Jerry, The issue about Peirce's new foundation for existential graphs (in May - June 1911) is the recognition that there had been a mistake in dating the manuscripts. Don Robert's book on EGs had been considered the best treatment on the subject. (It is still a very good intro and overview, and it can be freely downloaded.) But Don had used a mistaken date of 1909 for MS 514, which summarized Peirce's version of 1911. As a result, Peirce seemed to be using two different foundations for EGs. Since the version in MS14 was much clearer and simpler, most people. including me, had assumed it was just a simplified version. But that version is now recognized as a draft of the final version in L231 (June 1911).
I was misled by that mistake when I published an article in a special issue of Semiotica on Existential Graphs in 1911. In that article, I mistakenly assumed that Peice's version in MS 514 was just a tutorial. For a copy, see "Peirce's tutorial on existential graphs", https://jfsowa.com/pubs/egtut.pdf But when the dates had been corrected, all controversy vanished. In early May 1911 ( R699), he adopted his original discovery that a scroll was a good choice for the EG foundation. But in R670, he had recognized his mistake, and he adopted conjunction and negation as the two primary Boolean operators. He then defined the scroll as an optional way of drawing a nest of two negations. But in June 1911 (L231), He produced his clearest and best foundation ever. He never again drew or mentioned a scroll. in any MS, letter, or the logic notebook. He also used the 1911 foundation for later MSS and letters, including his last two known EGs in his long letter of 1913. After June 1911, Peirce never again mentioned the word 'scroll' in any MS, letter, or the LNB. And he never again drew a scroll. He always drew a nest of two negations. That evidence is sufficient to show that R669 was the end of the line for the scroll as a primitive. But even more important is the recognition of the 1911 foundation as the "logic of the future". See "Reasoning with diagrams and images", Journal of Applied Logics, p. 987 ff, https://www.collegepublications.co.uk/downloads/ifcolog00025.pdf Note that the review board of that article contains a list of professional logicians. My article and several others were chosen from a workshop by invitation, hosted by Zalamea in Columbia. The editors for the special edition participated in that workshop, and they invited me to write my presentation for that journal. The people at the workshop were experts on Peirce, and EGs, and logic in general. I got some good suggestions at the workshop, but nobody mentioned any objections to the conclusions. Ahti, by the way, was another of the participants. We had some good discussions, but he had no objections to my conclusions. The evidence that the scroll was gone after June 1911 is conclusive. None of the experts on EGs had any objections whatever. If anybody can find anyone who might object, tell them to read that article in the Journal of Applied Logics. John ---------------------------------------- From: "Jerry LR Chandler" <jerry_lr_chand...@icloud.com> Sent: 1/12/24 6:31 PM List: Jon, John: Obviously, both of you are struggling with what I am seeking to communicate. Perhaps the following paragraph will open your minds, your cognitive capabilities for understanding, to navigating a semantic “symbol space” more like a biological organism (the sonar system of a bat) than a machine (an oil tanker with massive momentum). I think that cognitive triadic relations are “real” - mens re. I continue to struggle with how CSP navigated the symbolic channels of the quantitative chemical notational system into a theory of logic. This is not merely a question of semantics or classical symbolic logic. According to some, Schelling had a powerful influence on CSP. "Was Schelling’s “Identitatssystem” a contributing factor to organizing the trichotomies?” is a rhetorical question worthy of significant perusal . Cheers Jerry Research Professor (Retired) Krasnow Institute for Advanced Study George Mason University From: Daniel Whistler. Symbolic Language ‘Symbol’ is one of the most polysemic words in theoretical discourse. Its connotations can be logico-mathematical, Lacanian, Peircean, anthropo- logical, liturgical, or romantic—and more often than not the symbol plays on a mixture of more than one of these discursive frameworks. What is more, the symbol takes on divergent, often opposed forms depending on the conno- tations one has in mind: the slippage and deferral constitutive of the Lacanian symbolic realm stand opposed to the unity of meaning and being in ‘the romantic symbol’. Nevertheless, the following is not a Begriffsgeschichte of the symbol, but a study of its fate in the hands of F. W. J. Schelling alone. What matters is not how we understand the term ‘symbol’ today, but how Schelling did: the contexts on which he drew and the conversations into which he entered when forming his theory of the symbol. In what follows, therefore, I will be almost entirely concerned with ‘the romantic symbol’ which emerged in German aesthetics and philosophy at the turn of the nineteenth century— even if one of my aims in what follows is to problematize the very existence of one, monolithic ‘romantic’ symbol. Part I of this book is devoted to the context in which Schelling’s construc- tion of symbolic language takes place. The present chapter considers theories of the symbol written during the Goethezeit, prior to Schelling’s own. I initially consider them historically, then from a synchronic viewpoint, examining in particular the essential properties of a symbol and the typical ways in which it was interpreted. As always, it is the interplay between ‘the romantic symbol’ and the Schellingian symbol in which I am interested: to what extent is Schelling to be positioned unproblematically in a genealogy of ‘the romantic symbol’ and to what extent does his theory in fact react against such an interpretation of the symbol? On Jan 11, 2024, at 6:16 PM, John F Sowa <s...@bestweb.net> wrote: Jon, Jerry, List, We had discussed this issue many times before. R 669 was an attempt by Peirce to relate all the versions of EGs he had written, published, and toyed with. The result (R 669) was a hodge-podge that had many ad hoc constructions that Peirce was unable to justify by any convincing proof. He knew that it was bad. In R 670, he began to sketch out a new version, and a few weeks later he produced his clearest, most precise, and most elegant foundation for EGs. And he confirmed that version as his final choice in his last major letter in 2013. Peirce's three primitives are conjunction (AND), negation (NOT), and the existential quantifier (line of identity). These three primitives with Peirce's 1911 rules of inference are so general and powerful, that they unify and simplify Gerhard Gentzen's two systems -- clause form and natural deduction. As a result an unsolved research problem about the relationship between the two systems (stated in the 1970s) was finally solved by a simple proof when translated to Peirce's 1911 notation and rules of inference. That is conclusive evidence beyond any shadow of a doubt that Peirce's 1911 system is one of his most brilliant achievements. I'll send another note with all the references. John ---------------------------------------- From: "Jon Alan Schmidt" <jonalanschm...@gmail.com> Sent: 1/11/24 6:13 PM Jerry, List: JLRC: The classical logic of mathematical reasoning (symbolized by five signs - negation, conjunction, disjunction, material conditional, and bi-conditional. Actually, Peirce points out that only two signs are needed as primitives, with the others being derived from them. CSP: Out of the conceptions of non-relative deductive logic, such as consequence, coexistence or composition, aggregation, incompossibility, negation, etc., it is only necessary to select two, and almost any two at that, to have the material needed for defining the others. What ones are to be selected is a question the decision of which transcends the function of this branch of logic. (CP 2.379, 1902) For example, in the Alpha part of Existential Graphs for propositional logic, the simplest approach is to select the two primitives as juxtaposition for conjunction (coexistence) and shading for negation* such that disjunction is then defined as multiple unshaded areas within a shaded area, material conditional (consequence) as one unshaded area within a shaded area (scroll), and bi-conditional as juxtaposed scrolls with the antecedent and consequent reversed. The Beta part for first-order predicate logic adds one more primitive, the line of identity for existential quantification such that universal quantification is then defined as a line of identity whose outermost part is within a shaded area. *As I have discussed on the List many times before, although this choice is practically more efficient and easier to explain, Peirce suggests on several occasions that it is philosophically more accurate to select the scroll for material implication as the second primitive such that negation is then defined as a scroll with a blackened inner close shrunk to infinitesimal size, signifying that every proposition is true if the antecedent is true (CP 4.454-456, 1903; CP 4.564n, c. 1906; R 300:[47-51], 1908; R 669:[16-18], 1911). Regards, Jon Alan Schmidt
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