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
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