Jon, Edwinia, List: The citation "What, in a general way, does the Diagram of Existential Graphs represent the mode of structure of the Phaneron to be like? The question calls for a comparison, and in answering it a little flight of fancy will be in order. It represents the structure of the Phaneron to be quite like that of a chemical compound. ... Each Elementary Graph, like each chemical element, has its definite Valency ... . This is resemblance enough. (NEM 4:320-321, 1906)”
further confirms the extraordinarily deep role of the science of chemistry in the deepest structures of CSP’s rhetorical stance and semantic forms. This strikes me as being an extraordinary surprise! Why? Because a chemical compound has a chemical formula. Because the chemical formula has a specific RELATIVE weight. Because the chemical elements are bound together by valence, thereby becoming RELATIVES. Because these three terms are RELATED by exact mathematical calculations from semiotic references from the table of elements and from the quali-signs and indices of individual compounds. Consequently, these propositional terms unite unequivocally the existence, the logic and the semiotics of natural objects. Hence the logic of relatives. The assertion rests on human experience, augmented by simple mathematics of addition. These cause-effect theses follow from the semiotics proposed by John Dalton at the turn of the 19th Century. While modern chemistry requires further information to define an individual molecular compound, these implications are historically reasonable. The last words, "This is resemblance enough.” is equally surprising. Enough for what? In the chemical sciences at that time, these three terms were sufficient to experimentally determine the molecular structures of many compounds. And to recognize that that the valences of elements varied with the relations to other elements. Thus, these assertions are sufficient for the thesis that the semantics of trichotomy was grounded on the sufficiency of these terms for analysis and synthesis of chemical compounds. Consequently, it can be asserted that the trichotomy was a direct restatement of the logic of chemistry as it was understood at that time. What other logical assertions are supported by this conceptualization of the phaneron? In particularly, what are the implications for the current hypothesizes that relate CSP’s writings to biosemiotics? Cheers Jerry > On Jul 16, 2021, at 9:42 PM, Jon Alan Schmidt <jonalanschm...@gmail.com> > wrote: > > Gary R., List: > > GR: Is it in that "next chapter" that Peirce takes up the logic of relations? > > This seems to have been the plan that he had in mind when he was writing "The > Simplest Mathematics" as chapter 3 of Minute Logic (R 429, CP 4.227-323, > 1902). > > CSP: In this chapter, I propose to consider certain extremely simple branches > of mathematics which, owing to their utility in logic, have to be treated in > considerable detail, although to the mathematician they are hardly worth > consideration. In Chapter 4, I shall take up those branches of mathematics > upon which the interest of mathematicians is centred, but shall do no more > than make a rapid examination of their logical procedure. In Chapter 5, I > shall treat formal logic by the aid of mathematics. There can really be > little logical matter in these chapters; but they seem to me to be quite > indispensable preliminaries to the study of logic. (CP 4.227) > > There are at least two other manuscript drafts of chapter 3 (R 430-431), but > the manuscripts for chapter 4 (R 432-434) all bear a very different > title--"Ethics"--and there are no manuscripts catalogued by Robin for chapter > 5. However, in one of the manuscripts for How to Reason: A Critick of > Arguments (1893)--which is supposed to be published in its entirety someday > as Volume 10 of the Chronological Edition--Peirce states, "We now come to the > Logic of Relations ... which was only brought to essential completion in > 1884" (R 481:5). In an accompanying footnote, he cites his own landmark > paper, "On the Algebra of Logic: A Contribution to the Philosophy of > Notation" (CP 3.359-403, 1885); but "logic of relations" never appears in > that text, only "logic of relatives." He proceeds to explain why. > > CSP: A relation is precisely defined as a fact about several subjects. A fact > is an element of the truth expressible as a proposition. As all logic deals > with relations, it is more accurate to describe the branch of logic which I > am going to expound as the logic of relatives, i.e. relative terms. Relations > as relatives are either dual, as in "A loves B" or plural, as "A gives B to > C." (R 481:5) > > Hence, it appears that Atkins is right not to see much difference between > "the -adicity of relative terms themselves" and "propositional forms." > Nevertheless, both terms and propositions are obviously signs, and I believe > that it is important to maintain the distinction between the formal logic of > relations/relatives as pure mathematics and its application to terms and > propositions within the normative science of logic as semeiotic. Of course, > Peirce was writing Minute Logic right about the time when he first fully > recognized the need to insert phenomenology/phaneroscopy, esthetics, and > ethics into his classification of the sciences between mathematics and > (normative) logic--a major revision to his earlier outline, in which logic as > the first branch of empirics comes right after mathematics. > > Again, Bellucci suggests that Existential Graphs are the "best notational > expression" of the logic of relatives. It thus seems plausible to view > Peirce's abundant writings about EGs as replacing whatever he might otherwise > have written about the logic of relations/relatives in the missing chapters 4 > and 5 of Minute Logic. Moreover, as Gary F. reminds us occasionally, Peirce > considers EGs to be a highly useful tool not only for logic, but also for > phaneroscopy. > > CSP: Let us call the collective whole of all that could ever be present to > the mind in any way or in any sense, the Phaneron. ... The Phaneron being > itself far too elusive for direct observation, there can be no better method > of studying it than through the Diagram of it which the System of Existential > Graphs puts at our disposition. ... > What, in a general way, does the Diagram of Existential Graphs represent the > mode of structure of the Phaneron to be like? The question calls for a > comparison, and in answering it a little flight of fancy will be in order. It > represents the structure of the Phaneron to be quite like that of a chemical > compound. ... Each Elementary Graph, like each chemical element, has its > definite Valency ... . This is resemblance enough. (NEM 4:320-321, 1906) > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Structural Engineer, Synechist Philosopher, Lutheran Christian > www.LinkedIn.com/in/JonAlanSchmidt > <http://www.linkedin.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt > <http://twitter.com/JonAlanSchmidt>
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