[PEIRCE-L] Re: C.S. Peirce, Spencer Brown, & Me
Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 4 https://inquiryintoinquiry.com/2017/08/06/charles-sanders-peirce-george-spencer-brown-and-me-4/ All, Two things that had a big impact on my studies of Peirce and Spencer Brown over the years were my parallel studies in mathematics and computer science. In the overlap between those areas came courses in logic, mathematical linguistics, and the theory of formal languages, grammars, and automata. My intellectual wanderings over a nine-year undergraduate career would take me through a cycle of majors from math and physics, to communication, psychology, philosophy, and a cross-cultural liberal arts program, then back to grad school in mathematics. The puzzles Peirce and Spencer Brown beset my brain with were a big part of what drove me back to math, since I could see I had no chance of resolving them without learning a lot more algebra, logic, and topology than I had learned till then. Resources = Prospects for Inquiry Driven Systems https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#Bibliography Mathematical Notes https://oeis.org/wiki/User:Jon_Awbrey/Mathematical_Notes Regards, Jon _ _ _ _ _ _ _ _ _ _ ► 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: Nominalism vs. Realism
Thanks, Dan, That brings me a twinge of pleasant nostalgia, but there a few fresh things I could say about it all from my current perspective when I next get a chance. Very generally speaking, however, so much of current philosophical thought, in or out of the Peirce realm, is so deeply entrenched in nominalism that I started a few years back using the term Dunning–Kruger Nominalism (DKN) to describe it. Regards, Jon On 1/23/2021 10:21 AM, Daniel L. Everett wrote: This is by a philosopher of language who is not normally associated with Peirce, J Katz, a highly influential figure in the early history of Chomskyan linguistics. But this older paper of his, which I was reminded of recently by a co-author of Katz’s with whom I was discussing some of my ideas on Peirce’s ideas in linguistics, is potentially of interest to readers of this list. So I send it along. Dan Everett _ _ _ _ _ _ _ _ _ _ ► 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: Nominalism vs. Realism
Thanks, Jon. Any comments would be welcome. I do like Katz’s work. The title of the book I am doing for OUP (I had to put off the bio of Peirce until libraries open back up) is Peircean Linguistics: A Chapter in the History of Realist Thought. Hence my more than passing interest in linguistic realism. Dan > On Jan 23, 2021, at 1:02 PM, Jon Awbrey wrote: > > Thanks, Dan, > > That brings me a twinge of pleasant nostalgia, but there a few fresh things > I could say about it all from my current perspective when I next get a chance. > Very generally speaking, however, so much of current philosophical thought, > in or out of the Peirce realm, is so deeply entrenched in nominalism that > I started a few years back using the term Dunning–Kruger Nominalism (DKN) > to describe it. > > Regards, > > Jon > >> On 1/23/2021 10:21 AM, Daniel L. Everett wrote: >> This is by a philosopher of language who is not normally associated with >> Peirce, J Katz, a highly influential figure in the early history of >> Chomskyan linguistics. But this older paper of his, which I was reminded of >> recently by a co-author of Katz’s with whom I was discussing some of my >> ideas on Peirce’s ideas in linguistics, is potentially of interest to >> readers of this list. So I send it along. >> Dan Everett > > _ _ _ _ _ _ _ _ _ _ > ► 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 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
John, List, All: JFS: 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. That it is his *last *version is a fact, as far as we know. That it is his *best *version is an opinion. By what criteria? Simplest and most iconic? Sure. Most analytical? Definitely not. JFS: Furthermore, Peirce's letters of Sept. and Dec. 1911 explicitly reject the version of 1906 on which R669 is based. This is false, and we have been over it before. What Peirce rejects in those two letters, as well as in another one that he wrote two years later, is not "the version of 1906" but his lengthy and convoluted *description *of EGs in "Prolegomena to an Apology for Pragmaticism." That is perfectly consistent with my hypothesis that in June 1911, Peirce merely decided to simplify his *presentation *of EGs for the uninitiated--the National Academy of Sciences (R 670), J. H. Kehler (RL 231), A. Robert (RL 378), A. D. Risteen (RL 376), and F. A. Woods (RL 477). Moreover, he tells Risteen that the badness of the "Prolegomena" description was "in great contrast to the one Dr. Carus rejected" way back in 1896-7, and that the 1903 Lowell Lectures with accompanying Syllabus was "the better exposition." He then tells Woods that the 1896-7 attempt was "the most lucid and interesting paper I have ever written." In other words, Peirce not only never *rejects *those earlier explanations, he explicitly *reaffirms *them. What he has come to recognize, as he mentions to Risteen, is that shading is vastly superior to cuts for distinguishing evenly and oddly enclosed areas--something that I have repeatedly acknowledged myself, and even implemented in my recently posted Synechistic EGs ( https://list.iupui.edu/sympa/arc/peirce-l/2021-01/msg00011.html). However, it would be more accurate to say that he *rediscovers *this utility, because he had already noticed it before. "The *blue *tint, however, of the area within the cut is a great aid to the understanding" (R 490:13, 1906). "Some slight shading with a blue pencil of the oddly enclosed areas will conduce to clearness" (CP 4.617, 1908). JFS: The most efficient theorem proving methods today do *not* depend on a sign for if-then. So what? Peirce was consistently adamant that the proper purpose of the *philosophical* science of logic is not efficiency in proving theorems, but thoroughness in analyzing the process of inference into its most basic constituents. Treating negation as a primitive makes EGs more useful to a mathematician as a calculus (minimum steps) but detracts from the primary reason why Peirce the logician created them in the first place (maximum steps). I have said it before, I will say it again--we have different purposes, so we reach different conclusions. JFS: 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. One more time--Peirce never "demotes" the scroll; on the contrary, he *explicitly denies* that a consequence can be reduced to two negations. CSP: Indeed, so far is the concept of *Sequence* from being a composite of two Negations, that, on the contrary, the concept of the Negation of any state of things, X, is, precisely, a composite of which one element is the concept of Sequence. Namely, it is the concept of a sequence from X of the essence of falsity. (R 300:50[51], 1908) Again, as your own slide 11 rightly affirms, "Even negation ~ must be inferred." Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sat, Jan 23, 2021 at 4:42 PM John F. Sowa wrote: > 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 re
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.
