Gary R., Mike, List: I am also late to this discussion, having been engaged in several others over the past week.
GR: I read that Peirce once described the Gamma Graphs as something like "the calculus of reasoning about 'would-be’s'." Do you have a citation? I have not been able to find anything along these lines in Peirce's writings, and it seems unlikely to me that he would use the word "calculus" when describing EG since he repeatedly insists that it "is not intended as a calculus or general tool of reasoning, but is only meant for use in the study of logic" (LF 2/2:238, 1903). Specifically, "The principal desideratum in a calculus is that it should be able to pass with security at one bound over a series of difficult inferential steps. ... But in my algebras and graphs, far from anything of that sort being attempted, the whole effort has been to dissect the operations of inference into as many distinct steps as possible" (CP 4.424, LF 2/1:133, 1903). What he *does *say about Gamma EG, as I explored in the thread from which this one was spun off, is that (unlike Alpha and Beta EG) it facilitates the *study* of reasoning about qualities, collections, relations, and abstractions as *subjects *of propositions. GR: 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. Peirce does not present them that way in the 1903 Lowell Lectures; in fact, all three parts of EG implement strictly *deductive *logic. Although the eighth and final lecture is titled "Abduction," there is not one mention of EG in it, unlike the first five that are *primarily *about EG. As Ahti-Veikko Pietarinen says, "Peirce did not quite close the circle and revisit these issues from the point of view of the *logic *of the science of abduction" (LF 2/2:42). He later provides the following image of two graphs that appear in a manuscript draft for the *Syllabus *(R 478), which "occur nowhere else in Peirce’s corpus" and "may represent Peirce’s unique attempt to begin sketching a graphical logic of abduction" (LF 2/2:106-7). Unfortunately, Peirce "does not explain the meaning of his two doodles in any way ... failing to recognise the potential importance that a graphical method for abduction could have in completing his theory and logic of science" (ibid.). [image: image.png] MB: I do not believe that mastering the EGs is essential to understand Peirce. I agree, but like Gary, I have found that getting familiar with them is helpful toward that end. MB: An icon is surely prescinded from natural language and therefore by definition more 'grounded'. But expressiveness also comes from a larger number of tokens, leading to as many rules and conventions as natural language affords. Iconic representations seem to have lower ceilings to convey expressiveness. To be fair, expressiveness was never one of Peirce's objectives in creating and developing EG. On the contrary, he was striving for "a method (1) as *simple *as possible (that is to say, with as small a number of arbitrary conventions as possible), for representing propositions (2) as *iconically*, or diagrammatically and (3) as *analytically *as possible" (CP 4.561n, LF 3/1:393, 1908). MB: Semiosis has undue prominence in the inspection of Peirce's insights. Maybe so, but Peirce himself likely would not have considered this problematic. By his own testimony, "it has never been in my power to study anything,--mathematics, ethics, metaphysics, gravitation, thermodynamics, optics, chemistry, comparative anatomy, astronomy, psychology, phonetics, economics, the history of science, whist, men and women, wine, metrology, except as a study of semeiotic" (SS 85-6, 1908 Dec 23). MB: I have oft stated my preference for grounding Peirce's architectonic in his universal categories. As Gary said, Peirce stated that preference himself; and it is especially important not to construe his three categories too narrowly, in accordance with just one application of them--for example, treating them as strictly "modes" for classifying signs according to the various correlates and relations. Among many other manifestations, they are discovered as quality/reaction/mediation in phaneroscopy, modeled as monadic/dyadic/triadic relations in mathematics, pursued as ends of feeling/action/thought in the normative sciences, and associated with possibility/actuality/necessity in metaphysics. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Thu, Oct 23, 2025 at 1:27 AM Gary Richmond <[email protected]> wrote: > Mike, List, > > Excuse my delay in responding to your post.Of course I'm happy that you > concur with this idea: > > GR: ". . .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. > > You remarked that as a member of the KR community that what piqued your > interest in semiotics wasn't EGs as such but Sowa's presentation of > semiosis in such a way that motivated you to explore semiotic concepts in > the context of the semantic Web.. > > My own involvement in the KG community was rather intensive for a time. I > attended, presented at, gave keynote addresses, and developed and > participated in workshops for over a decade at the ICCS conferences > developed by John Sowa and Mary Keeler around KR in general and CGs in > particular (and, so, necessarily, also EGs upon which Sowa's CGs are > based). I will never be able to express my thanks to Keeler for bringing me > into that KR fold of brilliant mathematicians, logicians, scientists and > philosophers. Although in truth I have no more interest in CGs than in EGs, > I learned a great deal from my colleagues there, for example, De Moor, > Delugach, Polovina (and many others). One memorable moment in that creative > period was when Aldo de Moor, Mary Keeler, and I, already very interested > in the developic of the syntactic and semantic web, wrote one of the first, > if not *the* first, paper on a proposed pragmatic web. > > MB: I appreciate the formalization of the logic afforded by the graphs, > and the cleaner presentation of relations provided by the graphs (in their > various Alpha to Gamma guises), but they have never really "spoken" to me. > The application of semiosis to natural language is the blackboard I prefer. > I suspect we align on this. > > GR: We do agree to some extent. While Peirce once characterized EGs as 'a > moving picture of thought', I never saw the 'picture' in the icons of those > EGs I studied. However, I hope that there are others working on developing > "more iconic" expressions of logical relations, including trichotomic ones. > I am still in the process of developing my trikonic diagrams as a "more > iconic" way of presenting Peirce three category theory, especially as it > relates to phenomenology, semeiotics, and metaphysics. I'm now doing > further work on trikonic vectors, how each of these six relate to each > other in interesting ways, the possibility of trikonic vector cycles, etc. > > If [Gamma Graphs or related represent the syntax of abduction], 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. > > MB: Reasoned argument and natural language can accomplish the same end, > one which is more easily nuanced than diagrammatic icons. (In other words, > Peirce could have thought and written another 100 years but would still be > frustrated at his 'zeta graphs' to express his intentions.) > > > GR: Again, I think that EGs may not prove capable of truly providing "a > movie picture" of modality, possibilities, would-be's. It would seem that > Peirce himself found their development challenging. But they are not the > only graphical logic that can be put to bear on Peirce's semeiotic, three > category theory, and his profound understanding of continuity. > > MB: I do not believe that mastering the EGs is essential to understand > Peirce. I think I understand Peirce's objectives with his graphs, and they > have mostly to do with the frustration of being able to precisely > communicate in any medium or context. [. . . but ] expressiveness also > comes from a larger number of tokens, leading to as many rules and > conventions as natural language affords. Iconic representations seem to > have lower ceilings to convey expressiveness". > > GR: While I agree that it is not essential for Peirce scholars to master > EGs (although I do think that at least a basic study of them is valuable), > I see no reason why some *other* iconic representations need to have > lower ceilings to convey expressiveness. Having said that, I believe that > EGs (and CGs) indeed do not allow for much expressiveness. I just wouldn't > generalize this to *all *iconic representations, however. > > MB: Semiosis has undue prominence in the inspection of Peirce's insights. > I have oft stated my preference for grounding Peirce's architectonic in his > universal categories. > > GR: I agree that Peirce's architectonic needs to be grounded in his > categories -- he said as much. But this architectonic 'system'* lives* in > its rich investigatory details as the various sciences unfold, grow, show > us more of 'reality' with each advance. And here the study and application > of semeiotics is of great value. > > MB: I also find his insights on cosmology, evolution, and logic nuances > (aside from the categories and the three reasoning methods) more fertile > grounds for finding insights relevant to modern science and epistemological > questions than the semiotic process per se. > > GR: I see no reason not to employ *all* these kinds and modes of research > -- including, and I would say, along with the categories, semeiotic are of > great utility -- in consideration of matters "relevant to modern science > and epistemological questions." Of course we are all to some extent > 'specialist' (Peirce was a prominent exception). Let's just all do our best > work and hope others are doing theirs. > > Best, > > Gary R > >> Hi Gary, >> >> I very much concur with this sentiment: >> On 10/17/2025 9:46 PM, Gary Richmond wrote: >> >> 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. >> >> Yet, as a member of the 'Knowledge Representation (KR) community' as you >> refer, and one first introduced to Peirce by Sowa, it was not Sowa's >> tutorials on existential graphs (EGs) or EGs more broadly that peaked my >> interest. It was Sowa's presentation of semiosis in a dynamic way that >> struck a cord. I first wrote about this connection in 2010 when I was >> exploring the idea of concepts and reference in the context of the semantic >> Web [1]. >> >> I think I understand Peirce's view that an icon is more primitive than an >> expression, but I find the syntactic latitude presented by Peirce's graphs >> to not be compelling for the contexts I want to express. I appreciate the >> formalization of the logic afforded by the graphs, and the cleaner >> presentation of relations provided by the graphs (in their various Alpha to >> Gamma guises), but they have never really "spoken" to me. The application >> of semiosis to natural language is the blackboard I prefer. I suspect we >> align on this. >> >> You go on to speculate: >> >> If [Gamma Graphs or related repesent the syntax of abduction] 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. >> >> The iconicity of Gamma graphs may do just that, but I do not believe that >> is the only path. Reasoned argument and natural language can accomplish the >> same end, one which is more easily nuanced than diagrammatic icons. (In >> other words, Peirce could have thought and written another 100 years but >> would still be frustrated at his 'zeta graphs' to express his intentions.) >> >> Your observations brought to the fore two observations I would make about >> the Peircean scholarship community generally. Observation 1): I do not >> believe that mastering the EGs is essential to understand Peirce. I think I >> understand Peirce's objectives with his graphs, and they have mostly to do >> with the frustration of being able to precisely communicate in any medium >> or context. An icon is surely prescinded from natural language and >> therefore by definition more 'grounded'. But expressiveness also comes from >> a larger number of tokens, leading to as many rules and conventions as >> natural language affords. Iconic representations seem to have lower >> ceilings to convey expressiveness. Observation 2): Semiosis has undue >> prominence in the inspection of Peirce's insights. I have oft stated my >> preference for grounding Peirce's architectonic in his universal >> categories. I also find his insights on cosmology, evolution, and logic >> nuances (aside from the categories and the three reasoning methods) more >> fertile grounds for finding insights relevant to modern science and >> epistemological questions than the semiotic process per se. >> >> Best, Mike >> >> [1] My blog post was on "What is a Reference Concept? >> <https://www.mkbergman.com/938/what-is-a-reference-concept/>". My >> reference to Sowa was John Sowa, 2000. “Ontology, Metadata, and Semiotics,” >> presented at ICCS’2000 in Darmstadt, Germany, on August 14, 2000; see >> http://www.jfsowa.com/ontology/ontometa.htm. >> On 10/17/2025 9:46 PM, Gary Richmond wrote: >> >> 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 >> >>
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