Gary R., List: I already mentioned valency, but wanted to comment briefly on the "data principle" and the "principle principle" as described by Atkins, since Jeff once disputed them in an off-List exchange with me. This is what Atkins referenced.
CSP: I would classify the sciences upon the general principle set forth by Auguste Comte, that is, in the order of abstractness of their objects, so that each science may largely rest for its principles upon those above it in the scale while drawing its data in part from those below it. (RLT 114; 1898) There is a similar comment in the Collected Papers ... CSP: ... the sciences may be arranged in a series with reference to the abstractness of their objects; and that each science draws regulating principles from those superior to it in abstractness, while drawing data for its inductions from the sciences inferior to it in abstractness. (CP 3.427; 1896) ... and this morning I came across another clear statement of them, quoted in Kenneth Ketner's introduction to *The Logic of Interdisciplinarity*. CSP: This classification (which has been worked out in minute detail) is to be regarded as simply Comte's classification, corrected. That is to say, the endeavor has been so to arrange the scheme that each science ought to make appeal, for its *general principles*, exclusively to the sciences placed above it, while for instances and special facts, it will find the sciences below it more serviceable. (R L 107; 1904) Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sat, Feb 9, 2019 at 4:35 PM Gary Richmond <[email protected]> wrote: > Jeff, Gary f, Jon, > > Jeff wrote: > > The question of what is necessary for each of the three main classes of > argument to be valid seems to be at least as important--if not more--than > the question of what is necessary for a proposition to represent a fact in > the effort to provide an *internal* grounding for the claim that there > must be three elemental formal relations: monadic, dyadic and triadic. > > > I would think that the "*internal* grounding for the claim that there > must be three elemental formal relations: monadic, dyadic and triadic" > would be found, not in normative logic, but within first science, > mathematics, and there within the logic of mathematics. > > It was that inquiry which, I believe, led Peirce to his famous, and only > recently mathematically proved*, 'Reduction Thesis', "that all relations, > relations of arbitrary adicity, may be constructed from triadic relations > alone, whereas monadic and dyadic relations alone are not sufficient to > allow the construction of even a single “non-degenerate” (that is: > non-Cartesian-factorable) triadic relation" (Robert Burch in his article, > "Peirce," in the *Stanford Encyclopedia of Philosophy*)*.* > > Peirce illustrated his valence theory in diagrams such as those at A & G > below (the other diagrams should be ignored) illustrating the possible > joining of elemental diagrams. > > [image: image.png] > > > Ken Ketner called such diagrams valental graphs in several papers > including, and especially, "Identifying Peirce's "Most Lucid and > Interesting Paper" in *Transactions of the Charles S. Peirce Society*, Vol. > 23, No. 4 (Fall, 1987), pp. 539-555 > > I think that it's important, even necessary--at least as a kind of > propaedeutic to formal logical inquiries--to consider this work in > mathematical logic, the *simplest math*, which precedes not only logic as > semeiotic, but, also phenomenology. It seems to me that to leap to the > consideration of propositions and arguments in this matter, and even the > possibility of representing categorial relations in EGs, before considering > valence theory (which, btw, was most likely suggested by Peirce's work in > Chemisty)** is to put the proverbial cart before the horse in consideration > of Peirce's phenomenology. > > *Hereth Correia, Joachim > <http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/c/Correia:Joachim_Hereth.html> > and > Pöschel, Reinhard (2006), "The Teridentity and Peircean Algebraic Logic" in > *Conceptual > Structures: Inspiration and Application* (ICCS 2006): 229-246, Springer > <http://www.springerlink.com/content/42v7r03v4x08l831/>. Frithjof Dau calls > it > <http://www.nabble.com/Re%3A-Peircean-Reduction-Thesis-Was%3A-CG%3A-typical-distribution-of-arities--p11722802.html> > "the > strong version" of proof of Peirce's Reduction Thesis. > **This following what Atkins calls, in relation to Peirce's Classification > of Sciences, the *data principle*, "that the less abstract sciences [in > the present case, Chemistry] supply data to the more abstract sciences > [here, Mathematics]. Of course it works vice versa, such that what he calls > the *principle principle* holds "that the more abstract sciences [in the > present consideration, Mathematics and Phenomenology] provide the less > abstract science [here, Logic as Semeiotic] with principles (Richard > Kenneth Atkins in *Charles S. Peirce's Phenomenology: Analysis and > Consciousness*, 23). > > Best, > > Gary R > > *Gary Richmond* > *Philosophy and Critical Thinking* > *Communication Studies* > *LaGuardia College of the City University of New York* > *718 482-5690* >
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