Gary, Jon Gary,
Your good notes here capture many of the remarks I had pending, and so I make a few comments before I catch up with other threads. The main idea I had was that, amongst Peirce's own contemporaries, I think it was Josiah Royce who had the most thoroughgoing understanding of Peirce in his lifetime. I think this is instructive for contemporary Peirce scholars that Peirce (as you note) and Royce were each developing their philosophical approaches within a logical* and *metaphysical framework. Peirce indeed considered himself a logician and recognized Royce as a fine fellow logician. Historically, we know from the lecture notes that Harry Costello took at Royse's lectures of 1913 on Metaphysics how frequently he referred to Peirce. Cf. *Josiah Royce's Seminar*, 1913-1914 edited by Grover Smith, Rutgers Univ Pr 1963. pp 37, and more. In the lectures of April 1914, you will find Royce speaking of Peirce's Arch of Theories, Planck, and Einstein. Earlier, in Royce's October 7, 1904 contribution to the Science journal (The Science of the Ideal), I think you will find that Royce adopts a rather Peircean point of view; "Pure mathematics is concerned with the investigation of the logical consequences of certain exactly stable postulates of hypotheses - such, for instance, as the postulates upon which arithmetic and analysis are founded, or such as the postulates that lie at the basis of any type of geometry. For the pure mathematician, the truth of these hypotheses or postulates depends, not upon the fact that physical nature contains phenomena answering to the postulates, but solely upon the fact that the mathematician is able, with rational consistency, to state these assumed first principles, and to develop their consequences." (p. 451) Royce concludes his address, "In a word: Our common problem is the theory of the categories. That problem can be solved only by the cooperation of the mathematicians and of the philosophers." (p. 462 [Science Journal N. 8. Vol XX. No.510] Let me continue to admonish Royce's thorough reading of Kempe in 1905 and his mentions of Peirce in his monograph on "The Relation of the Principles of Logic to the Foundations of Geometry." [Royce's Logical Essays ed. by Daniel S. Robinson 1951]. And more recently, the editions by Randall Auxier *Critical Responses to Royce *Vols 2 & 3. Getting back to Peirce, I have been rereading Christopher Hookway's Peirce book (1985), which bears fruit, and would like Gary to add it to the list he provided in his earlier post. More on that tomorrow if able, since I am still in the process of replying to earlier threads, Atila On Fri, Oct 17, 2025 at 10:47 PM Gary Richmond <[email protected]> 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 > > 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. > > _ _ _ _ _ _ _ _ _ _ > ► 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.
_ _ _ _ _ _ _ _ _ _ ► 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.
