Gary F., List: Coincidentally, today I read through Francesco Bellucci's 2012 paper, "Peirce's Continuous Predicates <https://www.researchgate.net/publication/259734578_Peirce's_Continuous_Predicates>." He posits that Peirce did not write explicitly about Continuous Predicates after 1908 because he instead focused on EGs as a *better *way to make his point. Specifically, the blank Sheet of Assertion corresponds to the Continuous Predicate, "_____ coexists with _____"; and the Line of Identity corresponds to the Continuous Predicate, "_____ is identical to _____."
CSP: Among Existential Graphs there are two that are remarkable for being truly *continuous *both in their Matter and in their corresponding Signification. There would be nothing remarkable in their being continuous in either, or in both respects; but that the continuity of the Matter should correspond to that of the Signification is sufficiently remarkable to limit these Graphs to two; the Graph of Identity represented by the Line of Identity, and the Graph of coëxistence, represented by the Blank. (NEM 4:324; 1906) The additional step that I am taking is to recognize that "_____ is identical to _____" is not the *only *Continuous Predicate that a Line of Identity, or combinations of multiple Lines of Identity, can represent. For example, throwing everything into the *predicate*, the Graph of "Some roses are red" is analyzed as "Something that is a rose *is identical to* something that is red"; but throwing everything into the *subject *instead, it is analyzed as "A rose that I could designate *possesses the character of* redness." Bellucci cites another passage where Peirce clearly endorsed just such an analysis. CSP: In the first place, I mean by the Subject (capitalized) of an assertion or question, not the name or description so called by the grammarians, but that which is named, described, or referred to, to which the predicate relates. In the second place, the grammarians usually limit the term to the subject nominative, while I term anything named in the assertion a Subject, and although I do not always express myself so accurately, I regard everything to which the assertion relates and to which reference can be removed from the predicate, although what is referred to be a quality, relation, state of things, etc. as a Subject. Thus one assertion may have any number of Subjects. Thus, in the assertion "Some roses are red," i.e. possess the color redness, the color redness is one of the Subjects; but I do not make "possession" a Subject, as if the assertion were, "Some roses are in the relation of possession to redness," because this would not remove relation from the predicate, since the words "are in" are here equivalent to "are subjects of," that is, are related to the relation of possession of redness. For to be in relation to X, and to be in relation to a relation to X mean the same thing. If therefore I were to put "relation" into the subject at all, I ought in consistency to put it in infinitely many times, and indeed this would not be sufficient. It is like a continuous line: no matter what one cuts off from it a line remains. So I do not attempt to regard "A is B" as meaning "A is identical with something that is B." I call "is in the relation to" and "is identical with" Continuous Relations, and I leave such in the Predicate. The Predicate is that part of the assertion which is signified as the logical connexion between the Subjects. But I sometimes term the whole set of Subjects the Subject-System. (R 611:8-10[13-15]; 1908) In this approach, every Spot in an EG indeed represents a Subject, and all of the Lines of Identity *together *represent the Continuous Predicate--whether it is "_____ is identical to_____," "_____ possesses the character of _____," "_____ is a member of the class of _____," "_____ is in the dyadic relation of _____ to _____," "_____ is in the triadic relation of _____ of _____ to _____," etc. Although the Lines of Identity in the last two cases are "interrupted" by the Spot for the hypostatically abstracted relation (such as "killing"), the resulting "parts" *do not* differ from each other--as *material *parts of a *continuous *line, they are likewise continuous lines. Alternatively, they *could *instead be scribed as a *single *line, with branches at Spots of Teridentity as needed, in order to maintain their continuity. CSP: Any indefinitely small dot may be a spot replica called a *spot of teridentity*, and three lines of identity may be attached to such a spot. (CP 4.416; 1903) CSP: ... there is one more reform that needs to be made in the system of existential graphs. Namely, the line of identity must be totally abolished, or *rather *must be understood quite differently. We must hereafter understand it to be *potentially *the graph of *teridentity *by which means there always will virtually be at least one loose end in every graph. In fact, it will not be truly a graph of *teridentity *but a graph of indefinitely multiple identity. (CP 4.583; 1906) Each Subject Spot would then have exactly one Peg connecting it to one of the branches. Again, as Peirce explained in his letter to Jourdain, valency is a property of the *Continuous *Predicate and directly corresponds to the number of *Subjects *that are "married" by it into a *complete *Proposition. As is already the case for multiple Pegs on a predicate Spot, there would simply need to be an arbitrary convention specified and maintained for which branch corresponds to each blank; e.g., the giver, giving, the gift, and the recipient for "_____ is in the triadic relation of _____ of _____ to _____," 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 11:47 AM <[email protected]> wrote: > 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 >
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