I agree with how you have segmented this, and good source quotes again. Thanks Jon
On Tue, Oct 7, 2025 at 11:38 PM Jon Alan Schmidt <[email protected]> wrote: > Atila, List: > > I changed the subject line since this post is not about cosmology at all. > The quoted passage from Turrisi's edition of Peirce's 1903 Harvard Lectures > is immediately preceded by the following. > > CSP: Answer number three is that Kempe not only fails altogether to > represent general relations, but simply gives an icon. His graphs never > express *propositions*, far less *necessary consequences*. Now I invented > and developed a good many years ago such a modification of Kempe's method > of representation as was required to make it really express everything in > mathematics. I inserted a slight sketch of it into Baldwin's *Dictionary*. > It has never been published otherwise. In consequence of my great interest > in the working of that system, my studies of it had always followed that > line and, until I came to write this lecture, it had never occurred to me > to examine it in respect to its relation to the categories. On doing so, > ... (PPMRT 186, EP 2:176) > > > Conveniently, the EP editors provide an endnote identifying "symbolic > logic" as the referenced entry in Baldwin's *Dictionary of Philosophy and > Psychology* (1902) and revealing that it is reproduced at CP 4.372-93. As > one might guess from the clues here, it turns out that the "slight sketch" > in that text is of Existential Graphs (EG), which *do *express > propositions and necessary consequences, and which had not yet been > published anywhere else at that time. Moreover, in an earlier draft > paragraph that Turrisi includes but EP omits, Peirce offers these parallel > remarks. > > CSP: My third answer to Mr. Kempe's objection is that he has not > considered all relationships. In the first place, he has not considered any > that are of a general nature and generality is the home and special domain > of Category the 3rd. In the second place even among sets of singulars he > has not considered the chief relationships with which mathematics deals, > namely, those which concern infinite collections of individuals; and it is > among those especially, among singular relationships, that 3ns should be > expected to appear. For that reason, no conclusion adverse to 3ns can > logically be drawn from Mr. Kempe's graphs until his system has received > the modifications that are necessary to enable it to express all kinds of > relations. Now these modifications I have developed in the simplest and > most analytic method possible,--a method so thoroughly analytic that it > dissects a simple syllogism into eight or nine distinct inferential steps, > so that it is by long odds the most thoroughly analytic system of logical > representation yet developed, and if this system is unable to resolve 3ns > into anything else, it is safe to say that no other system can come near to > doing so. It would require a long course of lectures to present this system > in anything like its fullness, but I will outline some of its main > features. (PPMRT 184) > > > Sure enough, this alternate text goes on to present a very brief > introduction to EG, and Peirce ended up having the opportunity to present > "a long course of lectures" about them later that same year--the 1903 > Lowell Lectures, now published in volume 2/2 of *Logic of the Future*, > while volume 2/1 contains the "Logical Tracts" that he composed in > preparation for those lectures. This is when he introduced the division of > EG into three parts--Alpha for propositional logic, Beta for first-order > predicate logic, and Gamma for various extensions including modal logic, > second-order logic, and metalanguage. > > We are now left with a couple of intriguing questions. What was the > "certain fault in the system" as presented in 1902 for which Peirce was > able to identify the remedy in 1903, upon examining it specifically "from > the point of view of the categories"? What "new possibilities of > perfectionment" did he also discover on that occasion? I hope to spend some > time in the near future comparing CP 4.372-93, which is also slated for > inclusion in forthcoming LF 3/2, and other early explanations of EG with > his later ones to see if any candidates for answers to these questions > become apparent. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Structural Engineer, Synechist Philosopher, Lutheran Christian > www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt > > On Tue, Oct 7, 2025 at 10:42 AM Atila Bayat <[email protected]> wrote: > >> List, +Robert Marty >> >> I must concur that this is a serious analysis of cosmology. Yet what are >> we talking about when we talk cosmology for Peirce? It’s a normative >> science and metaphysical discourse, a physical metaphysics, a bridge >> between general metaphysics and psychical metaphysics, and in the 1898 >> lecture 8 (p. 267), “mathematical metaphysics.” >> >> His cosmology is construed as an “evolutionary” metaphysics; Peirce will >> invoke the categories to render that bridge explicit. Cf. Lectures 2-3 in >> Turrisi’s Harvard Lectures on Pragmatism, which I often consider my leading >> resource of explication. See her initial commentary, Peirce’s 3 drafts of >> Lecture 2 published there, and 1 full complete Lecture 3. Turrisi well >> observes that there were 5 extant manuscripts for Lecture 2, and 3 printed >> in her book. Let me drop this a moment. Lecture 3, which I call the Kempe >> lecture, for me is mostly about mathematical form. Peirce writes, in the >> course of examining Kempe’s system; >> >> “…I found the three Categories copiously illustrated in the system. But >> what was still more interesting, a certain fault in the system, by no means >> of the fatal kind but still a vexatious inelegance which I had often >> remarked but could see no way of remedying, now when looked upon from the >> point of view of the categories, appeared in a new and stronger light than >> ever before, showing me not only how to remedy the defect that I had seen, >> but opening my eyes to *new* *possibilities of perfectionment* that I >> had never dreamed of. I wish I could *present all this to you,* for it >> is very beautiful and interesting as well as very instructive, but it would >> require several lectures and lead me quite away from Pragmatism.” >> (Pragmatism as a Principle and Method of Right Thinking, 1997, SUNY, p.186). >> >> Now we are left on our heels by Peirce, “it would require several >> lectures and lead me quite a way from Pragmatism.” Thus no explication from >> Peirce that I know of since. It thwarted me, perhaps as if one were in that >> lecture room with Peirce, how would we react? >> >> Now my point (for another time) is that lecture 2 left me unsatisfied >> about 1ns. It seemed the most defective and inadequate of the categories, >> dangling apart from 3ns; perhaps a kind of quantum logic might render it >> more intelligible. Notice that Hartshorne and Weiss themselves, back to the >> 1940s-50s, noted that Peirce didn’t have the advantage of quantum mechanics >> (which Edwina hints as well). Particularly, Hartshorne found there were >> some matters of inconsistency in Peirce on continuity, and others have >> perhaps noted. Not sure we want to go there yet. I just want to raise >> consciousness at this stage, something rather imperfect here, yet >> fascinating. >> >> I will pick this up further in a reply to Robert Marty’s earlier and >> noteworthy post, which is overdue, in which I take up quantum logic and >> lattices. >> >> Atila >> > _ _ _ _ _ _ _ _ _ _ > ► 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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