Re: [PEIRCE-L] Existential Graphs in 1911
John, Auke, List, All: JFS: 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. This is false, Peirce states no such thing. Here is the entire relevant portion of the referenced letter. CSP: This syntax, which I have hitherto called the “system of Existential Graphs,” was suggested to me in reading the proof sheets of an article by me that was published in the *Monist *of Jan. 1897; and I at once wrote a full account of it for the same journal. But Dr. Carus would not print it. I gave an oral account of it, 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. (RL 376, R 500:1-3, 1911 Dec 6) Peirce criticizes his *description *of EGs in the "Prolegomena" article of 1906, directly contrasts it with his very first account of EGs in 1896-7, and explicitly calls the Lowell Lectures and accompanying Syllabus "the better exposition of 1903." He never *rejects *these or any other earlier versions, and certainly never expresses the opinion that either R 670 or RL 231 from June 1911 is his "best" version. What he does say is that shading is an improvement over cuts for distinguishing different areas--an assessment with which I agree, as I have repeatedly acknowledged. JFS: This problem is important for automatically relating two different proof procedures. Again, so what? Peirce's own words are unmistakably clear, over and over, that he was not interested in facilitating "automatic" reasoning or otherwise improving the efficiency of proof procedures, except as a very secondary consideration. Instead, his overriding priority as a logician was to analyze reasoning into its most fundamental and irreducible elements, maximizing rather than minimizing the number of steps. He states this many times, including but not limited to passages from 1880 (CP 3.173n), 1891 (8.316), 1902 (3.618, 4.373-375, 4.239), 1903 (4.424), and 1906 (4.581). JFS: The 1911 EGs can be generalized beyond two dimensions for "stereoscopic moving images". This is true, but irrelevant. The scroll could be employed in three dimensions simply by maintaining the requirement for a single point of intersection between the outer and inner boundaries. JFS: Note that observing if-then is impossible This is false, as I already pointed out by quoting CP 3.363 (1885). We observe if-then *diagrammatically *when we "see" that the consequent follows necessarily from the antecedent, just like the deductive conclusion of an argumentation follows necessarily from the premisses. As such, it is a *logical* relation, not an *existential* relation. In fact, according to Peirce, the same goes for coexistence (existence plus conjunction) and identity. CSP: We remark among Existential Graphs two that are *continuous*; that is, they may be regarded as consisting of parts; but all parts of them are perfectly homogeneous with the whole. Continuity is not an Existential character; it only belongs to the Object of the nature of Laws. Consequently, the Continuous Graphs do not express Existential Predicates but only Logical Predicates. The two continuous Graphs are the Blank, which expresses Coëxistence and the Line of Identity, which expresses Numerical (i.e. individual) “Sameness.” (R 499(s):33, 1906) Moreover, according to Peirce, it is incorrect to think that we become acquainted with any of these *logical *relations by means of *existential * observations. CSP: The *Copulants *are likewise indispensable and have the property of being *Continuant*. What I mean is that the sign "A is red" can be decomposed so as to separate "is red" into a Copulative and a Descriptive, thus: "A possesses the character of redness." But if we attempt to analyze "possesses the character" in like manner, we get "A possesses the character of the possession of the character of Redness"; and so on *ad infinitum*. So it is, with "A implies B," "A implies its implication of B," etc. So with "It rains and hails," "It rains concurrently
[PEIRCE-L] Re: C.S. Peirce, Spencer Brown, & Me
Cf: Charles Sanders Peirce, George Spencer Brown, and Me • 5 https://inquiryintoinquiry.com/2017/08/12/charles-sanders-peirce-george-spencer-brown-and-me-5/ All, | Continuing the salvage and update of posts lost when Yahoo! Groups defuncted. | That's just the way the internet cookie crumbles when capitalism incorpulent | takes over the web that a science-minded ARPA once built at taxpayer expense. Peirce's Law Proof Animation https://inquiryintoinquiry.files.wordpress.com/2012/01/peirces-law-2-0-animation.gif Here are blog and wiki versions of an article I wrote on Peirce’s Law, an axiom or theorem (depending on your choice of logical basis) which distinguishes classical from intuitionistic propositional calculus. Aside from its pivotal logical status it affords a nice illustration of several important features of logical graphs in the style of Peirce and Spencer Brown. Peirce’s Law • Inquiry Blog ( https://inquiryintoinquiry.com/2008/10/06/peirces-law/ ) • OEIS Wiki ( https://oeis.org/wiki/Peirce%27s_law ) • MyWikiBiz ( http://mywikibiz.com/Peirce's_law ) • Wikiversity ( https://en.wikiversity.org/wiki/Peirce's_law ) Here's another resource on the relationship between Classical and Intuitionistic Propositional Calculus: Propositions As Types Analogy • https://oeis.org/wiki/Propositions_As_Types_Analogy 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.
Re: [PEIRCE-L] Existential Graphs in 1911
From the list perspective: Jas wrote: I have said it before, I will say it again--we have different purposes, so we reach different conclusions. -- Since perspective is important, it might be a good idea to explicate the differences in purpose each of you entertain. best, Auke > Op 24 januari 2021 om 5:32 schreef "John F. Sowa" : > > > 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. > _ _ _ _ _ _ _ _ _ _ ► 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.
