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* On Sat, Feb 9, 2019 at 4:08 PM Jeffrey Brian Downard < [email protected]> wrote: > Gary F, Jon S, List, > > > Is there some textual reason to give priority to the analysis of the > proposition in the argument for the categories? > > > For my part, I take the logical arguments for the categories to be based > on the requirements for having valid arguments as well as meaningful > propositions and terms. The question that he articulates in "On the Logic > of Mathematics, an attempt to develop my categories from within" is: what > are the elemental kinds of relations--both formal and material--that are > necessary for logic? 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. > > > --Jeff > > > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 > > > ------------------------------ > *From:* [email protected] <[email protected]> > *Sent:* Saturday, February 9, 2019 10:47 AM > *To:* [email protected] > *Subject:* RE: [PEIRCE-L] EGs and phaneroscopy > > > Jon, list, > > If you’ve read the whole of the Atkins book I’ll have to catch up with > you, as I’m only on Chapter 5 (of 7). But we could begin this thread with > what Atkins calls the “Modified Kantian Insight”: *The phenomenological > categories somehow are based on, are derived from, are generated by, or > otherwise correspond to the logical forms of propositions as discovered in > formal logic, which is a part of mathematics.* > > I’m inclined to agree with Atkins that Peirce never abandoned this > “insight,” *and* that from 1902 on, Peirce’s phenomenology included *both* > logical analysis and “inspective analysis.” I associate the latter with > Peirce’s more experiential descriptions of the categories, such as his > description of Secondness as the “double consciousness” of effort and > resistance we experience when pushing against a door that refuses to open. > This corresponds to a dyadic relation in the formal logic of relations. > This in turn is represented in EGs by a rhema or predicate that takes two > subjects, such as “_____ kills _____”, which appears on the sheet of > assertion (or phemic sheet) as a “Spot” with two “Pegs.” Attach a Line of > Identity to each Peg and you have an icon of a proposition (not a *pure* > icon, of course, because the interpretation is conventional, and because > the Spot has a verbal label). It is logically analyzed into a predicate > represented by the Spot with its Pegs, and two subjects represented by the > two Lines of Identity. > > If you’ve gone along with this so far, I need to ask why you seem to posit > a correspondence between continuous predicates and Lines of Identity in > your recent posts -- for instance in your recent reply to John S., > referring to “the continuity of the single predicate being represented by > continuous Lines of Identity.” Lines of Identity are of course continuous, > but how can they come to represent a *predicate* rather than a *subject*? > (Are you possibly reading the verbal label on a Spot as a subject?) If > you’ve already explained this, I must have missed it. > > My own best guess at the moment is that Peirce’s *continuous predicate* > cannot be diagrammed with EG’s at all. It is continuous because it cannot > be analyzed into parts which differ from one another, and I don’t see how > *this* kind of continuity can be represented in EGs. I have a similar > hunch that modality cannot be represented visually, at least not in the > iconic way that EGs represent the -adicity or “valency” of predicates, and > that Peirce eventually abandoned the Gamma graphs for precisely that > reason. I would love to be proved wrong on both counts, because for years I > have been looking for a way to use visual diagrams to explain the > phenomenological categories to people untrained in logic or mathematics. So > far my efforts to use the EGs for that purpose have come to naught. They > are fine for logical analysis, but their correspondence to the > *experiential* basis of the “indecomposable elements of the phaneron” is > not obvious, at least not to me. Or rather it’s not obvious *how* they > correspond; the Atkins formulation of the modified Kantian insight says > they correspond “*somehow*”, but I’d like to make that less vague by > visual means. > > Hence my interest in this topic. > > Gary f. > > } For a burning would is come to dance inane. [Finnegans Wake 250] { > > http://gnusystems.ca/wp/ }{ *Turning Signs* gateway > > > > > > *From:* Jon Alan Schmidt <[email protected]> > *Sent:* 8-Feb-19 14:35 > *To:* [email protected] > *Subject:* Re: [PEIRCE-L] EGs and phaneroscopy > > > > Gary F., List: > > > > I, for one, am *very *interested in the topic that you are proposing, > having recently read Atkins's book myself. In fact, his insights about the > correspondence of the forms of propositions to the Categories, especially > in Peirce's early writings, prompted some of my own thinking that led to > many of my recent posts. Of course, I always welcome your (and others') > feedback on those, as well. > > > > Regards, > > > Jon Alan Schmidt - Olathe, Kansas, USA > > Professional Engineer, Amateur Philosopher, Lutheran Layman > > www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt > > > > On Fri, Feb 8, 2019 at 9:18 AM <[email protected]> wrote: > > John S., you wrote: > > “Everything Peirce wrote about semeiotic, from first to last, was based on > his math and logic. Since math and logic are precise, they can resolve any > doubts or questions about the semeiotic.” > > Given your emphasis on precision, you are apparently referring to *formal* > (i.e. mathematical) logic, and not to logic as semeiotic. That is, you are > talking about *necessary reasoning* — which is able to “resolve any > doubts” because it is not concerned with the experiential basis of its > premisses. In doing so, you seem to have skipped over the science which > comes between mathematics and logic/semeiotic in Peirce’s classification of > the sciences, namely Phenomenology (or Phaneroscopy, his preferred term > after 1904). You’ve also removed the experiential basis of logic/semeiotic, > which according to Peirce is a positive science (unlike mathematics). He > was very clear that logic as semeiotic draws its principles from *both* > mathematics and phenomenology, and involves *inductive* reasoning — hence > its fallibility. > > I think this oversight (or overstatement?) might be rectified by taking a > closer look at the relationship between Existential Graphs and Peircean > phenomenology (hence my new subject line, as this post doesn’t contribute > to the debate between you and JAS). I’ve been thinking about this for some > time, but haven’t found much written about it — until the new Atkins book > on *Charles S. Peirce’s Phenomenology*, which Gary Richmond mentioned a > few days ago. Atkins has quite a lot to say about the overlaps among logic, > semeiotic, EGs and phenomenology, which I haven’t fully digested yet, and I > wondered whether you (as an authority on EGs) might have something to say > on the subject, as I don’t recall reading anything of yours in that > specific connection. > > The main reason I was looking into this connection before the Atkins book > came out is this passage from Peirce’s “PAP” (R 293, a draft leading up to > the 1906 “Prolegomena to an Apology for Pragmaticism”): > > [[ The System of Existential Graphs the development of which has only > been begun by a solitary student, furnishes already the best diagram of the > contents of the logical Quasi-mind that has ever yet been found and > promises much future perfectionment. 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*. Then the substance of every Thought (and of much beside > Thought proper) will be a Consistituent [sic] of 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. We have already > tasted the first-fruits of this method, we shall soon gather more, and I, > for my part, am in confident hope that by-and-by (not in my brief time) a > rich harvest may be garnered by this means. ]] > > > ----------------------------- > 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] . To UNSUBSCRIBE, send a message not to PEIRCE-L > but to [email protected] with the line "UNSubscribe PEIRCE-L" in the > BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm > . > > > > >
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