Jon, list, I think you’ve made a number of unwarranted inferences from the Peirce passages you quoted, but rather than a detailed critique of your post, I’m going to quote another passage from Peirce’s “PAP” draft which I think deals more directly with the issue in our subject line, and then comment on your post in that light.
[[ … there is a rational explanation of the precedence of Form over Matter in natural classifications. For such classifications are intended to render the composition of the entire classified collection rationally intelligible,—no matter what else they may be intended to show; and Form is something that the mind can “take in,” assimilate, and comprehend; while Matter is always foreign to it, and though recognizable, is incomprehensible. The reason of this, again, is plain enough: Matter is that by virtue of which an object gains Existence, a fact known only by an Index, which is connected with the object only by brute force; while Form, being that by which the object is such as it is, is comprehensible. It follows that, assuming that there are any indecomposable constituents of the Phaneron, since each of these has a definite Valency, or number of Pegs to its Graph-Instance, this is the only Form, or, at any rate, the only intelligible Form, the Element of the Phaneron can have, the Classification of Elements of the Phaneron must, in the first place, be classified according to their Valency, just as are the chemical elements. We call a Spot a Medad, Monad, Dyad, Triad, Tetrad, or by some other such name, according as its Valency, or the number of its Pegs, is 0, 1, 2, 3, 4, etc. It is to be remarked that a Graph not only has attachments to other Graphs through its Pegs and through Lines of Identity, but is also attached to the Area on which it is scribed, this Area being a Sign of a logical Universe. But it is not the same kind of attachment, since the Entire Graph of the Area is after a fashion predicated of that Universe, while the Lines of Identity represent Individual Subjects of which the two connected Spots are predicated either being regarded as determining the other. ] NEM 4, 322 (1906)] Your proposal is to reverse what Peirce says in that last sentence, to read the Spots as Subjects and the Lines of Identity as (continuous) Predicates. But that would amount to eliminating the difference between identity and relation. As far as I can see, that would deprive the Existential Graphs of all utility for logical analysis. In Peirce’s system, the kind of continuity a Line of Identity has is the kind we attribute to an individual subject (such as Napoleon) when we waive the requirement of an individual in the strict sense that it is determinate in all respects, including exact time and place. This is what we do whenever we refer to a person as an “individual.” This is different from the continuity of the blank Sheet of Assertion which corresponds to the Continuous Predicate “____ coexists with ____”. I don’t see this difference being eliminated in any of your quotations from Peirce (below). Gary f. From: Jon Alan Schmidt <[email protected]> Sent: 9-Feb-19 17:43 To: [email protected] Subject: Re: [PEIRCE-L] EGs and phaneroscopy 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
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