John, List: JFS: If Peirce thought that the notations for his Gamma graphs of 1903 were adequate to represent everything in Delta graphs, why did he claim that the he needed to add a fourth part to his system of EGs?
If the Gamma EGs of 1903 were adequate to represent metalanguage (as I have demonstrated), then why would Peirce need to add a new Delta part for *that* purpose in 1911? JFS: In your diagram below, the row of four EGs on the left represent pure first-order predicate calculus. Any sentences outside of the EGs (whether in English or EGs or some other notation) do nothing to change those sentences from FOL to any version of modal logic. They are pure, unadulterated FOL. No, I have refuted this claim repeatedly. There is a fundamental semiotic difference between describing indefinite individuals (lines of identity) with general concepts (names) and describing possible states of things (lines of compossibility) with propositions (letters). The additional axioms of modal propositional logic do not translate into valid theorems of first-order predicate logic as implemented by Beta EGs, and there are no counterparts in the latter for iterated modalities and propositions that are *actually *true instead of *possibly *true (analogous to *existentially *quantified) or *necessarily *true (analogous to *universally *quantified). JFS: In short, that thin line attached to an oval is Peirce's 1898 notation for metalanguage--five years before the Gamma graphs. I agree with you about that. I thanked you for correcting my mistake (and Ketner's) in misreading the thin line in the second EG on RLT 151 as part of the cursive "i" in the rheme "is false." I brought to your attention Peirce's slight revision of that 1898 notation in 1903, only changing from the thinly drawn oval and line to the dotted oval and line, presumably to distinguish them from the thinly drawn lines that still represented cuts at that time. I suppose that it makes little difference once shading replaces cuts, but I prefer the dotted oval and line to minimize the potential for confusion. JFS: The metalanguage of 1898 combined with EGs that contain symbols such as "possibly true" in a verb phrase does represent modality. Exactly! That is why it is very unlikely that Peirce had *this *in mind when he said in 1911 that he needed to add a new Delta part "in order to deal with modals." JAS: As I have spelled out in a soon-to-be-published paper, "Peirce and Modal Logic: Delta Existential Graphs and Pragmaticism" ... JFS: I suggest that you study the paper I'm writing, since any peer-reviewed paper that makes any claims about modal logic is likely to be reviewed by two kinds of people: My paper has *already *been peer-reviewed, revised in response to comments, and accepted for publication. I suggest that you study it when it comes out, and maybe even consider referencing it in yours, especially if you remain convinced that your conjecture about what Peirce intended for Delta EGs is more plausible than mine. You might also want to think about changing your title to be less similar to mine. JFS: Ordinary readers who will assume that any talk about specifications in a paragraph that immediately follows "I shall now have to add a Delta part in order to deal with modals" is very likely to be a specification of something called Delta. ... How could any reader think that those conventions do not specify Delta graphs? Because what immediately precedes "I shall now have to add a *Delta *part in order to deal with modals" is "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 ..." Accordingly, ordinary readers will assume that any subsequent talk about specifications is very likely to be about *all four parts*, especially when everything that follows turns out to be applicable to Alpha, Beta, and Gamma--there is nothing in the extant 19 pages of the letter that deals with modals or would otherwise be unique to the new Delta part. I ask again, can you provide *any *exact quotations from it to the contrary? CSP: 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. A cross division of the description which here, as in that of 1903, is given precedence over the other is into the conventions, the Rules, and the working of the System. THE CONVENTIONS. The ultimate purpose of contriving this diagrammatic syntax, is to enable one with facility to divide any *necessary*, or *mathematical*, reasoning into its ultimate logical steps. JFS: Note especially the words 'now', 'here', and 'conventions' in the ending of the first paragraph, and the title "The conventions" at the beginning of the second paragraph. The word "now" appears only once, referring to the new Delta part; but "here" appears in the first two sentences--as well as "1903" and "division"--in both cases referring to the Alpha, Beta, and Gamma parts. According to the second sentence, what will follow is "a cross division" into "the conventions, the Rules, and the working of the System"--i.e., these three aspects apply equally to *all *the parts of EGs, just as they did in "the better exposition of 1903." The first sentence of the next paragraph confirms this--the common purpose of *all *the parts of EGs is to analyze necessary/mathematical/deductive reasoning into its ultimate logical steps. JFS: Finally, if Peirce thought that the notations in his Gamma graphs of 1903 were adequate to represent everything in the Delta graphs, why did he claim that he needed to add a fourth part to his system of EGs? There must be something in those Delta graphs that cannot be represented with just some excerpts from the old Gamma graphs. Indeed, given that Peirce *already *had a notation for metalanguage in his 1903 Gamma EGs--in fact, five years earlier--how could *that* be what he had in mind for the new Delta part that he felt the need to add in 1911? What exactly are *you *proposing to add that goes beyond the dotted (or thinly drawn) oval and line for asserting propositions about propositions? Is there any evidence that *Peirce *ever used that notation to represent a modal proposition by writing "is possible" or "is necessary" as the attached rheme? On the other hand, consider what he says in the four sentences right before the one where he mentions the need for "a *Delta *part in order to deal with modals." CSP: In this ["Prolegomena," 1906] 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 [in 1897]. 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 broken cuts of 1903 and the tinctures of 1906 were Peirce's previous attempts to "deal with modals," but they were ultimately unsatisfactory--even "nonsensical" in the case of the tinctures, as he called them two years later (R L477, LF 3/2, 1913 Nov 8). The badness of his *description *of EGs in 1906 was chiefly due to the use of cuts, a deficiency that he had already rectified by replacing them with shading (R 670, LF 3/1, 1911 Jun 11-12). What he needed now was a better *graphical *notation, compatible with shading, for representing and reasoning about modal propositions. Attaching heavy lines denoting possible states of things to the top of letters denoting propositions that would be true in them fits the bill. Moreover, Peirce himself suggested this solution (R 339:[340r], LF 1:624, 1909 Jan 7), although he evidently never worked out the details. I believe that I have done so in my forthcoming paper. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Fri, Mar 15, 2024 at 6:34 PM John F Sowa <s...@bestweb.net> wrote: > Jon, > > Before saying anything more, I'd like to ask a question: If Peirce > thought that the notations for his Gamma graphs of 1903 were adequate to > represent everything in Delta graphs, why did he claim that the he needed > to add a fourth part to his system of EGs? There must be something in > those Delta graphs that cannot be represented with just some excerpts from > the old Gamma graphs. > > Next point: In your diagram below, the row of four EGs on the left > represent pure first-order predicate calculus. Any sentences outside of > the EGs (whether in English or EGs or some other notation) do nothing to > change those sentences from FOL to any version of modal logic. They are > pure, unadulterated FOL. > > In RLT in 1898, I agreed with you that a thin line attached to an oval is > not a line of identity. As Peirce explained, it is a way of making a > statement about the nested EG: The EG for "You are a good girl" describes > a situation THAT is "much to be wished". > > Since the word 'metalanguage' was introduced about 20 years after Peirce > died, he did not give a name to that thin line. But after Tarski and > others introduced the word 'metalanguage' into English (and equivalents in > other languages), there can be no doubt that the thin line is equivalent to > the English conjunction 'that'. In short, that thin line attached to an > oval is Peirce's 1898 notation for metalanguage -- five years before the > Gamma graphs, > > JAS: I posted an example of this last night--proposition B = "C is a good > girl" fills the blank in "___ is possibly true," and that entire > proposition then fills the blank in "A thinks ____." In English, each > instance of a dotted oval/line corresponds to the word "that," e.g., "A > thinks *that *it is possibly true *that *C is a good girl." > > I basically agree, but note that the 1898 example has a SOLID oval > attached to a thin line. There is no need for anything from 1903. The > metalanguage of 1898 combined with EGs that contain symbols such as > "possibly true" in a verb phrase does represent modality. But note the > huge difference between EGs that *CONTAIN *words like 'possible' or > 'necessary' from EGs that do *NOT **CONTAIN *any symbols (words or other > notations) that indicate modality. > > JAS: As I have spelled out in a soon-to-be-published paper, "Peirce and > Modal Logic: Delta Existential Graphs and Pragmaticism... > > I suggest that you study the paper I'm writing, since any peer-reviewed > paper that makes any claims about modal logic is likely to be reviewed by > two kinds of people: (1) Logicians who know modal logic; and (2) Ordinary > readers who will assume that any talk about specifications in a paragraph > that immediately follows "I shall now have to add a *Delta *part in order > to deal with modals" is very likely to be a specification of something > called Delta. > > Peirce had discussed many kinds of logics in the years between 1903 and > 1911 without mentioning or drawing any of the 1903 modal graphs. During > those years, he wrote various MSS about modal logic and modal reasoning > that were very different from any of the 1903 EGs. > > Look at the transition between the two paragraphs below. Note especially > the words 'now', 'here', and 'conventions' in the ending of the first > paragraph, and the title "The conventions" at the beginning of the second > paragraph. How could any reader think that those conventions do not > specify Delta graphs? > > Excerpt from L376: I shall now have to add a Delta part in order to deal > with modals. A cross division of the description which here, as in that of > 1903, is given precedence over the other is into the conventions, the > Rules, and the working of the System. > > Excerpt from the beginning of the next paragraph: The Conventions. The > ultimate purpose of contriving this diagrammatic syntax, is to enable one > with facility to divide any necessary, or mathematical, reasoning into its > ultimate logical steps. > > If the reviewers see that transition, they will immediately ask very > serious questions. If you don't include the full L376 in an appendix (as I > am doing in my article), reviewers will ask why not? > > Finally, if Peirce thought that the notations in his Gamma graphs of 1903 > were adequate to represent everything in the Delta graphs, why did he claim > that the he needed to add a fourth part to his system of EGs? There must > be something in those Delta graphs that cannot be represented with just > some excerpts from the old Gamma graphs. > > John >
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