John, List: JFS: The first is that all modern versions of modal logic after C. I. Lewis (including those based on post-1970 methods) are consistent with or variations of one or more of the versions specified by Lewis.
Indeed, Lewis specified *S1*-*S5* in 1932, of which only *S4* and *S5* are normal modal logics that include distributive axiom K, which is named for Kripke. Feys specified *T* in 1937 by subtracting axiom 4 from *S4*, and Von Wright specified *M* in 1951, which was later proved to be equivalent to *T*. Lemmon offered simplified specifications for *S1*-*S5 *and *T* in 1957, along with a new system *S0.5* that matches *T* except that instead of all theorems being necessarily true, only tautologies are necessarily true. *B* is named for Brouwer and is an alternative to *S4* since both contain *T* and are contained in *S5*, but neither contains the other. Pollock specified *P* (my suggested name) in 1967, which matches *S0.5* and *T* except that iterated modalities are prohibited. JFS: But the papers of Delta graphs can represent more information about each world, including the reasons why it happens to be possible, actual, necessary, or impossible. ... The specifications about papers in L376 would allow a tree structure of papers. Again, the only purpose that Peirce states in R L436 for needing to add a Delta part to EGs is "in order to deal with modals," which he consistently defines elsewhere as propositions involving possibility or necessity/certainty. There is no evidence in the 19 extant pages of R L436 (or elsewhere) that he expects Delta EGs to address other kinds of modality, incorporate any kind of metalanguage, or involve "a tree structure." Peirce also does not say nor imply in R L436 that the "many papers" are unique to Delta. In fact, as described there, they are equally applicable to Alpha, Beta, and Gamma. We know this because he discusses in some earlier writings the idea that an individual page represents only a *portion *of the much larger sheet of assertion or phemic sheet, namely, the part that "is before the common attention" of the utterer and interpreter at any given time. CSP: Two parties are, in our make-believe, feigned to be concerned in the scribing of graphs; the one called the Graphist, the other the interpreter. Namely, although the sheet that is actually employed may be quite small, we make believe that the so-called sheet of assertion is only a particular region, or area, of an immense surface; namely, the former is that part of the latter that falls within the field of view of the interpreter. Upon the great surface the Graphist alone has the power to scribe any graph; while he scribes what he sees fit. The interpreter, for his part, has the power, with more or less effort, to move the graph-instances about as he pleases, so long as he keeps them separate from one another, so that no two shall touch. In particular, he can move such ones as he likes and as many as he likes into his field of view, the sheet of assertion; or he can move them away. We further conceive that this feigned sensible state of things is the icon or emblem of a mental state of things. Namely, the immense surface with the graphs scribed upon it is the image of the interpreter’s experience, while the sheet of assertion, his field of view is the image of his field of attention. His experience is forced upon him, while he attends to what he pleases, if he puts forth sufficient effort. (R 280, c. 1905) CSP: Moreover, the Phemic Sheet iconizes the Universe of Discourse, since it more immediately represents a field of Thought, or Mental Experience, which is itself directed to the Universe of Discourse, and considered as a sign, denotes that Universe. Moreover, it [is because it must be understood] *as *being directed to that Universe, that it is iconized by the Phemic Sheet. So, on the principle that logicians call "the *Nota notae*" that the sign of anything, X, is itself a sign of the very same X, the Phemic Sheet, in representing the field of attention, represents the general object of that attention, the Universe of Discourse. This being the case, the continuity of the Phemic Sheet in those places, where, nothing being scribed, no *particular *attention is paid, is the most appropriate Icon possible of the continuity of the Universe of Discourse--where it only receives *general *attention as that Universe--that is to say of the continuity in experiential appearance of the Universe, relatively to any objects represented as belonging to it. (CP 4.561n, 1908) In the complete absence of any exact quotations from Peirce spelling out what (if anything) he had in mind for Delta EGs *beyond *dealing with modals, any proposed candidate going farther than that can only be offered as a hypothesis, not treated as a definitive specification. I am still wondering exactly how yours would represent the five modal propositions that he wrote in his Logic Notebook, if not exactly as he scribed their EGs on that page (R 339:[340r], 1909 Jan 7). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Sat, Mar 2, 2024 at 5:18 PM John F Sowa <s...@bestweb.net> wrote: > Jon, > > There are several points that must be considered. The first is that all > modern versions of modal logic after C. I. Lewis (including those based on > post-1970 methods) are consistent with or variations of one or more of the > versions specified by Lewis). That includes the versions of modal logic > supported by the IKL logic of 2006. Further qualifiers such as wishing, > hoping, fearing, specified in Holy Scriptures. . . may be *ADDED *to the > specifications that determine possibility, actuality, or necessity. > > Second, Lewis was inspired by Peirce's 1903 specifications, and no one > knows how many other MSS Lewis may have read. But Lewis adopted the much > more readable basic operators, represented by □ and ◇. For readability, > they correspond to the words 'necessary' and 'possible' in English or their > equivalents in other languages. > > Third, all of Peirce's 1903 combinations can be represented by > combinations of those two symbols and negation. But the papers of Delta > graphs can represent more information about each world, including the > reasons why it happens to be possible, actual, necessary, or impossible. > That is also true of the worlds specified by Hintikka, Dunn, IKL, and > others. The specifications of those worlds can also add further > information beyond just those two operators plus negation. > > Fourth, more issues of modality related to Peirce and modern variations > were discussed at a workshop in Bogota hosted by invitation of Zalamea. > Some of the presentations were published in the *Journal of Applied > Logics* *5:5*, 2018. > http://www.collegepublications.co.uk/downloads/ifcolog00025.pdf . Others > in the Journal Zalamea edited, *Cuadernos de Sistemática Peirceana* *8*, > 2016. https://ucaldas.academia.edu/CuadernosSistem%C3%A1ticaPeirceana . > (Although this version is dated 2016, it was delayed by late submissions > and editing until 2019.) > > Fifth, Risteen's background was significant. He was a former student of > Peirce's at Johns Hopkins, and he was a paid assistant to Peirce for > definitions in the *Century Dictionary* from S to Z. His most important > contribution (at least for Delta graphs) was his note about Cayley's > mathematical trees for the dictionary entry and in the discussions with > Peirce in December 1911. It would have been wonderful to have a YouTube of > their discussions on 3 Dec. 1911. > > The specifications about papers in L376 would allow a tree structure of > papers. Risteen's knowledge of mathematical trees is a likely reason why > Peirce had invited him to visit in December and why he was writing that > letter to him shortly after the visit. > > And note the very strange coincidence that occurred shortly after Peirce > began the letter L376: Juliette had washed and scrubbed the floor in > December after a visitor had left. There were papers on the floor. Peirce > slipped on the floor in an unusual fall that caused the kind of injury that > occurs in a twisting motion. And the injury took six months to heal. > > Scientists, engineers, and crime investigators do not believe in strange > coincidences that involve two or more unusual causes. They search for a > hidden connection. > > John >
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