with the enclosed graph in white. But Peirce added "It is needless to say that the process of making a black surface with a diagram upon it in white is insufferably inconvenient." For that reason, he used his earlier notation, but he said that the "bounding ovals", which he called 'cuts', "have no meaning at all... It is only the color of the area itself which has the force of affirming if it be white or evenly enclosed ... or of denying if it be shaded or oddly enclosed." For a copy of R670, as transcribed by Ahti Pietarinen, see http://jfsowa.com/peirce/r670.pdf A few days later, when Peirce wrote L231, he found a simpler solution: shade the negated areas in pencil. That elimminated any use for the meaningless word 'cut' or its synonym 'sep'. He also dropped the word 'scroll' because a scroll is just a way of drawing two cuts. He dropped the word 'spot' because no line of identity is ever attached to a rhema or predicate that has no name; it's always attached to a word or other symbol. He did keep the word 'peg', but dropped the synonym 'hook'. The words 'spot', 'blot', and 'dot' are English words that have no obvious translations to other languages. Fortunately, there is no need for them in English. On 29 September 1911, Peirce wrote L378, a letter in French to A. Robert. In it, he included a brief introduction to existential graphs with the same notation as L231. In French, he made the following comment: "I use a diagrammatic syntax, which I described very badly and at an intolerable length in the Monist of October 1906, even though I was in possession of this syntax since December 1896." For the original French of L378, see http://jfsowa.com/peirce/L378.pdf . This is a PDF of the microfiche, in which the pencil shading was lost, but it can be inferred from the descriptions. For a brief summary in English, see http://jfsowaa.com/peirce/L378.htm . >From L376 (December 6-9, 1911), Letter to Alan Douglas Risteen, p. 1: "I gave an oral account of [the System of Existential Graphs], soon after, to the National Academy of Sciences; and in 1903 for my audience of a course of Lectures before the Lowell Institute, I printed a brief account of it. An account of slightly further development of it was given in the Monist of Oct. 1906. In this I made an attempt to make the syntax cover Modals; but it has not satisfied me. The description was, on the whole, as bad as it well could be, in great contrast to the one Dr. Carus rejected. For although the system itself is marked by extreme simplicity, the description fills 55 pages, and defines over a hundred technical terms applying to it. The necessity for these was chiefly due to the lines called 'cuts' which simply appear in the present description as the boundaries of shadings, or shaded parts of the sheet. The better exposition of 1903 divided the system into three parts, distinguished as the Alpha, the Beta, and the Gamma, parts; a division I shall here adhere to, although I shall now have to add a Delta part in order to deal with modals. A cross division of the description which, here, as in that of 1903, is given precedence over the other is into the Conventions, the Rules, and the working of the system." L376 breaks off at the end of p
Re: Fw: [PEIRCE-L] Re: The Logic of Interpretation
Jeff, I strongly agree with the points you made in this thread. My only recommendation is to modify the last line below by replacing "seems to involve facts" with "requires facts and actions". Peirce made the strongest possible justification for that change: "The elements of every concept enter into logical thought at the gate of perception and make their exit at the gate of purposive action; and whatever cannot show its passports at both those two gates is to be arrested as unauthorized by reason." (CP 5.212) That quotation by Peirce is based on his many years of work in work in logic, mathematics, and experimental science. His late writings are the distilled essence of his experience. It's impossible to appreciate their meaning without relating them to that work. Although we can't go back to the 19th c and observe him directly, we can relate his late writings to his descriptions of his work -- for example, his book on Photometric Researches -- *and* to 20th and 21st c work on similar subjects. John JBD> This approach to reading important texts in the history of science has been adopted by schools such as St. John's [College, Annapolis, MD] where students learn to understand Newton's inquiries and theories by building an experimental apparatus--such as the one Galileo used for rolling balls down an inclined plane--and by then making the measurements for themselves. Having done so, they then draw out the conclusions from those measurements and compare their results to Newton's. In a number of places, Peirce says that something similar must be done to understand his inquiries in philosophy. Readers need to carry out the inquiries themselves and then check to see if they arrive at the same result. Carrying out these inquiries seems to involve facts that go beyond the words written on the pages. _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Re: The Logic of Interpretation
Robert, I agree with Peirce and with your interpretation. But the cost of your article is $42. Do you have a web site with a less costly version?"Let it be repeated that all the terms of the division must be strictly relevant to logic, and that consequently all accidents of experience, however universal, must be excluded. The result of this rule will necessarily be that the new concept of a "sign" will be defined exclusively by the forms of its logical relationships; and the utmost pains must be taken to understand those relations in a purely formal, or, as we may say, in a purely mathematical way."( EP2 : 389) I've studied this quote in :Marty, Robert, « A Purely Mathematical Way for Peirce's Semiotics », dans Charles Sanders Peirce in His Own Words: https://www.degruyter.com/view/book/9781614516415/10.1515/9781614516415.415.xml _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Re: [ontolog-forum] Brain regions for mathematical knowledge
Jon A and Paola, The amount of research in neuroscience in the past 50 years is immense compared to the studies of the left & right hemispheres in the 1970s. Among other things, the neuroscientists today have much more sympathy with introspective studies than they have with people (in the 1990s) who dismissed introspection as "folk psychology". With fMRI scanners, they can correlate what people say with what areas of the brain light up while they are talking. For the following discussion, please open the slides from Section 6 of eswc: http://jfsowa.com/temp/eswc6.pdf . Slides 2: Today's artificial NNs for machine learning are limited to learning functions. Andrew Ng (slide 3) observed that ANNs automate tasks that take less than one second of time for humans. That's important for perception and classification, but it can't do anything beyond a fish-level or cat-level of cognition (slide 4). Slides 5 to 8: A study of cognitive learning that goes far beyond anything that todays ANNs can do. Slides 9 to 11 relate that kind of learning to the categories by C. S. Peirce. Slide 13 shows a diagram by Robert Rosen (1985) who discussed the way formal reasoning can enable people to anticipate (predict) what will happen. But animals that don't know language or logic can also anticipate the future. Slide 14 shows an extension to Rosen's diagram based on two kinds of reasoning: simulation of mental models and logical inference with symbolic models. Slides 15 to 18 discuss the importance of the cerebellum for mathematics and for a much broader range of mental imagery. It confirms Peirce's claim about the importance of imagery (icons and diagrams). Slide 19 states introspective reports by the mathematician Paul Halmos and the physicist Albert Einstein. Their comments are consistent with the comments by C. S. Peirce about his own methods of reasoning. For more detail, see the slides about Peirce, Polya, and Euclid -- all of whom used imagery as the *foundation* for reasoning in mathematics. As they say, a formal proof is just useful for (a) checking to make sure that no details were omitted, and (b) communicating a precise statement with other mathematicians. But mental imagery is essential for thinking about a problem and discovering a solution. For even more detail, see the 117 slides (with references) about "The virtual reality of the mind", http://jfsowa.com/talks/vrmind.pdf . In particular, see Section 2 "The role of the cerebellum" in slides 33 to 54. Tare are a small number of people who were born without a cerebellum and survived. But their ability to do any kind of complex reasoning is extremely limited. John Jon A and Paola,The amount of research in neuroscience in the past 50 years is immense compared to the studies of the left & right hemispheres in the 1970s. Among other things, the neuroscientists today have much more sympathy with introspective studies than they have with people (in the 1990s) who dismissed introspection as "folk psychology".With fMRI scanners, they can correlate what people say with what areas of the brain light up while they are talking. For the following discussion, please open the slides from Section 6 of eswc: http://jfsowa.com/temp/eswc6.pdf .Slides 2: Today's artificial NNs for machine learning are limited to learning functions. Andrew Ng (slide 3) observed that ANNs automate tasks that take less than one second of time for humans. That's important for perception and classification, but it can't do anything beyond a fish-level or cat-level of cognition (slide 4).Slides 5 to 8: A study of cogni tive learning that goes far beyond anything that todays ANNs can do. Slides 9 to 11 relate that kind of learning to the categories by C. S. Peirce.Slide 13 shows a diagram by Robert Rosen (1985) who discussed the way formal reasoning can enable people to anticipate (predict) what will happen. But animals that don't know language or logic can also anticipate the future. Slide 14 shows an extension to Rosen's diagram based on two kinds of reasoning: simulation of mental models and logical inference with symbolic models.Slides 15 to 18 discuss the importance of the cerebellum for mathematics and for a much broader range of mental imagery. It confirms Peirce's claim about the importance of imagery (icons and diagrams). Slide 19 states introspective reports by the mathematician Paul Halmos and the physicist Albert Einstein. Their comments are consistent with the comments by C. S. Peirce about his own methods of reasoning.For more detail, see the slide s about Peirce, Polya, and Euclid -- all of whom used imagery as the *foundation* for reasoning in mathematics. As they say, a formal proof is just useful for (a) checking to make sure that no details were omitted, and (b) communicating a precise statement with other mathematicians. But mental imagery is essential for thinking about a problem and discovering a solutionFor even more detail, see the 117
[PEIRCE-L] Brain regions for mathematical knowledge
The following article is relevant to our recent discussions about mathematics, logic, and reasoning in words. "Cortical circuits for mathematical knowledge: evidence for a major subdivision within the brain's semantic networks" Marie Amalric and Stanislas Dehaene https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5784042/pdf/rstb20160515.pdf Abstract: Is mathematical language similar to natural language? Are language areas used by mathematicians when they do mathematics? And does the brain comprise a generic semantic system that stores mathematical knowledge alongside knowledge of history, geography or famous people? Here, we refute those views by reviewing three functional MRI studies of the representation and manipulation of high-level mathematical knowledge in professional mathematicians. The results reveal that brain activity during professional mathematical reflection spares perisylvian language-related brain regions as well as temporal lobe areas classically involved in general semantic knowledge. Instead, mathematical reflection recycles bilateral intraparietal and ventral temporal regions involved in elementary number sense. Even simple fact retrieval, such as remembering that the sine function is periodical or that London buses are red, activates dissociated areas for math versus non-math knowledge. Together with other fMRI and recent intracranial studies, our results indicated a major separation between two brain networks for mathematical and non-mathematical semantics, which goes a long way to explain a variety of facts in neuroimaging, neuropsychology and developmental disorders. These issues are related to the slides about Peirce, Polya, and Euclid: http://jfsowa.com/talks/ppe.pdf . John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
RE: [PEIRCE-L] The Pragmatic Trivium
Gary F, I have a great deal of sympathy for your Turning Signs. And I believe that issues of normative science deserve a great deal of attention especially now. For any points that I may criticize or quibble, I emphasize that my comments are about details, rather than the main issues you discuss. For example, I learned a lot about formal logic from Rudolf Carnap. But I strongly reject his goal of purifying language by using formal logic to define all words in terms of observable features. Carnap's strongest condemnation of any subject was "That's poetry!" As a response to Carnap, I like your quotation from EP 2.193: CSP> I hear you say: 'All that is not fact; it is poetry.' Nonsense! Bad poetry is false, I grant; but nothing is truer than true poetry. And let me tell the scientific men that the artists are much finer and more accurate observers than they are, except of the special minutiae that the scientific man is looking for. One quibble I would make is about the word 'logic'. In the 19th century, logic for most people meant a course based on the Trivium. That is the way Peirce defined logic in CP 1.191: "Logic is the theory of selfcontrolled, or deliberate, thought; and as such, must appeal to ethics for its principles. It also depends upon phenomenology and upon mathematics. All thought being performed by means of signs, logic may be regarded as the science of the general laws of signs..." This definition is acceptable for readers who had studied 19th century textbooks. But in CP 1.185, Peirce wrote "Mathematics may be divided into a. the Mathematics of Logic; b. the Mathematics of Discrete Series; c. the Mathematics of Continua and Pseudocontinua." He also used the terms 'mathematical logic' (9 instances in CP) and 'formal logic' (191 instances) as synonyms for the mathematics of logic. See CP 1.29, where he mentions "mathematico-formal logic". Elsewhere, he drops the prefix 'mathematico-". Today, all our readers live in the 21st century. Mathematical or formal logic is the foundation for anything running on a digital computer. All courses about logic teach formal logic. Any discussions of the way people think use terms such as 'informal logic' or 'natural logic'. To avoid confusion for today's readers, it's important to put an adjective, such as 'normative', in front of the word 'logic'. It's not necessary to include the adjective at every occurrence, but it is importat to put it in front of the first occurrence in any context. On a related issue, the first six chapters of my 1984 book Conceptual Structures presented technical material about cognitive science and aritificial intelligence. But the final chapter 7 had the title "Limits of conceptualization". In it, I talked about the exaggerated claims for AI and the unsolved problems and open-ended questions that nobody knew how to address. Today, the earlier chapters would require a great deal of updating, but the questions in chapter 7 are as relevant as they ever were. See http://jfsowa.com/pubs/cs7.pdf . I believe that most of my chapter 7 is compatible with Turning Signs. But I also believe that it's important to distinguish several critcal terms: experience in the phaneron, mental imagery, percept, concept, icon, symbol, proposition, sentence, and word. When Peirce uses the word 'thought', it's not clear which of those words he means. For more examples about the sources of vagueness and mbiguities in language, see the first 20 slides for the talk "Natural logic": http://jfsowa.com/talks/natlog.pdf . In particular, note slide 18 about two professional lexicographers who admitted "I don't believe in word senses." Since Peirce was also a professional lexicographer who encountered the same issues, I believe that he would agree with them. Also note slide 17 about the word 'microsense', which was coined by the linguist Allen Cruse. He emphasized the tiny variations that occur in the meaning of a word even in different occurrences in the same document. For these reasons, there are serious issues about assuming that two occurrences of a word even in the same document have exactly the same "meaning". When they occur in different documents written in different years, discrepancies are even more likely. That's why careful attention to methodology is essential. The emphasis on methodology is one of Peirce's major concerns; note the 1024 instances of 'method' in CP (with various suffixes). John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Please disregard my offline note to Gary R.
I apologize for accidentally sending my note to Peirce-L. I intended it only for Gary and with a cc to Auke and Edwina. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] (offline) Nasty behavior by JAS
Gary, I agree with Auke that JAS is frustrating to the point of nastiness Trying to communicate with JAS is like beating your head against a concrete wall. See the thread attached below. JAS has a right to his own opinions. But instead of recognizing that other people are making valid observations, JAS unleashes a barrage of quotations that do not support his position. We all agree with Peirce. But we do not agree with JAS's interpretation of Peirce. And we're frustrated by his wall of irrelevant quotations. I keep emphasizing that Peirce's writings are just the tip of an iceberg. In order to understand his words, it's essential to understand his methods. That is not just my opinion, please look at the 1024 instances of method- (with various endings) in CP. I did my best in trying to get through to JAS. But instead of reprimanding him, you told me that you would cut off my access to Peirce-L. My solution: direct messages from JAS to directly to Trash. But I keep seeing copies of his messages in notes by people I respect. John --- Begin Message --- Jon Alen, You are a nasty kind of guy, trying to expose yourself by reading all kind of opinion to be corrected in others messages. Disgusting rethorical tactics. As disgusting as the neighbour cat that allways is pissing against the same doorpost. Auke > Op 27 juni 2020 om 2:12 schreef Jon Alan Schmidt : > > Auke, Edwina, List: > > Just to clarify, according to Peirce neither the absolutely indeterminate > "initial stage" (1ns) nor the absolutely determinate "final stage" (2ns) is > actual. Instead, these are ideal limits that correspond to the infinite past > and the infinite future, respectively. In the meantime, all three categories > are always operative. > > > > > CSP: We look back toward a point in the infinitely > distant past when there was no law but mere indeterminacy; we look forward to > a point in the infinitely distant future when there will be no indeterminacy > or chance but a complete reign of law. But at any assignable date in the > past, however early, there was already some tendency toward uniformity; and > at any assignable date in the future there will be some slight aberrancy from > law. (CP 1.409, EP 1:277, 1887-8) > > > > > > > > > > CSP: The state of things in the infinite past is chaos, > tohu bohu, the nothingness of which consists in the total absence of > regularity. The state of things in the infinite future is death, the > nothingness of which consists in the complete triumph of law and absence of > all spontaneity. Between these, we have on our side a state of things in > which there is some absolute spontaneity counter to all law, and some degree > of conformity to law, which is constantly on the increase owing to the growth > of habit. (CP 8.317, 1891) > > > > > > In other words, the ongoing evolution (3ns) of our existing universe is > such that it is always becoming more determinate in accordance with Gary > Richmond's vector > https://arisbe.sitehost.iu.edu/menu/library/aboutcsp/richmond/trikonic.htm of > process (1ns→3ns→2ns). > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Professional Engineer, Amateur Philosopher, Lutheran > Laymanhttp://www.LinkedIn.com/in/JonAlanSchmidt > -http://twitter.com/JonAlanSchmidt > > On Fri, Jun 26, 2020 at 2:19 PM Edwina Taborsky < tabor...@primus.ca > mailto:tabor...@primus.ca > wrote: > > > > > > Yes - I like that outline by Peirce as well. The first stage if we > > can call it that, after 'nothing', is chaos [Firstness] and then, the > > second stage is Thirdness where Mind begins to take charge and develop > > habits of organization - which permit the discrete 'bits' of Secondness to > > actually exist for more than a nanosecond, and, to reproduce as types > > [whether as chemical molecules or as cells]. > > > > Firstness continues within Thirdness; and therefore, there cannot > > be a final state of pure habits. > > > > Edwina > > > > On Fri 26/06/20 2:59 PM , Auke van Breemen peirce-l@list.iupui.edu > > mailto:peirce-l@list.iupui.edu sent: > > > > > > > > > > Edwina, > > > > > > With regard to the estimate of final stage I always am of the > > > opinion that we can only reasonably discuss it afterwards as to its true > > > nature. > > > > > > I have no religious inclinations, but can have sympathy with > > > certain religious expressions. I do like Spinoza's naturalization of > > > god. What I did value in Peirce's estimate is this fragment: > > > > > > We exist in time, which is the second stage of cosmological > > > evolution, that of thirdness, characterized by both regularity (laws) and > > > diversity (spontaneity and "chance"). As the universe evolves, laws and > > > habits develop and become more and more reg
Re: [PEIRCE-L] Re: The Pragmatic Trivium
Iris and Jerry R, The question of what Peirce knew or thought about deriving ethics from esthetics is problematical. He analyzed issues of science and logic to such a great depth, that his knowledge of esthetics would seem trivial by comparison, at least to himself. But before claiming that Peirce was incompetent about esthetics or ethics, we should compare his writings to someone who was more competent. Who might that be? Iris> Jerry Rhee asks, "Is it not obvious that Peirce was incompetent for the task imposed upon him of defining the esthetically good?" In some ways, I think he might be right: it's easier to ask questions about the pragmatic trivium as it relates to today's world than to find satisfying answers in Peirce's writings. Yes. Questions are very important. The greatest philosophers of all time have been asking such questions. Has anyone found answers about the normative sciences that are more satisfying than Peirce's? Who? CP 2.197> We shall next take up the logic of the normative sciences, of which logic itself is only the third, being preceded by Esthetics and Ethics. It is now forty-seven years ago that I undertook to expound Schiller's Aesthetische Briefe to my dear friend, Horatio Paine. We spent every afternoon for long months upon it, picking the matter to pieces as well as we boys knew how to do. In those days, I read various works on esthetics; but on the whole, I must confess that, like most logicians, I have pondered that subject far too little. The books do seem so feeble. CP has 129 passages about esthetics. He said that he read various works on the subject, but he found those books "so feeble". Can anyone point to books that are not "feeble" according to the standards that Peirce set for himself? John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Mind fusion: Inter-brain neural synchronization
I came across a recent article that sheds some light on what Peirce may have meant by "fusing minds" that share a common experience. See below for the abstract of the article, the URL, and some excerpts. >From Peirce's brief comments about that issue, we can only guess what he meant. But the issues mentioned below (and discussed in more detail in the full article) are intriguing. Peirce very likely participated in some such activities. He may have had a feeling (an experience in his phaneron) for which the word 'fusion' might have been a good description. And by way, this article is just one example of the kind of evidence that can help us interpret what Peirce meant. He couldn't have imagined his own brain waves synchronized with others, and neither could we -- until we read about actual measurements in an fMRI scanner. His writings, of course, are essential evidence. But the writings are just the tip of an immense iceberg. They represent a tiny fraction of what he knew, felt, thought, and did. To interpret those writings, we need to study as much as we can about his life, his reading, and the effects he had on his contemporaries and on his readers up to the present day. As we know very well, Peirce had deep insights that anticipated and often went far beyond the insights of scientists and philosophers up to and including the present. Just reading a recent article that has no mention of Peirce might give us a crucial bit of evidence that can enable us to interpert something he wrote over a century ago. John --- Authors: Ana Lucía Valencia & Tom Froese (2020) Title: What binds us? Inter-brain neural synchronization and its implications for theories of human consciousness Abstract: The association between neural oscillations and functional integration is widely recognized in the study of human cognition. Large-scale synchronization of neural activity has also been proposed as the neural basis of consciousness. Intriguingly, a growing number of studies in social cognitive neuroscience reveal that phase synchronization similarly appears across brains during meaningful social interaction. Moreover, this inter-brain synchronization has been associated with subjective reports of social connectedness, engagement, and cooperativeness, as well as experiences of social cohesion and self-other merging. These findings challenge the standard view of human consciousness as essentially first-person singular and private. We therefore revisit the recent controversy over the possibility of extended consciousness and argue that evidence of inter-brain synchronization in the fastest frequency bands overcomes the hitherto most convincing sceptical position. If this proposal is on the right track, our understanding of human consciousness would be profoundly transformed, and we propose a method to test this proposal experimentally. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7288734/ Behavioural studies in psychology have consistently shown that synchrony during joint action (such as rocking, marching, walking, or dancing) promotes cooperative ability and increases empathy, liking, rapport, and prosocial behaviour (Hari and Kujala 2009; Hove and Risen 2009; Wiltermuth and Heath 2009; Valdesolo et al. 2010; Valdesolo and DeSteno 2011; Mogan et al. 2017). From such studies, it has been suggested that dynamics of neuronal coupling could play an important role in the emergence of such interactive synchrony (Wilson and Wilson 2005; Dumas et al. 2011; Hasson et al. 2012). Importantly, the development of the hyperscanning technique by Montague et al. (2002) has allowed for the measurement and analysis of such inter-brain dynamics (Babiloni and Astolfi 2014; Czeszumski et al. 2020). Using functional magnetic resonance imaging (fMRI), functional near-infrared spectroscopy (fNIRS), electroencephalography (EEG) or magnetoencephalography (MEG), hyperscanning paradigms simultaneously record the brain activity of two or more individuals, thus permitting the assessment of neural activity during real-time social interaction (Babiloni and Astolfi 2014; Czeszumski et al. 2020)... Greater neural synchronization also appeared between subjects completing a puzzle together, compared to when the same subjects completed identical puzzles individually, or watched others complete the puzzle (in front of them or through video recording) (Fishburn et al. 2018). A similar study revealed inter-brain synchronization between two individuals when singing together, but not when singing individually yet close to each other (this effect was not observed in random pairs) (Osaka et al. 2015) _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe
RE: [PEIRCE-L] Peirce's Way of Thinking (was Theory and Analysis of Semeiosis)
Terry, That's a good way to explain the issues -- especially because you and Peirce illustrate your interpretations with concrete examples. A definition or discussion of any new term must have one or more examples to show (1) that the term is not vacuous, and (2) the kinds of features or characteristics a typical instance may have. Examples from astronomy illustrate the issues very clearly. Immediately after the Big Bang, the universe was too hot for any living things to exist. But today, astronomers are routinely seeing and interpreting marks from billions of years ago as tokens of various types. Historians and anthropologists have shown how people from different cultures have interpreted similar marks in the sky as tokens of very different types. Although some of their interpretations may have been fanciful, much of what they said was true as far as it was tested in practice. The Polynesians, for example, were using the stars to guide their travels across the Pacific for centuries before the Europeans ventured far from shore. John TLR> I find it helpful to think of at least some possible signs or protosigns or pre-incarnate signs as being cognitively incomplete signs. Familiar example from PWP 104 & CP 2.304: An index is a sign which would, at once, lose the character which makes it a sign if its object were removed, but would not lose that character if there were no interpretant. Such, for instance, is a piece of mould with a bullet-hole in it as sign of a shot; for without the shot there would have been no hole; but there is a hole there, whether anybody has the sense to attribute it to a shot or not. Another striking (pun intended) example are the gravity waves emitted by the inspiral collision of two neutron stars identified in B. P. Abbot, et al.,GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral. Physical Review Letters 119, no. 161101 (October 16, 2017): 1-18. The shot and hole in the mould thus are manifest or incarnate causal-indexical signs but they remain cognitively incomplete unless and until somebody has the sense to attribute it to a shot, So too are the gravity waves and the inspiral collision of neutron stars that caused them manifest incarnate empirical signs until 130 million years later and 780 quintillion miles away astronomers on Earth had the sense to detect the waves and attribute them to that inspiral collision, thus cognitively completing those causal-indexical empirical signs as manifest, incarnate, actual interpretants in the mind of an Interpreter. _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Peirce's Way of Thinking (was Theory and Analysis of Semeiosis)
Robert, That's an excellent summary of the issues. For my comments, I divided it in three parts: > The representamen should therefore be rehabilitated in order to confine it to the universe of possibilities andthe term sign should be reserved to the incarnate form. This is the reason why in my formalization process, I called these possible signs "protosigns". Protosigns are the a priori forms of all possible signs and the distinction must be made carefully with the "actual" signs that are these incarnate signs. And it's essential to note that the possible signs include all the hypotheses (patterns) in Peirce's universe of possibilities. Because of continuity, that universe is uncountably infinite. But the set of available words for incarnating signs is finite. Therefore, the process of incarnating signs will always lose information: a many to one mapping cannot preserve distinctions among the many. > The question will be: "Are we talking about the forms a priori in the universe of possibilities or of these same forms inscribed in the real world"? The form can only be represented by becoming a sensitive form in the real world and be perceived to be communicated. Yes. And that communication depends on a mapping from an uncountable infinity to a finite set of words. The exact meaning in any particular context depends on an open-ended variety of "collateral experience" shared by the speaker and listener in any particular context. Since no two contexts and the people in them can be identical, discrepancies are inevitable. (The metaphor of "mind fusion" is too vague to be useful in this discussion.) > This shows how literalism can function as an obstacle to a truly scientific approach, disconnecting Peirce's semiotics from its pragmatism through conceptualist arguments and offering alternatives devoid of practical applications. Yes. The principle of "charity" implies that the listener must make some allowance for the inevitable ambiguities. That allowance is some implicit, context-dependent proposition. But no two occurrences of a word have exactly the same context, even in a single document. If we're lucky, those implicit propositions may be small enough to be irrelevant. But when the sentences occur in different documents, written on different occasions for different purposes, we can't depend on luck. Fundamental principle: The meanings of words depend on context. Charity may provide some useful background information, but there is no guarantee that the charitable information will be identical for different sentences, even in the same document. For different documents, written on different days, months, years, differences are inevitable. Any information contributed by charity must be made explicit, and it must be carefully analyzed for relevance and reliability. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Communicating an Idea (was commens and commons)
Gary F, Edwina, Jon AS, List, I am delighted to read about GF's applications of Peirce's writings to the issues that Edwina copied: "the continuity between the processes of semiosis and those of life itself" and "the recursive and nonlinear nature of those processes". In 2006, I wrote an article on "Peirce's contributions to the 21st century", which summarized a few of the many ways in which Peirce not only anticipated, but frequently *improved upon* his successors: http:/jfsowa.com/pubs/csp21st.pdf . Some of the writings by Susan Haack, John Deely, Terry Deacon, and Frederick Stjernfelt influenced that article. In the 14 years since then, I have found many more examples. Last week, I presented a talk (virtually) at the European Semantic Web Conference in which I emphasized ways in which Peirce's work can help guide the future developments. Following is an extended version of the slides I presented: http://jfsowa.com/talks/escw.pdf . As Peirce said, the meaning of a general principle always lies in the future. I believe that is an important area for discussions on Peirce-L. I also agree with GF on the following issues: GF> I look forward to your [JAS's] complete transcription of R 787. It occurs to me that much of your recent contribution to the list and to Peircean scholarship has been to restore the integrity of Peirces manuscripts... And the following is especially important for students who can't afford the exorbitant costs of the published versions: GF> Ive tried to contribute to the restoration by using the manuscript images put online by Jeff Downard and the SPIN project to produce an online edition of the Lowell Lectures of 1903: http://www.gnusystems.ca/Lowells.htm But I must add that I have much less faith in Jon's plan to produce a coherent synthesis of Peirce's later writings. Peirce's ideas on every one of his major interests were constantly growing. He tried several times to write a book that summarized his ideas. But every time he tried, his ideas developed so rapidly, that the later sections made the earlier sections obsolete. If Peirce himself couldn't write a coherent synthesis, I don't believe that anyone else could or should attempt it. But I'll stop on this note of agreement (at least for now). John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Peirce's Way of Thinking (was Theory and Analysis of Semeiosis)
Bernard Morand summarized the meaningful content of this debate in one sentence plus one image: BM> In place of the old, often recurring debates on this subject I propose to muse over a painting from René Magritte entitled "Le sens des réalités" That image, which shows a large boulder suspended in the middle of the clouds, is an excellent illustration of the way JAS assembles "fireworks of quotations" (RM's phrase) to state a hypothesis (AKA guess) and defend as if it were gospel truth. JAS does some useful work in assembling a collection of quotations about some topic. I have found many of his assemblies interesting and thought provoking. JAS has every right to state his own opinions about how those quotations are related. But other people may have different opinions that are equally interesting and thought provoking. But all those opinions are just hypotheses (AKA abductions, AKA guesses). For them to be considered as more than a wild guess, much more work must be done. JAS> as I have pointed out before, in Peirce's entire vast corpus of writings he used "commens" only twice and "commind" only once; and all three occurrences are in two consecutive paragraphs of a single 1906 letter... he explicitly defines it as a "mind" that results from the fusing or welding of distinct minds... First point: There is a huge difference between a metaphor and a definition. The verbs 'fuse' and 'weld' state actions that are performed on solid objects of metal or glass that are heated to the point where they begin to melt. Then the objects are forced together and allowed to cool. As a result, they stick together as one object. Second: Minds are not solid objects, and the verbs 'fuse', 'weld', 'heat','force', 'cool', and 'stick' can't be applied, literally, to minds. Whatever meaning Peirce may have intended is at best a rather vague, but colorful metaphor. Third: Peirce was a logician, mathematician, scientist, and engineer. He knew how to state precise definitions, use them in complex reasoning, and solve theoretical as well as practical problems. Fourth: The fact that Peirce used that metaphor in just two paragraphs of a single letter indicates that he did not consider it to be an important part of his system of logic or semiotic. Therefore, the opinion JAS stated is a dubious hypothesis about a minor comment by Peirce. Therefore, in this tiresome thread, JAS is the guilty party who has extended it beyond any reasonable length. Unfortunately, this is just one of many such threads John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Peirce's Way of Thinking (was Theory and Analysis of Semeiosis)
Jon AS, Gary F, and Edwina, No two people think alike, and anybody as complex and insightful as Peirce has a wide range of different ways of thinking. I agree that discussions about methodologies outside of any particular context are of minor interest to this list. But the most important methodologies that are relevant to the interpretation of Peirce's writings are Peirce's own. The interpretation of what any author said or did depends critically on "collateral knowledge" about that author's way of thinking. I won't attempt to explain Peirce's metaphor of "mind fusion", but it certainly includes much more than a list of quotations. . GF> The only 'method' I've seen that JAS outlines, is to provide quotations from Peirce texts. Unfortunately, that's true. Peirce drew a distinction between a naturalist and a scientist. A naturalist describes appearances and classifies specimens on the basis of their resemblance to other specimens. Jon processes quotations as if they were butterflies -- sticking pins through them and displaying them in a sample tray. ET> When some of us, for example, ask repeatedly for real world examples of the interpretations offered - and don't get them, are we supposed to accept that the conclusions of this rather authoritarian method... must be accepted as valid? That's my primary complaint. Naturalists provide an important service in collecting data. But scientists take the next steps of induction and abduction to develop theories. Even more important than the theories is the testing by deduction, prediction, and observation of multiple *examples*. Without testing, the theories are unfounded hypotheses. GF> newer members of the list who may not immediately recognize the futility [of some of these debates]. They deserve more substantial content on the Peirce list, and indeed require it if they are going to learn as much from participation Absolutely! We have to demonstrate that studying Peirce involves much more work than just butterfly collecting. He wrote many articles about methodology, and they all involve the fundamental issues of relating perception to action -- and the intermediate steps of induction, abduction, deduction, testing, observation, and repeat. That kind of hard work can only be demonstrated and *learned* by applying Peirce's ideas to serious problems. JAS> I continue to find these strictly methodological criticisms tiresome... The only way to ascertain Peirce's way of thinking in the first place is interpret his words according to is way of thinking. It's certainly tiresome. We have to get out of this rut of just butterfly collecting. William James spent half a century listening to and reading Peirce's words, and he never grasped the principles that Peirce spent years in trying to teach him. The reason why James couldn't understand the words is that he never worked his way through the words to the thinking behind them. JAS> quoting Peirce's own words is the best--really, the only--method for supporting one's interpretations of his writings No That statement shows a hopelessly misguided interpretation of everything Peirce wrote. His words are necessary as the starting point. But if they were sufficient, William James would have been the world's leading expert on Peirce. It's impossible to understand any text on logic, mathematics, or science of any kind without doing the homework -- the exercises at the end of each chapter of a textbook or the detailed analysis of the mathematics in a research paper. Peirce did that kind of work on every subject he studied from childhood to the end. Peirce developed his ideas through a lifetime of working on difficult problems in mathematics, science, logic, and engineering -- starting with his father in early childhood, with his Sunday dinners with the leading intellectuals who visited Harvard, his 30 years of science and engineering with USCGS, his teaching at JHU, and his various lectures and discussions with colleagues. Since you are an engineer, you must have done a similar kind of homework to earn a degree. Since then, you must have done some related work on the job. I'm sure that you learned much more by finishing a difficult engineering problem than you knew by just reading a book. The same principle is true in studying Peirce. Just reading his words is sufficient for a superficial knowledge -- the ability to parrot the words. But understanding requires serious work in applying his writings to some challenging problems. I've been doing that in books, articles, and lectures for years. Following is the most recent lecture in which I applied some of Peirce's ideas: http://jfsowa.com/talks/eswc.pdf . The last page of eswc.pdf has more references to articles that apply Peirce's ideas to various problems in logic, linguistics, artificial intelligence, and computer software. John _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to th
[PEIRCE-L] Quantification (was Pragmatic Theory Of Truth
David,JFS> Until 1270, bell ringers depended on sun dials and hour glasses. But by 1300, every town in Europe of any size had a church with a clock that automatically rang the bells. DP> Do you have a reference for that? I recommend a rather short book (245 pp.): Crosby, Alfred W. (1997) The Measure of Reality: Quantification and Western Society, 1250-1600, Cambridge University Press. Following are two reviews of the book: https://www.latimes.com/archives/la-xpm-1997-01-26-bk-22112-story.html https://www.stolaf.edu/other/ql/crosby.html There is, of course, much more to be said about all these issues. Quantification alone would not be sufficient for the great advances that took place during those centuries, but without quantification the advances in science would not have been possible. The great universities that were established in the 12th c and the printing press in the 15th c were also essential. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Re: Pragmatic Theory Of Truth
Jon A, Those three criteria (copied below) are Plato's. Aristotle's father was a physician, and he trained his son for the first 18 years. Aristotle admitted that Plato's mathematical forms are perfect, but he recognized the need to value and deal with the facts of life and the world. Aristotle's writings on biology are more voluminous than his writings on philosophy. Philo Judaeus of Alexandria was an early neoplatonist, who wrote many volumes to reconcile the Torah with Greek philosophy. Until the 13th century, most philosophers and theologians were neoplatonists, who accepted as much of Aristotle's writings as they could force into a Platonic framework. But the rediscovery of Aristotle and the commentaries by Averroes (Ibn Rushd), originally from Arabic translations and later from the original Greek, revolutionized theology (Aquinas) as well as science (Roger Bacon). Until 1270, bell ringers depended on sun dials and hour glasses. But by 1300, every town in Europe of any size had a church with a clock that automatically rang the bells. Aristotle made imperfections safe for philosophy, science, and engineering. With his three universes, Peirce reconciled Plato (mathematics) and Aristotle (actuality). Mathematics includes the universe of possibilities (all hypotheses) and necessities (all theorems provable from the hypotheses). The laws of science are mathematical theorems whose hypotheses have been tested to a high level of confidence. John __JA> According to John Dewey, it is because of the human quest for perfect certainty that philosophy has inherited three problematic viewpoints: the first, that certainty, security, can be found only in the fixed and unchanging; the second, that knowledge is the only road to that which is intrinsically stable and certain; the third, that practical activity is an inferior sort of thing, necessary simply because of mans animal nature and the necessity for winning subsistence from the environment. John Dewey The Quest for Certainty Jon A, Those three criteria (quoted below) are Plato's.Aristotle's father was a physician, and he trained his son for the first 18 years. Aristotle admitted that Plato's abstract forms were perfect, but he recognized the need to value and deal with the imperfections of life and the world.Philo Judaeus of Alexandria was an early Neoplatonist, who wrote many volumes to reconcile the Torah with Greek philosophy._ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Re: Theory and Analysis of Semeiosis (was Destinate Interpretant and Predestinate Opinion)
Gary R, Jon AS, and Robert, There are many ways of thinking, and no method is ideal for all purposes. But when trying to understand what Peirce wrote, it's essential to interpret his words according to his way of thinking. GR> I must immediately add that I do not see Jon as distorting Peirce's thinking in any way, and in particular in consideration of the type-token distinction and the commens. In my opinion, Jon's use of quotations has been apt and judicious in supporting his interpretations. The reason why you always agree with Jon is that you both happen to think in the same way. Robert and I are not claiming that your way is a bad way. We're just saying that it's not the way Peirce was thinking. Therefore, it's unreliable as a method for deriving any conclusions from his writings.RM> I think you [JAS] are distorting Peirce's thinking in this way, and I am clearly opposed to it. I also think you are trying to compensate for the weakness of your arguments with incessant "literalist" activism. Yes. I strongly agree with Robert's objections to a "literalist' method of just quoting words. See the excerpts from CP 1.6 and 1.7 (copied below). Note Peirce's emphasis on mathematics and science, and his point about metaphysicians. Since Jon has an engineering background, he would have had enough training in science and mathematics that he could learn to appreciate Peirce's way of thinking. Unfortunately. Peirce's late writings present his conclusions without going into the details of how he derived his results. Those writings are good for learning Peirce's conclusions, but they don't show how to draw any further inferences from them. To understand Peirce's way of analyzing any subject and systematically working through the evidence, I suggested his book _Photometric Researches_ (1878). That book is an excellent companion to his article "How to make our ideas clear", which was also published in 1878. Together, they show Peirce's mind at work. For 16 pages of excerpts from that book, see http://jfsowa.com/peirce/PRexcerpts.pdf . That is sufficient for a start, but browsing through the rest of the book is also useful. John CP 1.6: The works of Duns Scotus have strongly influenced me. If his logic and metaphysics, not slavishly worshipped, but torn away from its medievalism, be adapted to modern culture, under continual wholesome reminders of nominalistic criticisms, I am convinced that it will go far toward supplying the philosophy which is best to harmonize with physical science. But other conceptions have to be drawn from the history of science and from mathematics. CP 1.7. Thus, in brief, my philosophy may be described as the attempt of a physicist to make such conjecture as to the constitution of the universe as the methods of science may permit, with the aid of all that has been done by previous philosophers. I shall support my propositions by such arguments as I can. Demonstrative proof is not to be thought of. The demonstrations of the metaphysicians are all moonshine. The best that can be done is to supply a hypothesis, not devoid of all likelihood, in the general line of growth of scientific ideas, and capable of being verified or refuted by future observers Gary R, Jon AS, and Robert,There are many ways of thinking, and no method is ideal for all purposes. But when trying to understand what Peirce wrote, it's essential to interpret his words according to his way of thinking.GR> I must immediately add that I do not see Jon as distorting Peirce's thinking in any way, and in particular in consideration of the type-token distinction and the commens. In my opinion, Jon's use of quotations has been apt and judicious in supporting his interpretations. The reason why you always agree with Jon is that you both happen to think in the same way. Robert and I are not claiming that your way is a bad way. We're just saying that it's not the way Peirce was thinking.RM>Gary,We've gone over these issues before, and you keep missing the point.GR> I must immediately add that I do not see Jon as distorting Peirce's thinking in any way, and in particular in consideration of the type-token distinction and the commens. In my opinion, Jon's use of quotations has been apt and judicious in supporting his interpretations. Peirce's writings are an important *starting point* . They represent the end result of deep thinking by a brilliant mathematician, logician, scientist, and philosopher who was -- in some areas -- a century ahead of his time. Just reading his writings provides a useful, but superficial overview of what he thought.Benjamin P. taught Charles mathematics, Greek, and Latin from early childhood._ _ _ _ _ _ _ _ _ _ ► 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...
RE: [PEIRCE-L] Theory and Analysis of Semeiosis (was Destinate Interpretant and Predestinate Opinion)
Terry, I agree that Peirce's "mind fusion" is a good metaphor. It reminds me of Spock's "mind meld" in Star Trek. But the Trekkies don't explain how the Vulcan neural system (in conjunction with the human neural system) could establish that meld. TR> Im delighted to find this remark in Peirce! For my $0.02, thinking of Peirces fusion as harmoniously resonant semiosis (very large SNR) e.g., as in all waveforms from music to radiation and gravity, and in the cognitive commens of sentient and sapient community, wed be fine if dissonant discord over our differences werent, to put it mildly these days, so dissonant and discordant. But what does it mean? If two people don't have sufficient "collateral experience" to understand one another, they don't do a Vulcan mind meld. What they do is to find some way to get the experience. If it's musical, they practice performing, listening to, and dancing to music. If it's something physical, like playing Cricket, they may have to watch a game with somebody explaining each move. If it's a color, they have to look at colored things or pictures of them. If it's some scientific theory, they have to read a book , take a course, or do some experiments. In each case, people can gain the collateral experience by doing something. Just repeating or quoting Peirce's words is insufficient to explain what he meant. It's necessary to explain "mind fusion" in terms of some method for getting the experience. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Theory and Analysis of Semeiosis (was Destinate Interpretant and Predestinate Opinion)
Robert and Jon, To determine whether students understand a topic, teachers often ask them to explain it in their own words. Since much of Peirce's terminology is radically different from common usage today, it would be a good exercise to translate or at least explain his comments in 21st c. English. For example, consider Jon's point: JAS> Again, Peirce explicitly defines "the commens" as "that mind into which the minds of utterer and interpreter have to be fused in order that any communication should take place ... It consists of all that is, and must be, well understood between utterer and interpreter, at the outset, in order that the sign in question should fulfill its function" (EP 2:478, 1906, bold added). In other words, the commens is clearly not "universal" and "independent of all these minds"; on the contrary, it is the one mind into which two or more minds are "welded" or "fused" by one sign. Peirce's use of the words 'mind' and 'fuse' is highly unusual. I don't believe that anyone other than Peirce has ever used those two words to explain how people communicate. For the word 'it' in "It consists of all that is, and must be, well understood between utterer and interpreter, at the outset, in order that the sign in question should fulfill its function", consider the following substitutions: (1) presupposition. (2) background knowledge. (3) common assumptions. (4) cultural background. (5) experience with the subject matter. Are any of those five phrases (or some combination of two or more) sufficient to explain how utterer and interpreter can understand one another? If not, why not? If so, what aspects of the answer correspond to Peirce's use of the words 'mind' and 'fuse'? In fact, Peirce's own ethics of terminology would require him to tailor his terminology to the common usage of the day. I doubt that Peirce himself would continue to talk about fusing minds if he were among us. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Three kinds of logic (was Sign relations
Jon A, I agree that (NEM 4:20) is one of Peirce's best definitions of 'sign'. I also believe that it is his clearest definition of 'formal semiotic'. But in talking about Peirce's logic. it's essential to distinguish three distinct kinds of logic that he developed in detail: mathematical logic, formal semiotic, and normative logic. Elsewhere. he wrote that mathematical logic is the smallest part. But without mathematical logic as the foundation, formal semiotic would not be possible. And without formal semiotic, normative logic would not be possible. A huge amount of confusion on Peirce-L could be avoided by distinguishing which of the three senses of 'logic' is intended in any occurrence of the word in Peirce's writing. JA> One of Peirce's clearest and most complete definitions of a sign is one he gives in the context of providing a definition for logic, and so it is informative to view it in that setting. CSP> Logic will here be defined as formal semiotic. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C. It is from this definition, together with a definition of formal, that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non-psychological conception of logic has virtually been quite generally held, though not generally recognized. (NEM 4, 2021). Note the word 'here' in the first sentence: "Logic will here be defined as formal semiotic." That does not rule out other senses of the word 'logic' in other writings. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Theory and Analysis of Semeiosis (was Destinate Interpretant and Predestinate Opinion)
Jon, Peirce devoted his life to developing mathematical-logical methods for making all the sciences, including philosophy, as clear and precise as possible. JAS> This post ... consists mostly of Peirce's words, with a few of mine interspersed, but I hope that the arrangement enables it all to make sense. I have never seen any paraphrase of Peirce's words that was clearer or more precise than his own. The only way to make words more precise is to use the method he developed and presented to the world: logic. And he showed how to use logic by applying it to numerous examples. If you don't want to use logical notations, you can use specific examples that show how Peirce's words (or yours) are applied in practice. Without examples or logical notation, piling up words upon words upon words creates more confusion than it can ever clarify. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] The sciences: mathematical and classificatory
Robert and Jon, I was browsing through and deleting some old email, and I came across the points quoted below. I also remember that Jon claimed that Peirce's word 'classificatory' for normative science made it sound trivial. But there are only three kinds of science: (1) mathematical, (2) classificatory. and (3) some combination of #1 and #2 in various proportions. Physics, after Galileo and Newton, became highly mathematical, but it has always depended on classification for its choice of hypotheses. Chemistry began as the classificatory science of alchemy, but it became more and more mathematical as it used physics to interpret and develop its study of the phenomena. And biology was almost purely classificatory until the late 20th century. As for phaneroscopy, Peirce derived his semeiotic by applying mathematics to the analysis of experiences in the phaneron. (See R602, Photometric Researches, and the sections of CP vol. 1 which the editors labeled 'Phenomenology'.) Pure mathematics (which includes mathematical logic) is the only science that is purely mathematical. But mathematics in practice depends on the classificatory sciences for the choice of various hypotheses to study. As for phaneroscopy, Peirce derived his semeiotic by applying mathematics to the analysis of experiences in the phaneron. (See R602, Photometric Researches, and the sections of CP vol. 1, which the editors labeled 'Phenomenology'.) That is why I used the term "formal semeiotic" for the methods Peirce used to derive his categories. And I agree that mathematical category theory is a powerful method for analyzing the structure. I believe that it makes a strong case for the label "formal". The next step after deriving formal semeiotic is to use it to classify the open-ended variety of phenomena labeled aesthetics, ethics, and rhetoric -- essentially every book on those subjects from Aristotle to the present. All the work on government and legal matters combines ethics and rhetoric with some logic (mostly limited to Aristotle's version). All that work is classificatory, and it's by no means trivial. John --- RM> Thank you very much John for these texts I did not ... I could have known the R602 since I had access to microfilmed manuscripts, but at the time, I was mainly interested in sign classifications and I did not think that this ms could contain such assertions . I particularly remember this sentence: "Phaneroscopic research requires a previous study of mathematics. The type of mathematics depends on the application, and there is no limit on the amount and depth of mathematics that may be needed" that I have had the opportunity to show to all those who will tell me that it does not have the ability to access the elementary definitions of category theory ... "Scientific research is a fighting sport".--JFS> Your summary of the issues is very good, and I strongly agree with the need for examples. In a search for examples, I went back to _Photometric Researches_, which I believe is essential for understanding the development of Peirce's philosophy. It's not an accident that it was published in 1878, the same year in which "How to make our ideas clear" was published in _Popular Science Monthly_. (Peirce met the editor of that magazine when they were both in Sicily, observing the solar eclipse.) The title of Chapter 1 is "The sensation of light." See http://jfsowa.com/peirce/PRexcerpts.pdf . On page 2, he wrote "Light considered purely as something in the external world may be called _noumenal light_. Light considered as an appearance, and as a function of the sensation, such that it is measured by the convention just mentioned, may be termed _phenomenal light_. Photometry generally concerns phenomenal light..." Just reading a few pages (my PRexperts, for example) is enough to show how deeply Peirce's phaneroscopy is grounded in his scientific and engineering research. It's also important to compare that research with R602, which was written after his 1903 classification of the sciences. See http://jfsowa.com/peirce/r602.htm : p 12> But preliminary to normative science, which is essentially classificatory, stop to take that well in, I beg you, gentle reader, there should be a nomological science, which shall make out all the different indecomposable elements which enter into everything that is conceivably possible, discriminates them with care, and shows how they can be varied and combined. This science I hesitate to call phenomenology after Hegal, for fear of marring his peculiar conception of it; and therefore, though I think it is essentially the same thing under a somewhat different aspect, I will name phaneroscopy. p 13> It is the science of the different elementary constituents of all ideas. Its material [m13] is, of course, universal experience, experience I mean of the fanciful and the abstract, as well as of the concrete and real. Yet to suppose that
Re: [PEIRCE-L] Sign Relations
Biosemiotic has two branches: zoosemiotic and phytosemiotic. For a review of the literature about plants up to 2016, see "Intelligence, cognition, and language of green plants", by Anthony Trewavas: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4845027/ The Wikipedia article on plant perception also has a good survey of the issues: https://en.wikipedia.org/wiki/Plant_perception_(physiology) . Among many other examples, it mentions the sunflower. Some trees recognize their own seedlings, and they can exert some control over soil humidity and nutrients that can give their own seedlings a competitive advantage. These are among the many reasons why an exclusive emphasis on human cognition does not provide enough perspective on the issues of semeiosis. The fundamental definitions should be broad enough to cover "any scientific intelligence", by which Peirce meant the ability to learn from experience. As examples, Peirce mentioned dogs and parrots. But plants can also learn from experience, and they can communicate with other plants of the same or different species. When you mow the lawn and enjoy the pleasant smell of freshly cut grass, you are detecting the alarm call of the grass plants. (I apologize if that point disturbs your enjoyment.) John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] The plethora of Interpretants
Jon and Auke, General principle: Never assume that Peirce was unaware of or hadn't considered some issue. Peirce had studied Aristotle in depth, and he would certainly be familiar with the first paragraph of _On Interpretation_: Aristotle> First we must determine what are noun (onoma) and verb (rhêma); and after that, what are negation (apophasis), assertion (kataphasis), proposition (apophansis), and sentence (logos). Those in speech (phonê) are symbols (symbola) of affections (pathêmata) in the psyche, and those written (graphomena) are symbols of those in speech. As letters (grammata), so are speech sounds not the same for everyone. But they are signs (sêmeia) primarily of the affections in the psyche, which are the same for everyone, and so are the objects (pragmata) of which they are likenesses (homoiômata). On these matters we speak in the treatise on the psyche, for it is a different subject. (16a1) JAS> One difference that I have with Peirce is that I consider the written and spoken versions of the same language to be two distinct systems of signs. AvB> This is an interesting point. I entertained the same idea as you did until I recognized that we may distinguish legisigns in two classes. 1. legisigns by comparison: the sinsign icons belong to a family either of visual or auditive signs 2. legisigns by convention. legisigns of two families (visual and auditive) are conjoined and recognaized as the same type. The bridge is furnished by the very same symbol called forth by either of the signs, i.e. the spoken and written forms of horse. This distintion is similar to the point that Aristotle was making. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Destinate Interpretant and Predestinate Opinion
Robert, I strongly agree with the issues you raised and your interpretation of them.RM> it may not be a good methodology to give such a preference for interpretation in semiosis without focusing the analysis on the whole process... how individual semiosis articulates with global semiosis?Yes. While observing the solar eclipse of 1870 (in Sicily), Peirce was impressed by the importance of the international scientific community in making observations, interpreting results, proposing hypotheses, communicating them, and testing them. RM> signs being obligated interfaces (a medium for the communication of a form for example) between the outside world and the inner world it is necessary to grasp by "a same movement of thought", the before-sign and the after-sign with the physiological perception of the sign as a connection between these two worlds.Yes. The signs we use for interpreting "experiences in the phaneron" include a huge number that we inherited from our culture. Some words are recent creations and others have an ancestry of thousands of years. Our words for wheel and axle, for example, are derived from Proto-Indo-European roots for circle (PIE 'kwel') and shoulder (PIE 'aks'). Some estimates place the invention of the wheel about 3400 BC -- based on archaeology and linguistics. CSP> But while I say this, it must not be inferred that I regard consciousness as a mere "epiphenomenon"; though I heartily grant that the hypothesis that it is so has done good service to science. To my apprehension, consciousness may be defined as that congeries of non-relative predicates, varying greatly in quality and in intensity, which are symptomatic of the interaction of the outer world -- the world of those causes that are exceedingly compulsive upon the modes of consciousness, with general disturbance sometimes amounting to shock, and are acted upon only slightly, and only by a special kind of effort, muscular effort -- and of the inner world, apparently derived from the outer, and amenable to direct effort of various kinds with feeble reactions; the interaction of these two worlds chiefly consisting of a direct action of the outer world upon the inner and an indirect action of the inner world upon the outer through the operation of habits. If this be a correct account of consciousness, i.e., of the congeries of feelings, it seems to me that it exercises a real function in self-control, since without it, or at least without that of which it is symptomatic, the resolves and exercises of the inner world could not affect the real determinations and habits of the outer world. I say that these belong to the outer world because they are not mere fantasies but are real agencies." CP (5.493 ,Pragmatism, 1906) RM> But this fundamental text alone does not solve the question posed by Edwina because it obviously lacks the commens, this concept that dominates both the emission of signs and their receptions. A concept that is added to this text allows us to situate Peirce's semiotics in the social field, his study in sociology and his practice among social practices. But the commens as Peirce presents it is a general framework in which individual signs are supposed to cooperate to arrive at a kind of social semiosis whose dynamics feed on individual variations... Unfortunately, Peirce's discussions of semeiosis do not include enough examples to illustrate and clarify his methods for deriving his terminology and applying it in practice. That is why I suggested his _Photometric Researches_ as an extended series of examples that show how he analyzed observations, used the terminology and results of other scientists, and communicated his results to the scientific community. He did the research from 1872 to 1875, shortly after his experiences with the scientific community during the solar eclipse. He published that book in the same year as the article "How to make our ideas clear" in the _Popular Science Monthly_. And the editor of that magazine was one of the people he met in Sicily during the solar eclipse. The book and the article don't use the abstract terminology he developed 20 or 30 years later, but they more clearly show his individual and social thinking processes that inspired that terminology. For my selection of 16 pages from his 273-page book, see http://jfsowa.com/peirce/PRexcerpts.pdf . The complete book has many more examples of the way Peirce related his own observations to the work by the entire community of scientists. John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-man
Re: [PEIRCE-L] Lambda expressions (was Parts of Propositions
Jon AS, I noticed that I hadn't answered the question about incomplete propositions. In the 1930s, the logician Alonzo Church introduced lambda expressions as a notation for deriving a predicate (rheme) from a proposition. In effect, Peirce invented "lambda expressions" about 40 years before Church: every proposition with N-blanks (for Peirce) is equivalent to an N-adic lambda expression for Church and all logicians following Church.CSP: In the first place, I say that every relationship concerns some definite number of correlates ... We may express this as saying that every relation has a definite number of blanks to be filled by indices, or otherwise ...In a complete proposition there are no blanks. (CP 3.464-465, 1897)CSP: By a rheme, or predicate, will here be meant a blank form of proposition which might have resulted by striking out certain parts of a proposition, and leaving a blank in the place of each, the parts stricken out being such that if each blank were filled with a proper name, a proposition (however nonsensical) would thereby be recomposed. (CP 4.560, 1906)JAS> Similar passages include CP 2.379 (1902), CP 2.272 (1903), and CP 4.454 (1903). Rhemes as incomplete propositions are monads, dyads, triads, etc. based on the number of blanks; but a complete proposition is a medad, because it has no blanks.fA proposition p: "2 + 2 = 4"A rheme derived from p: "_ + _ = _"A lambda expression derived from p: "(λ x, y, z) (x + y = z)"Peirce was ahead of his time, and his pioneering terminology may be confusing to a modern reader. The developments in logic during the 20th c and 21st c reinvented and built on many ideas that were introduced by Peirce. In some cases, they went beyond Peirce. But in other cases, Peirce still has a great deal to teach the 21st c logicians.In any case, studying 21st c logic is extremely helpful for understanding what Peirce meant and the importance of his insights for developments today.John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Destinate Interpretant and Predestinate Opinion
Jon, CP 4.240 must be read in the context of R602, p. 12: "But preliminary to normative science, which is essentially classificatory, stop to take that well in, I beg you, gentle reader, there should be a nomological science, which shall make out all the different indecomposable elements which enter into everything that is conceivably possible, discriminates them with care, and shows how they can be varied and combined. This science... I will name phaneroscopy.CSP: This is, at most, to say that it has to call in the aid of mathematics; that it has a mathematical branch. But so much may be said of every science. There is a mathematical logic, just as there is a mathematical optics and a mathematical economics. Mathematical logic is formal logic. Formal logic, however developed, is mathematics. Formal logic, however, is by no means the whole of logic, or even its principal part. It is hardly to be reckoned as a part of logic proper. (CP 4.240)JAS> Formal/mathematical logic is not the "principal part" of logic as semeiotic; in fact, "It is hardly to be reckoned as a part of logic proper." Hence logic as semeiotic is much more than merely "a classification of the ways that formal logic is applied to practice."The word 'merely' is misleading. Note that Peirce also uses the word 'classificatory' for biology, which is an immensely complex subject. Physics, by contrast, is tiny in the sense that the most powerful generalizations can be stated in just a few equations.If you look at mathematical logic, the axioms for every version that Peirce invented can be stated succinctly. But normative logic is huge -- because it must consider and *classify* every possible method of reasoning about every aspect of science and everyday life.Note Peirce's emphasis: "normative science, which is essentially classificatory, stop to take that well in, I beg you, gentle reader". To understand what that means, I recommend the excerpts from Photometric Researches: http://jfsowa.com/peirce.PRexcerpts.pdf .That book is a classification of the many semiotic issues in one relatively small branch of astronomy. To classify the logic/semiotic of all the branches of science would require a major library.John _ _ _ _ _ _ _ _ _ _ ► 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 no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by The PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Diagrammatic reasoning (was Forgot attachment..
Edwina, I certainly agree: > I don't think that Peircean semiosis is just about 'interpretation' in the sense of human language or communication When I cited Peirce's _Photometric Researches_ as a good source of examples, I wanted to show how the two sources of knowledge -- pure mathematics and phanersocopy -- serve as the foundation of every aspect of semeiosis in everything we know and do. By mathematics, I include the most elementary versions of counting and geometry up to the most advanced and abstract theories. By sciences, I include cooking, farming, amd gymnastics as well as physics, chemistry, and biology. I consider Simone Biles' gymnastics as an excellent example of the mathematical precision that is possible with diagrammatic reasoning or "steroscopic moving images" by Peirce. For example, note the words 'visual' and 'muscular' in the following quotation by Albert Einstein: AE> The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be voluntarily reproduced and combined... The abovementioned elements are, in my case, of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will. Compare that with comments by Peirce and other mathematicians in http://jfsowa.com/talks/ppe.pdf . John - 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 . PEIRCE-L is owned by The Peirce Group; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Destinate Interpretant and Predestinate Opinion
Robert, Your summary of the issues is very good, and I strongly agree with the need for examples. In a search for examples, I went back to _Photometric Researches_, which I believe is essential for understanding the development of Peirce's philosophy. It's not an accident that it was published in 1878, the same year in which "How to make our ideas clear" was published in the _Scientific American_. The title of Chapter 1 is "The sensation of light." See http://jfsowa.com/peirce/PRexcerpts.pdf . On page 2, he wrote "Light considered purely as something in the external world may be called _noumenal light_. Light considered as an appearance, and as a function of the sensation, such that it is measured by the convention just mentioned, may be termed _phenomenal light_. Photometry generally concerns phenomenal light..." Just reading a few pages (my PRexperts, for example) is enough to show how deeply Peirce's phaneroscopy is grounded in his scientific and engineering research. It's also important to compare that research with R602, which was written after his 1903 classification of the sciences. See http://jfsowa.com/peirce/r602.htm : p 12> But preliminary to normative science, which is essentially classificatory, stop to take that well in, I beg you, gentle reader, there should be a nomological science, which shall make out all the different indecomposable elements which enter into everything that is conceivably possible, discriminates them with care, and shows how they can be varied and combined. This science I hesitate to call phenomenology after Hegal, for fear of marring his peculiar conception of it; and therefore, though I think it is essentially the same thing under a somewhat different aspect, I will name phaneroscopy. p 13> It is the science of the different elementary constituents of all ideas. Its material [m13] is, of course, universal experience, experience I mean of the fanciful and the abstract, as well as of the concrete and real. Yet to suppose that in such experience the elements were to be found already separate would be to suppose the unimaginable and selfcontradictory. They must be separated by a process of thought that cannot be summoned up Hegel-wise on demand. They must be picked out of the fragments that necessary reasonings scatter; and therefore it is that phaneroscopic research requires a previous study of mathematics. Observation from p, 12: normative science is essentially _classificatory_. That implies that logic as semeiotic is a classification of the ways that formal logic is applied to practice. The reasoning methods of logic as semeiotic are derived from mathematical logic. Many people who talk about Peirce's semeiotic ignore the fact that the reasoning methods are based on mathematical logic. Observation from p, 13 of R602 and pp. 10 and 11 of PRexcerpts: Phaneroscopic research requires a previous study of mathematics. The kind of mathematics depends on the application, and there is no limit on the amount and depth of mathematics that may be needed. John - 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 . PEIRCE-L is owned by The Peirce Group; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Forgot attachment (was To put an end to the false debate...
Original Message Subject: Re: [Peirce-L] To put an end to the false debate on the classification of signs From: "John F. Sowa" Date:Tue, May 19, 2020 10:05 To: "Peirce-L" Robert M, Gary F, Jon AS, List For quotations by Peirce on these issues, see the attached file, science.txt. Also note the last quotation by Edward Moore: ECM> Peirce has left us, not any kind of final word, but a work in progress, one eminently worth carrying on, in the spirit of the one who started it. Which is to say that we must be as resolutely critical, and as ruthless in paring away what does not work, as Peirce was at his best. [E.C. Moore, "Is Synechism Necessary?" (2012), p. 12] In the many debates about what Peirce meant and how we should adopt his writings as a basis for our own work, it's essential to remember that his ideas were constantly growing. The year 1914 was a stopping point for him, but he made many comments about how future researchers might continue. I agree with Moore's comment, but there is, as always, much more to say. John Some quotations about science, philosophy, and truth. "The object of reasoning is to find out, from the consideration of what we already know, something else which we do not know" [CP 5.365]. -- there is one thing even more vital to science than intelligent methods; and that is, the sincere desire to find out the truth, whatever it may be -- [CP 5.84, Lecture 3, Lectures on Pragmatism (1903)] Indeed, out of a contrite fallibilism, combined with a high faith in the reality of knowledge, and an intense desire to find things out, all my philosophy has always seemed to me to grow... [CP 1.14, fragment, c. 1897] -- there is one thing even more vital to science than intelligent methods; and that is, the sincere desire to find out the truth, whatever it may be -- [CP 5.84, Lecture 3, Lectures on Pragmatism (1903)] The method of modern science is social in respect to the solidarity of its efforts. The scientific world is like a colony of insects, in that the individual strives to produce that which he himself cannot hope to enjoy. One generation collects premises in order that a distant generation may discover what they mean. Peirce (1902) 2.123. -- the mass of mankind -- are thoroughly persuaded that they reason well enough already. I do not mean to say that they maintain that none of them ever reasons wrong. Far from that; though they trust to common sense as affording all the security that could be desired for reasoning, yet their adhesion is majestically unanimous to the proposition that of all the race there is but one single individual who never falls into fallacy; and their only point of difference is that each is quite sure that he himself is that man. Unfortunately, to be cocksure that one is an infallible reasoner is to furnish conclusive evidence either that one does not reason at all, or that one reasons very badly, since that deluded state of mind prevents the constant self-criticism which is, as we shall see, the very life of reasoning. Congratulations, then, from my heart go out to you, my dear Reader, whom I assume to have a sincere desire to learn, not merely the dicta of common sense, but what good reasoning, scientifically examined, shall prove to be. You are already an unusually good logician. [Minute Logic, "Why Study Logic" (1902)] A comment about Peirce by Edward C. Moore: Peirce has left us, not any kind of final word, but a work in progress, one eminently worth carrying on, in the spirit of the one who started it. Which is to say that we must be as resolutely critical, and as ruthless in paring away what does not work, as Peirce was at his best. [E.C. Moore, "Is Synechism Necessary?" (2012), p. 12] - 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 .
[PEIRCE-L] Re: [Peirce-L] To put an end to the false debate on the classification of signs
Robert M, Gary F, Jon AS, List For quotations by Peirce on these issues, see the attached file, science.txt. Also note the last quotation by Edward Moore: ECM> Peirce has left us, not any kind of final word, but a work in progress, one eminently worth carrying on, in the spirit of the one who started it. Which is to say that we must be as resolutely critical, and as ruthless in paring away what does not work, as Peirce was at his best. [E.C. Moore, "Is Synechism Necessary?" (2012), p. 12] In the many debates about what Peirce meant and how we should adopt his writings as a basis for our own work, it's essential to remember that his ideas were constantly growing. The year 1914 was a stopping point for him, but he made many comments about how future reseachers might continue. I agree with Moore's comment, but there is, as always, much more to say. John - 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 .
Re: [PEIRCE-L] Parts of Propositions (was qualisigns)
Jerry and Jon, In mathematics -- including mathematical logic -- the notation is absolutely precise. Two different notations that are isomorphic (one-to-one mappings in both directions) have identical semantics, independent of any words used to describe them. JLRC> I suggest that CSP was consistent in his deployment of the triadic grammatical relatives (subject, copula, predicate). JAS> On my reading, Peirce did not consider the copula to be an essential part of a proposition in the same sense as the subjects and predicate. For Peirce (as for every mathematician), the notation is primary, and the words are useful only for explaining the notation to students. The first-order subset of Peirce's algebra of 1885 and the first-order subset of EGs (Alpha + Beta) have identical semantics. To understand exactly what Peirce intended, ignore the English words. Just translate his explanations to the algebra or the EGs. The words are useful only for teaching students. Mathematicians (as well as scientists and engineers who use mathematics) never talk about charity -- except for human charity in being sympathetic with students who are dong their best.. John - 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 .
Re: [PEIRCE-L] Methodology (was To put an end to the false debate...
Auke, The point I was trying make: Either/Or debates are a waste of time. There is an open-ended number of different ways of perceiving, thinking, talking, reasoning, and acting. In the abstract, there is no reason to debate whether method M175 is better or worse than method M837926. AB> I agree with your broadening up the seeming dichotomy to an open ended diversity. But I suggest to go all the way; also within a science we find different angles on the same subject matter. Semiotics not being excluded. Yes. Within any science -- say cooking, farming, chemistry, or phaneroscopy -- the number of "angles" or methods is unlimited. Just compare cooking in China, Italy, Mexico, or any other region. There is an immense diversity of methods, which is further subdivided by the specializations for each region, cook, and choice of ingredients. For any science, the diversity is as great as the number of applications times the number of practitioners. As Peirce said, there are just two sources of knowledge: pure mathematics and experiences in the phaneron. For both, the variations are potentially infinite. For phaneroscopy, Peirce's _Photometric Researches_ is an excellent textbook. It was published in 1878, the same year as the article "How to make our ideas clear". Peirce's many years of research was the basis for both, and the book provides examples that illustrate the open-ended variety of methods for analyzing experiences in the phaneron. Chapter 1, for example, has the title "The Sensation of Light." That is an unusual title for the first chapter of a book on science, and it illustrates Peirce's way of thinking. The remainder of the book discusses the many ways of analyzing those experiences by Peirce and other astronomers. I posted some excerpts from that book on my web site. I recommend Chapter 1 (six pages) and some browsing of the other excerpts: http://jfsowa.com/peirce/PRexcerpts.pdf . There is, of course, much more to be said. John - 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 .
[PEIRCE-L] Methodology (was To put an end to the false debate...
Robert and Auke, I agree with the points you made. But I believe that a good way to put an end to the "false debate" is to broaden the dichotomy to an open-ended diversity. Every branch of the sciences (i.e., every branch in Peirce's 1903 classification) has methods that are specialized for the subject matter. For that reason, I changed the subject line to "Methodology" -- Methodeutic would be an acceptable term, but Peirce's discussion of that term has too few examples to support all the issues that need to be considered. For example, the methods for studying linguistics, archaeology, chemisty, astronomy, and medicine are radically different. But they do have a common foundation: observation, induction, abduction, deduction, testing, and repeat. Although the theorems of mathematics are determined by deduction, mathematical discovery is just as empirical as any other science. For example, Euler: "The properties of the numbers known today have been mostly discovered by observations... long before their truth has been confirmed by rigid demonstrations." Laplace: "Even in the mathematical sciences, our principal instruments to discover the truth are induction and analogy." Paul Halmos: "Mathematics this may surprise or shock some is never deductive in its creation. The mathematician at work makes vague guesses, visualizes broad generalizations, and jumps to unwarranted conclusions. He arranges and rearranges his ideas, and becomes convinced of their truth long before he can write down a logical proof... the deductive stage, writing the results down, and writing its rigorous proof are relatively trivial once the real insight arrives; it is more the draftsmans work not the architects. * * Halmos, Paul R. (1968) Mathematics as a creative art, _American Scientist_, vol 56, pp. 375-389. There is, of course, much more to be said. John - 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 .
Re: [PEIRCE-L] Constellation of formal languages and the logic of time (was Charity
Michael, I strongly agree: MCJM> What we should be doing IMO is not so much "agreeing to differ" as leaving our ideas on the table for continued evaluation (at everybody's leisure). If we don't want to agree do we have to say more than "I shall think about it" or even just stay momentarily silent? Unfortunately, many threads go on far too long because two or more people want to have the last word. To break that endless cycle, we need some convention that allows people to state their final position and stop responding. Recommendation: If somebody has completed everything they want to say about some topic XYZ, they could change the subject line to "Final position on XYZ". That subject line would be a promise *not* to reply to any further message on the topic XYZ or on the topic "Final position on XYZ". Other people could continue to comment on XYZ, but the person who wrote "Final position" would not make any further comments on thread XYZ. John - 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 .
Re: Please Stop (was Re: [PEIRCE-L] Charity (was Categories and...)
Gary R, As Mike said, please stop. GR>To be perfectly clear, in my estimation this horrible 'harangue' began about a year ago, shortly after John Sowa joined the list and began harassing Jon Alan Schmidt, not on any substance of any of his post, but on his methodology. Thank you for providing more evidence of your blanket condemnations. I had subscribed to Peirce-L when Joe Ransdell was running it. But I lost the connection when I switched from one email service to another. And I picked it up again quite a few years ago. I never harrassed Jon. On the contrary, I pointed out errors that were caused by his methodology. Peirce was an outstanding logician and mathematician, and Jon did not have the background to interpret certain passages correctly. But Jon would never admit that there might be an interpretation that was different from his own. I apologize for trying to correct Jon's errors. I promise that I won't do that again. End of story. John - 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 .
Re: Please Stop (was Re: [PEIRCE-L] Charity (was Categories and...)
Mike, MB> Please stop. Excellent advice. I stated all the issues in my previous note, and I have no desire to continue. MB> Despite Gary R telling me offline to resign from the list, I will continue to monitor. I am curious to see if the human animal has the capacity to learn and grow. Evidence based on the way this list is going does not instill optimism. I sympathize. I also received an offline note. But I have been friendly wih him for years, and I can tolerate quite a bit. But not a blanket condemnation.JAS>Thanks for confirming that there are no specific examples to cite of Gary R. making the kinds of "blanket statements" of which he has been repeatedly and falsely accused. They made mse so angry that I deleted them.JAS> Many Peircean scholars have attempted to do that, not out of hubris but out of a sincere (even humble) desire to learn from Peirce's writings and then help others do likewise.Responsible Peirce scholars comment on, build on, and adapt ideas from Peirce's writings. Many have compiled lists of excerpts by Peirce on certain themes. But nobody has attempted to produce a single coherent presentation of what Peirce intended, but could not himself complete. There is nothing more to say. John - 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 .
Re: [PEIRCE-L] Charity (was Categories and...
Jon, et al. I just want to emphasize one point: It's extremely rare for anybody to approve or be satisfied with anybody else's summary or paraphrase of what they said or wrote. If it's highly favorable, they probably won't complain. But even then, they realize that the paraphrase is not what they themselves would have said. JAS> The debates are rarely about there being only one "right" interpretation of only one particular passage, but rather whether and how we can integrate different passages to arrive at an overall interpretation of Peirce's thought, usually stated in our own words rather than his. No!!! Even Peirce could not "integrate different passages to arrive at an overall interpretation of [his own] thought". No Peircean scholar or committee of scholars would attempt to do that. If Peirce himself couldn't do that, it's the height of hubris for anybody else to claim that they could. Note: I am not complaining about what you write -- provided that you state it as your own opinion. But I strongly object to any claim by anybody that they could do what Peirce himself could never accomplish. JAS> John Sowa recently claimed that "Peirce would cringe at most, if not all attempts to paraphrase his thoughts," but offered no citation or quote to support this projection of his own feelings onto Peirce. If you want to see people cringe at a paraphrase, just watch children cringe when their parents try to repeat what they said on some previous occasion. As for Peirce, I'll turn the question around. Can you find any paraphrase that Peirce approved? Look at his reviews of writings by William James or Ernst Schröder. Or note they way he introduced the word 'pragmaticism'. For more examples in ordinary language, look at any email debates on any list or blog on any subject: Few, if any people, fully agree with any paraphrase of what they said. Sometimes, they might admit that the other person made a clearer or better statement on the same topic. But an improvement is not an exact paraphrase. For my own writings, I have *never* seen any paraphrase -- favorable or unfavorable -- that I would consider accurate. Some of them are worse than others. But even the favorable comments are not exact.As for Peirce, his background and knowledge were unique. Even the best Peircean scholars can't write a truly accurate paraphrase of anything he wrote. I would never attempt to do that. But every mathematician, including Peirce, recognizes that mathematical derivations are guaranteed to absolutely precise or completely false. If anybody derives a conclusion from some proposition p in formal math or logic, the original authors will accept any statement derived from p -- *provided that* the derivation correctly follows the rules of inference for that notation. In mathematics, every derivation is either exactly correct or exactly false. There is no room for charity. But a good teacher can be charitable by being sympathetic and helpful in showing students how to correct and avoid mistakes. That is human charity, not mathematical charity. John - 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 .
Re: [PEIRCE-L] Charity (was Categories and...
Jon, Michael, Edwina, Robert M, and Gary R, Peirce's range of interests, talents, and research was so broad that there is no single best method for studying and interpreting his writings. For different aspects of his work, some methods are better than others. But even for those areas where one method may be dominant, other methods may also be appropriate for certain aspects. For these reasons, what triggered this thread is not what Jon wrote, but what Gary R wrote. As moderator, he's supposed to moderate. He has the right to state his opinions about any issue., But when he made a blanket statement about my competence, that was out of bounds. There are some areas for which Peirce depended very heavily on math and logic. The four volumes of NEM are prime examples. But there are also many topics in CP, EP, and W for which mathematics is essential for understanding the nuances. For topics that touch on those areas, someone who is not attentive to the mathematical issues may be misled. When I read comments that ignore those issues, I say so. Re principle of charity: That is necessary for interpreting philosophers who are not able to speak for themselves -- either because they are dead or merely because they are not present in the discussion. But if they are present, they can speak for themselves about any misunderstanding. I've known Gary R for years, and we've always been quite friendly. But I also know that Gary is not a mathemtician, and he has a tendency to downplay the influence of mathematics on Peirce's philosophy. I would not object to some criticism of an issue in which I emphasize the importance of mathematics and formal logic. I would then accept the burden of proof to show that math is indeed important for that particular topic. I've done that in some cases, and I'll continue to do so. John - 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 .
Re: [PEIRCE-L] Charity (was Categories and...
Jon, The principle of charity in philosophy does *not* require the listener/reader to assume that the statements by the speaker/author are true. Its only requirement is to assume that other participants in the discussion are rational human beings who are making meaningful statements, which they have some reason to believe are true. But charity does not require the listener to agree that they are true. Note the passage you quoted: Wikipedia> In philosophy and rhetoric, the principle of charity or charitable interpretation requires interpreting a speaker's statements in the most rational way possible and, in the case of any argument, considering its best, strongest possible interpretation. In its narrowest sense, the goal of this methodological principle is to avoid attributing irrationality, logical fallacies, or falsehoods to the others' statements, when a coherent, rational interpretation of the statements is available. According to Simon Blackburn "it constrains the interpreter to maximize the truth or rationality in the subject's sayings." I have never claimed that any of your statements were meaningless or irrational. What I criticized was the strength and methods of the argument. For the arguments I objected to, I showed that a charitable interpretation of what Peirce wrote led to a conclusion that was different from a charitable interpretation of what you wrote.JAS> We (supposedly) agree that it is inappropriate to make sweeping judgments about who is (or is not) capable of understanding Peirce's writings and discussing them intelligently. We (apparently) disagree about who among us has been guilty of doing exactly that.I never said that you were incapable of understanding Peirce. But I did criticize your method of stringing together multiple quotations from different contexts. I did not claim that was irrational. But I did say that the some of the critical quotations were taken out of contexts where charity toward Peirce would give them a different interpretation.JAS> On the contrary, Gary R. is consistently an exemplary model of the "generosity of attitude" that he advocates as List moderator.No. A list moderator has a right to admonish participants about making inappropriate statements. But a moderator has an obligation to quote the statement(s) explicitly and state exactly why they are inappropriate.But Gary R made a blanket statement about my ability to interpret Peirce without stating a single example where my statement was wrong or inappropriate. He also made a blanket statement that your arguments were superior to mine. On several occasions, he said that he agreed with you and not with me. But he never explained why any particular point I made was wrong.I never complained about anybody who might disagree with me for one reason or another. But Gary R stepped way out of bounds when he made a blanket condemnation of my writings without ever showing a single example that was inappropriate.JAS> Peirce's distaste for "metaphysicians" was prompted by their dogmatism...I checked CP for every occurrence of 'metaphysician'. There are 71 occurrences. I did not check every one of them. But in the great majority of the ones I checked, his complaint was about their methods of reasoning. The first occurrence is typical: "The demonstrations of the metaphysicians are all moonshine." (CP 1.7)In the second quotation (CP 1.29), he praised two of them because of their methods of reasoning: "These two men, Duns Scotus and William Ockham, are decidedly the greatest speculative minds of the middle ages, as well as two of the profoundest metaphysicians that ever lived."Methods of reasoning were one of Peirce's strongest interests from childhood to the end. In his criticisms of philosophers, his strongest praise and condemnation were about their reasoning. I won't claim that I am as good as Peirce in this respect. But I do admire and try to emulate his way of adapting the methods of reasoning in logic and mathematics to every subject he discussed.I won't claim that everybody must apply formal logic and mathematics to everything. In fact, Peirce himself had a high regard for vagueness. (249 instances of 'vague' in CP, with or without some ending.) In some cases, he criticized vagueness. But more often than not, he recognized that a vague statement was appropriate in the context. In fact, his pioneering work on probability was an attempt to quantify reasoning about statements that are not exactly true or false.John - 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 .
[PEIRCE-L] Charity (was Categories and...
Jon, Charity is an important virtue in dealing with people. What made me angry is Gary R's attitude that he is an authority who is capable of making blanket judgments about the accuracy of anybody else's arguments. He has the right to point out what he belives are mistakes, but he has an obligation to explain exactly what mistake was made in any particular instance. (See below for options.) But mathematics is the universe of pure possibility. The truths of mathematics do not depend in any way on what any humans may think. JAS> John Sowa has asserted, "In logic and mathematics, there is no such thing as charity ... No amount of charity can correct a mistake in logic or mathematics ... When it comes to logic and mathematics, charity does not apply." That's true.. Mathematics is so precise, that mathematicians, scientists, and engineers use proof checkers to test their computations. Google "Mathematica" and "Mathlab". A computation is either correct or incorrect. There is nothing in between. That is a fundamental principle of mathematics. Aliens in a far off galaxy would recognize the same theorems, but they would undoubtedly use very different notations. JAS> I also noted recently that according to Peirce, logic and mathematics are by no means exempt from fallibility, so I believe that charity does apply even in these rigorous fields. I agree that Peirce said that. But he was admitting that his own mathematical abilities, athough quite high, were merely human. No mathematician ever asks for or gives charity about the subject matter. If someone points out a mistake, a mathematician immediately recognizes it. The only charity is in the human to human interaction: The one who made the mistake immediately apologizes, and the one who found it is sympathetic. JAS> As I pointed out in my response at the time, we rarely (if ever) engage in rigorous "proofs" on the List; the discussion is mostly about philosophy, including the philosophy of logic and the philosophy of mathematics, where charity surely does apply. I admit that word 'charity' is a traditional term, But it's confusing because it blurs issues about the source of a discrepancy: a mistake, as in mathematics; an ambiguitiy, as in most words in ordinary language; a fallacy, as itemized by Aristotle and other logicians; a failure to recognize some implicit assumption that is required for a sound argument; or a deliberate choice to adopt a different set of axioms and definitions. But note Peirce's many comments about 'metaphysicians'. He was sympathetic to people who honestly wanted to learn. That's a good kind of charity. But he was not very sympathetic toward many others he criticized. John - 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 .
Re: [PEIRCE-L] The Peirce-L Forum principle of a "generosity of attitude."
Jon , On the following point, we agree. And since Gary R takes your side in all these issues, I wish you would tell him to accept it. JAS> I find it extremely inappropriate to make sweeping judgments about who is (or is not) capable of understanding Peirce's writings and discussing them intelligently. After all, "Different people have such wonderfully different ways of thinking" (CP 6.462, EP 2:437, 1908). Some are more inclined toward and adept at abstract theory, others prefer to pursue concrete applications, and others (like Peirce himself) can do both. But the point I was making is that if you want to understand Peirce, you must read his writings as coming from someone who spent a lifetime doing both. Unfortunately, the various collections (CP, W, and NEM) ignore a huge amount of his background in mathematics, science, and engineering. They emphasize the results of his thinking, but they skip the details about his practice. Examples: His father taught him Greek, Latin, and mathematics from early childhood. He was doing chemistry experiments from the age of 8, and he worked his way through the kinds of experiments a college student would be doing. He read his brother's logic textbook, cover to cover, when he was 12. And he published a pioneering book in astronomy in his first full-time job at the Harvard observatory. None of us can redo our early childhood experience. But when we read any theoretical statement by Peirce, we must remember his background, his criteria for evidence, and his 60+ years of empirical/critical methods As Peirce said, it's indeed wonderful that different people have very different ways of thinking. But in order to understand any of them, we must recognize their background in order to understand how and why they came to their conclusions. Otherwise, the evaluation is incomplete or superficial at best, misguided or false at worst John - 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 .
Re: [PEIRCE-L] The Peirce-L Forum principle of a "generosity of attitude."
Gary, That is the most anti-Peircean statement imaginable: GR> It would once again appear that Edwina and John expect everyone to have always and only the same interests as they do. Edwina, for example, characterizes anything else, notably, theorizing, as "an irrelevant exercise" undertaken only by people who "prefer the isolation and comfort of what [she calls] 'the seminar room'. . . far, far, far from the real empirical objective world." Well, that's her opinion. I, for one, do not share it. Theorizing is absolutely esssential for understanding anything. But Peirce insisted that any theory that has any claim to be scientific must be exhaustively tested against observations. And that most definitely includes his categories, which depend on the most careful possible testing against "experiences in the phaneron". You cannot understand anything Peirce wrote unless you repeat the kind of disciplined testing that he did in developing and revising his theories. Just quoting Peirce without repeating his very careful methods of analysis and testing produces nothing but superficial verbiage. John - 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 .
Re: [PEIRCE-L] Categories and Speculative Grammar Revisited (was Essay about categories and logical presuppositions)
Edwina, I strongly agree with that point: ET> Helmut - your own experiences in 'the real world' are what you should be trying to understand - semiosically. Abstract theories are useless, unless they can be applied to something useful. Chess and Go, for example, are mathematical theories whose only purposes are (1) mental training in methods of analysis and planning, and (2) the challenge of competing with other people who have similar training. But Chess and Go have no practical applications beyond the disciplined training they provide. Peirce would not belittle that training. But he designed his logic and semeiotic as tools for solving and resolving major problems and issues of science and society. In order to understand the value of Peirce's work, it's essential to do what he did: apply his theories to practical problems. John - 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 .
Re: [PEIRCE-L] Categories and Modes of Being (was Essay about categories and logical presuppositions)
Jon, Peirce was using the word 'category' in rhe tradition from Aristotle to Kant. That tradition is still alive and well in philosophy. It's unfortunate that the 20th c mathematicians used the same term for a different kind of mathematical theory. But as Robert M. hass been saying, it's possible to apply the mathematical category theory to analyze Peirce's theories. JAS> "A Categorical Manifesto" provides the kind of clear and succinct definition that I have been seeking.JG: To each species of mathematical structure, there corresponds a category whose objects have that structure, and whose morphisms preserve it. (p. 2)That simple statement may look clear and succinct, but underneath there's the kind of complexity that Robert was talking about.JAS> Would it then be accurate to say that Peirce's categories (1ns/2ns/3ns) are mathematical categories in the sense of corresponding to the structures of the three irreducible forms of relation (monadic/dyadic/triadic)?Short answer: No.The longer answer would be along the lines that Robert was talkinng about.John - 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 .
Re: [PEIRCE-L] Categories and Modes of Being (was Essay about categories and logical presuppositions)
Robert and Jon, As a mathematician, I appreciate the power of category theory. But I also spent 30 years working on reseach & development proejcts at IBM, where I had to present many mathematical issues in ways that engineers could appreciate. That gives me quite a bit of sympathy for Jon's reaction to category theory. I recommend the article by Joseph Goguen on "Tossing algebraic flowers down the great divide": http://cseweb.ucsd.edu/~goguen/pps/tcs97.pdf . Goguen was a pioneer in applying category theory to complex problems in computer science, but he was frustrated by the "great divide" between the theoreticians and the practitioners. That article is an auobiography of his efforts to bridge the divide. John - 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 .
Re: [PEIRCE-L] Different Semeiotic Analyses (was tree-structure)
Jon, When Peirce called a theory 'fallible, he did not mean "free to make adjustments". There is a huge difference between "free to apply to new areas" and "free to adjust (i.e. change) the theory itself"', The first (new applications) is "normal science" in Kuhn's terms. But the second is a "paradigm shift" caused by some serious error in the foundations of the theory. JAS> I agree that the conclusions of semeiotic are "eminently fallible," as Peirce himself described them. That is why we are not locked into treating his speculative grammar as rigid dogma but are free to make adjustments that we deem appropriate in accordance with the results of our own investigations. We simply need to be clear about those deviations and acknowledge that they are deviations, Question: What flaws, errors, or discrepancies have you found in Peirce's semeiotic? If you found some areas that Peirce did not cover, then doing further research to cover those areas is "normal science". That would require new data about aspects that Peirce did not address in his writings. But changing the theory (even "adjustments") is a very serious matter. That would only be justified if you found some serious contradictions that couldn't be covered by "normal science" -- i.e., making new observations and adding some methods for adapting Peirce's theories to the new data. What are your reasons for the adjustments? John - 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 .
