Jon, Atila, List, While over the decades I've taken only a modest interest in Peirce's Existential Graphs, early on I made a point of studying them since I quickly realized their relevance and importance for Peirce's logic and, so, for his entire semeiotic and metaphysics, truly, for all the branches of Discovery Science (Pure Research Science) beginning with mathematics. Indeed Peirce suggested that -- in good time -- no rush; get the semeiotics and metaphysics right first! -- he expected that some logical and metaphysical 'discoveries' and 'advances' would influence communities and societies (firstly, scientific communities).
I began my study of EGs as I believe many did (perhaps especially those involved in the Knowledge Representation (KR) community) with John Sowa's “Tutorial on Existential Graphs." That was the first of several 'tutorials' I diligently studied. But truth be told, I was especially influenced by Joseph Ransdell's and Kenneth Ketner's broader contexts for understanding the role of EGs within Peirce’s semeiotic and metaphysics. Joe was something of a mentor to me in my ongoing Peirce studies, while Ken and I had stimulating discussions on various aspects of Peirce's work. As for the Gamma Graphs, I got a brief introduction to them from a series of lectures -- actually two in as many years -- which Fernando Zalamea gave in NYC a few years ago. Some of those lectures were logically 'above my pay grade', but I did come away with one certainty: that Zalamea situates Gamma squarely within Peirce’s philosophy of continuity. In any event, I must admit that I was much more interested in those "broader contexts' of Joe and Ken (and many others) rather than to EGs as such. That is still the case as the rest of this post might suggest. As you know, both Peirce’s *Lowell Lectures on Some Topics of Logic* and his Harvard Lectures on Pragmatism were delivered in 1903. Recently I've been thinking that these lecture series may represent two aspects of one and the same project. In the *Lowell Lectures*, Peirce develops his EGs as a diagrammatic logic, while in the *Harvard Lectures* he characterizes pragmatism as “the logic of abduction.” As I see it, these two lecture series taken together seem to represent an attempt by Peirce to show that the process of reasoning, including the creation of meaning, commences as abductive inference -- the imaginative leap -- and that Peirce insists that this leap is a naturally human tendency to 'guess right' about certain matters: so, from experience to abduction/ hypothesis formation /retroduction. I read that Peirce once described the Gamma Graphs as something like "the calculus of reasoning about 'would-be’s'." [Note: in the 'real world', including the existential world, each possibility may-be, can-be, but only *'would-be'* if the conditions are such as to be conducive to realizing that possibility (biological evolution follows this logic).] So Gamma Graphs would then seem to serve as the *formal* counterpart to the kind of reasoning that guesses/ retroduces/ invents new ideas as hypotheses. [So, one might hope that Gamma Graphs -- or some other tool should the Gamma development of EGs prove impossible -- would eventually be developed to serve as a tool for helping to bring into being the conditions for the 'meliorization' (as Peirce puts it) of some aspect of life on earth (including, of course, the life of the Mind).] Another way of putting this is that Peirce's describing pragmatism as “the logic of abduction” suggests that he was extending his 'would-be' logic into the realm of meaning and conduct.This represents a process of creative thinking*** about the conceivable consequences of creating the conditions for *possible humane desiderata* to be realized (Peirce insisted on adding the 'e' to 'human' in its adjectival form). So Peirce's pragmatism would seem to offer the same logic of abduction that the Gamma Graphs would hope to express diagrammatically. ***parenthetically, critical and creative thinking are subjects I taught for a number of years at CUNY and The Cooper-Union: in my opinion, critical and creative thinking truly ought to be required subjects beginning in grammar school.] A helpful lesson I learned from Joe Ransdell, an expert in 'iconicity', was that just as EGs function as icons of the thought or situation it represents in that it reveals the logical relations among its parts that, similarly, Joe argued that *pragmatic meanings are also icons*. Further, meaning-icons represent not only possible effects in experience but they also can serve as guides to rational and humane conduct. To think abductively is to construct an icon of a possible world, which is to say that such an icon is a model of how things 'would-be' if the conditions were such as to be able to bring about some desirable change. For some years the scholar, Aldo de Moor and I were interested in how 'more iconic graphs' (such as EGs versus, say, Algebra) might function in relation to: syntax |> pragmatics semantics As I currently see it, Gamma Graphs -- or something functioning as they were intended by Peirce to function -- might represent the *syntax* of abduction as they have the promise of showing how icons of possible relations can be generated and manipulated within a given logical space. If that is so, then Pragmatism perhaps provides both the semantics and pragmatics (the semeiotic teleology of abduction, so to speak) explaining how those quite different icons acquire meaning through their bearing on practical life and inquiry. I am suggesting they are both expressions of Peirce’s broader semeiotic vision: that reasoning, meaning, and conduct all evolve through the continual creation, interpretation, and testing of *signs of possibility* by an open community of interest. Best, Gary R On Thu, Oct 16, 2025 at 5:23 PM Jon Alan Schmidt <[email protected]> wrote: > Atila, List: > > Following up on my previous post in this thread, Peirce begins his "slight > sketch" of Existential Graphs (EG) in the entry for "symbolic logic" in > Baldwin's *Dictionary of Philosophy and Psychology* (1902) by describing > what he later distinguishes as the Alpha part for propositional logic. > Rather than thin oval lines as cuts, "to facilitate the printing," he uses > square brackets, parentheses, and braces to enclose different areas; for > example, he represents "if A then B" as [A(B)]. > > > > Upon introducing the line of identity, Peirce does not immediately shift > to the (future) Beta part for first-order predicate logic, where it denotes > an indefinite individual to which general concepts are attributed by > attaching names. Instead, he initially uses a heavy line connecting A and B > to denote a "quasi-instant" at which both propositions are true. This > directly anticipates his Logic Notebook entry of 1909 Jan 7 (R 339:340r > <https://iiif.lib.harvard.edu/manifests/view/drs:15255301$637i>), where > the heavy line represents "circumstances" or "times" when propositions > attached to it are true--a candidate notation for implementing modal logic. > Accordingly, I have suggested in two recent papers (here > <https://revistas.pucsp.br/index.php/cognitiofilosofia/article/view/60449/46975> > and here <https://muse.jhu.edu/article/939654>) that this might be what > he had in mind nearly three years later when he expressed the need "to add > a *Delta* part in order to deal with modals" (R 500, 1911 Dec 6). > > > > Returning to Baldwin's *Dictionary*, Peirce does move on quickly to what > we know today as Beta, although he continues to attach capital letters to > lines of identity instead of names. The only exception is when he briefly > switches to lowercase letters when assigning specific words to them--*l* > for the relation of loving, *m* for man, *w* for woman, etc. He concludes > with the following remarks. > > > CSP: For all considerable steps in ratiocination, the reasoner has to > treat qualities, or collections, (they only differ grammatically), and > especially relations, or systems, as objects of relation about which > propositions are asserted and inferences drawn. It is, therefore, necessary > to make a special study of the logical relatives "____ is a member of the > collection ____," and "____ is in the relation ____ to ____." The key to > all that amounts to much in symbolical logic lies in the symbolization of > these relations. But we cannot enter into this extensive subject in this > article. (CP 4.390) > > > > After some further investigation, I now strongly suspect that this is the > "certain fault in the system" and "vexatious inelegance" that Peirce > mentions in his third 1903 Harvard Lecture (PPMRT 186, EP 2:176)--in the > Beta part of EG that implements first-order predicate logic, heavy lines of > identity *only* denote individuals, such that there is no way to denote > qualities, collections, relations, or abstractions as *subjects* of > propositions. The remedy, which he evidently discovered along with other > "new possibilities of perfectionment" upon reexamining EG "from the point > of view of the categories," was to develop the Gamma part that he > subsequently introduced in his 1903 Lowell Lectures. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Structural Engineer, Synechist Philosopher, Lutheran Christian > www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt > _ _ _ _ _ _ _ _ _ _ > ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . > ► <a href="mailto:[email protected]";>UNSUBSCRIBE FROM > PEIRCE-L</a> . But, if your subscribed email account is not your default > email account, then go to > https://list.iu.edu/sympa/signoff/peirce-l . > ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and > co-managed by him and Ben Udell.
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