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 >
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