Re: [PEIRCE-L] Four branches of existential graphs: Alpha, Beta, Gamma, Delta
List, John: > On Mar 20, 2024, at 3:16 PM, John F Sowa wrote: > > That quotation shows that Gamma graphs add one and only one NECESSARY feature > to Alpha + Beta graphs: the same or equivalent metalanguage feature used in > 1898 (RLT). When Peirce referred to the DIVISION of Gamma graphs, that is > the only feature required.He later did much more talking about modality > and with new notations. He never again used any of the notations that are > unique to the 1903 Gamma graphs. I am puzzled by this paragraph. If the critical concept that is under scrutiny here the issue of “graphs of graphs” , how is this related to the arithmetical notion of division? And what sort of mental operations would be required to assert the nature of a division of a “graph of graphs“? Cheers Jerry _ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Meta-languages. Re: Four branches of existential graphs: Alpha, Beta, Gamma, Delta
Jon, List > On Mar 20, 2024, at 12:46 PM, Jon Alan Schmidt > wrote: > > Peirce's 1898 and 1903 notations for metalanguage are identical, except that > the oval and line are lightly drawn in the former and dotted in the latter. > > Peirce's "red pencil" notation in R 514 has nothing to do with > metalanguage--it turns an entire sheet into nested cuts for implication, with > the antecedent (postulates) in the margin and the consequent (theorems) > inside the red line. > In these two paragraphs, the term “metalanguage” is used. Was I misled by the assertion (by another logician) that Tarski was the first to use this term? Although this may seem as a trivial point, it becomes rather critical from the perspectives of emergence and evolution with the putative levels of development and the corresponding grammatical distinctions between the social and natural sciences and current notions of “metalogics”. At issue is the languages in which propositions are posited. Cheers Jerry _ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Cuts are out. Tinctures are in.
John, List: JFS: It's not clear which "55 pages" Peirce was counting. On the contrary, here is the relevant text in R L376. CSP: 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. Peirce cites an "account" of EGs that appeared "in the *Monist* of Oct. 1906," then refers to "the description" twice, calling it "as bad as it well could be" and saying that it "fills 55 pages." He is clearly talking about "Prolegomena to an Apology for Pragmaticism" as originally published in *The Monist* (vol. 16, no. 4, Oct. 1906, pp. 492-546 = 55 pages). Moreover, for the forthcoming volume 3/1 of *Logic of the Future*, Ahti-Veikko Pietarinen has compiled an "Index to 'Prolegomena'" from R 292, R 1256, and R 1632, all dated 1910 or later. Sure enough, it lists "over a hundred technical terms" that are employed in that article. JFS: Following are excerpts from the Prolegomena prior to the specifications of tinctured EGs. They have strong similarities to related material in L376: I agree--they demonstrate that the "many papers" concept was not an innovation in 1911, and thus not unique to the new Delta part, just as I have been saying all along. It was already a well-established aspect of EGs as one of "the Conventions, the Rules, and the working of the System" that constitute "a cross division" orthogonal to the division into the Alpha, Beta, and Gamma parts--hence, applicable to *all* of them. JFS: an organization of the papers according to Cayley's trees, which Risteen had studied. (See the references to Risteen in EP2.) There are no "references to Risteen in EP2"--his name is not in the index, and a search turns up zero mentions. However, Nathan Houser's introduction to volume 8 of the *Writings *includes a paragraph about how "Peirce asked Risteen to add 'trees' to the list of mathematical subjects he was gathering information on for Peirce’s dictionary work" (W 8:xlviii-xlix). Nevertheless, this was in 1891--two full decades before Peirce wrote the letter to Risteen that we have been discussing, which itself says nothing whatsoever about Cayley's trees, nor any other particular "organization of the papers." Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Fri, Mar 22, 2024 at 4:33 PM John F Sowa wrote: > Jon, List, > > It's not clear which "55 pages" Peirce was counting. It may have been his > own MS. As for L477, he was probably recalling words that he remembered > from the letter to Risteen. In L477, he only mentioned one sentence on > that topic: "It cost me the trouble of my nonsensical 'tinctures' and > heraldry." The more detailed comments in L376 said that the "cuts" with > their recto/verso implications were responsible. But the word 'tinctured' > was prominent in the name of those EGs, and that is what Peirce (and his > readers) remembered. > > For the Gamma graphs of 1903, I commented on the absence of any later > use. I found a reference from 1906 that explains why Peirce never again > used the Gamma graphs: > > In my former exposition of Existential Graphs, I said that there must be a > department of the System which I called the Gamma part into which I was as > yet able to gain mere glimpses, sufficient only to show me its reality, and > to rouse my intense curiosity, without giving me any real insight into it. > The conception of the System which I have just set forth is a very recent > discovery. I have not had time as yet to trace out all its consequences. > But it is already plain that, in at least three places, it lifts the veil > from the Gamma part of the system. > > The new discovery, which sheds such a light is simply that, as the main > part of the sheet represents existence or actuality, so the area within a > cut, that is, the verso of the sheet, represents a kind of possibility. > (R490, April 1906; CP 4.576) > > The first paragraph above explains why Peirce never used his Gamma graphs > of 1906. It also shows that he was exploring cuts with recto/verso > options, which he continued to use until R669 (May 1911). He finally > abandoned recto/verso cuts in R670 (June 1911). > > But the text of the Prolegomena (other than the definition of the EGs) > helps to explain related text in L376. Following are excerpts from the > Prolegomena prior to the specifications of tinctured EGs. They have strong > similarities to related material in L376: > > Convention the First: Of the Agency of the Scripture. We are to imagine > that two parties* collaborate in
Re: [PEIRCE-L] Cuts are out. Tinctures are in.
Jon, List, It's not clear which "55 pages" Peirce was counting. It may have been his own MS. As for L477, he was probably recalling words that he remembered from the letter to Risteen. In L477, he only mentioned one sentence on that topic: "It cost me the trouble of my nonsensical 'tinctures' and heraldry." The more detailed comments in L376 said that the "cuts" with their recto/verso implications were responsible. But the word 'tinctured' was prominent in the name of those EGs, and that is what Peirce (and his readers) remembered. For the Gamma graphs of 1903, I commented on the absence of any later use. I found a reference from 1906 that explains why Peirce never again used the Gamma graphs: In my former exposition of Existential Graphs, I said that there must be a department of the System which I called the Gamma part into which I was as yet able to gain mere glimpses, sufficient only to show me its reality, and to rouse my intense curiosity, without giving me any real insight into it. The conception of the System which I have just set forth is a very recent discovery. I have not had time as yet to trace out all its consequences. But it is already plain that, in at least three places, it lifts the veil from the Gamma part of the system.The new discovery, which sheds such a light is simply that, as the main part of the sheet represents existence or actuality, so the area within a cut, that is, the verso of the sheet, represents a kind of possibility. (R490, April 1906; CP 4.576)The first paragraph above explains why Peirce never used his Gamma graphs of 1906. It also shows that he was exploring cuts with recto/verso options, which he continued to use until R669 (May 1911). He finally abandoned recto/verso cuts in R670 (June 1911). But the text of the Prolegomena (other than the definition of the EGs) helps to explain related text in L376. Following are excerpts from the Prolegomena prior to the specifications of tinctured EGs. They have strong similarities to related material in L376: Convention the First: Of the Agency of the Scripture. We are to imagine that two parties* collaborate in composing a Pheme, and in operating upon this so as to develop a Delome. [Provision shall be made in these Conventions for expressing every kind of Pheme as a Graph; and it is certain that the Method could be applied to aid the development and analysis of any kind of purposive thought. But hitherto no Graphs have been studied but such as are Propositions; so that, in the resulting uncertainty as to what modifications of the Conventions might be required for other applications, they have mostly been here stated as if they were only applicable to the expression of Phemes and the working out of necessary conclusions.The two collaborating parties shall be called the Graphist and the Interpreter. The Graphist shall responsibly scribe each original Graph and each addition to it, with the proper indications of the Modality to be attached to it the relative Quality* of its position, and every particular of its dependence on and connections with other graphs. The Interpreter is to make such erasures and insertions of the Graph delivered to him by the Graphist as may accord with the "General Permissions" deducible from the Conventions and with his own purposes. Convention the Second: Of the Matter of the Scripture, and the Modality of the Phemes expressed. The matter which the Graph-instances are to determine, and which thereby becomes the Quasi-mind in which the Graphist and Interpreter are at one. . . After a complex specification of the tinctured EGs, the document ends: In my next paper, the utility of this diagrammatization of thought in the discussion of the truth of Pragmaticism shall be made to appear.There was no "next paper" for Carus. But these topics are related to the text of L376. The critical issues are (a) A phemic sheet that consists of multiple papers; (b) A dialog between an utterer and an interpreter; (c) Options for each of them to designate the status (modality, time, intention) of any paper, whether indicated by a tincture or by postulates in the margin or by some other method; (c) an organization of the papers according to Cayley's trees, which Risteen had studied. (See the references to Risteen in EP2.) If Peirce had been healthy for the following six weeks, a continuation along these lines could have gone a long way toward establishing that proof of pragmaticism he had been working on for the last decade of his life. John From: "Jon Alan Schmidt" John, List: In the first passage that you quoted from R L376, I agree that Peirce is primarily condemning cuts, not tinctures. However, he is also condemning his entire 55-page description of EGs in "Prolegomena to an Apology for Pragmaticism"--that is the total length of the article as originally published in The Monist, which
