Helmut, List: The three dyadic relations that are involved in the genuine triadic relation of representing or (more generally) mediating are *not *S, S-O, and S-I. The first trichotomy in Peirce's initial taxonomies for classifying signs (qualisign/sinsign/legisign) is not according to any dyadic *relation*, it is according to the nature of the sign as a correlate *in itself* (EP 2:291, 1903; CP 8.334, SS 32, 1904 Oct 12); and in his later taxonomies (tone/token/type), it is according to the sign's own mode of being, apprehension, or presentation (EP 2:480-3, 1908 Dec 23-24). The third dyadic relation is, in fact, O-I; but there is no separate trichotomy for it in *any *of Peirce's taxonomies, presumably because it is always the *same *as the S-O relation.
CSP: A *Sign*, or *Representamen*, is a First which stands in such a genuine triadic relation to a Second, called its *Object*, as to be capable of determining a Third, called its *Interpretant*, to assume the same triadic relation to its Object in which it stands itself to the same Object. (CP 2.274, EP 2:272-3, 1903) CSP: A *Representamen *is the First Correlate of a triadic relation, the Second Correlate being termed its *Object*, and the possible Third Correlate being termed its *Interpretant*, by which triadic relation the possible Interpretant is determined to be the First Correlate of the same triadic relation to the same Object, and for some possible Interpretant. (CP 2.242, EP 2:290, 1903) As for "distinction," Peirce famously identifies three varieties in "On a New List of Categories" (CP 1.545-67, EP 1:1-10, 1867). CSP: The terms "precision" [later "prescission"] and "abstraction," which were formerly applied to every kind of separation, are now limited, not merely to mental separation, but to that which arises from *attention to* one element and *neglect of* the other. Exclusive attention consists in a definite conception or *supposition *of one part of an object, without any supposition of the other. Abstraction or precision ought to be carefully distinguished from two other modes of mental separation, which may be termed *discrimination *and *dissociation*. Discrimination has to do merely with the senses of terms, and only draws a distinction in meaning. Dissociation is that separation which, in the absence of a constant association, is permitted by the law of association of images. It is the consciousness of one thing, without the necessary simultaneous consciousness of the other. Abstraction or precision, therefore, supposes a greater separation than discrimination, but a less separation than dissociation. Thus I can discriminate red from blue, space from color, and color from space, but not red from color. I can prescind red from blue, and space from color (as is manifest from the fact that I actually believe there is an uncolored space between my face and the wall); but I cannot prescind color from space, nor red from color. I can dissociate red from blue, but not space from color, color from space, nor red from color. (CP 1.549, EP 1:2-3) Existential and entitative graphs are diagrammatic systems for representing propositions and their *logical *relations, and the blank page represents the continuum of true propositions in *both*. The rule for converting from one to the other in accordance with De Morgan's laws is to enclose each subgraph in a cut and then enclose the entire graph in another cut. When we do this on the blank page, we obtain an empty double cut, which can be scribed or erased in any area in either system, leaving us once again with the blank page. Scribing subgraphs A and B on the blank page iconically asserts "(A and B) is true" in existential graphs, but instead asserts "either A or B or (A and B) is true" in entitative graphs. As I understand it, the latter system *is *fully isomorphic with Spencer-Brown's laws of form; and Peirce himself says that *existential *graphs are about composition, specifically of concepts and ideas as well as terms, propositions, and arguments. CSP: A mystery, or paradox, has always overhung the question of the Composition of Concepts. Namely, if two concepts, A and B, are to be compounded, their composition would seem to be necessarily a third ingredient, Concept C, and the same difficulty will arise as to the Composition of A and C. But the Method of Existential Graphs solves this riddle instantly by showing that, as far as propositions go, and it must evidently be the same with Terms and Arguments, there is but one general way in which their Composition can possibly take place; namely, each component must be indeterminate in some respect or another; and in their composition each determines the other. On the recto this is obvious: "Some man is rich" is composed of "Something is a man" and "something is rich," and the two somethings merely explain each other's vagueness in a measure. Two simultaneous independent assertions are still connected in the same manner; for each is in itself vague as to the Universe or the "Province" in which its truth lies, and the two somewhat define each other in this respect. The composition of a Conditional Proposition is to be explained in the same way. The Antecedent is a Sign which is Indefinite as to its Interpretant; the Consequent is a Sign which is Indefinite as to its Object. They supply each the other's lack. Of course, the explanation of the structure of the Conditional gives the explanation of negation; for the negative is simply that from whose Truth it would be true to say that anything you please would follow *de inesse*. (CP 4.572, 1906) CSP: The System of Existential Graphs recognizes but one mode of combination of ideas, that by which two indefinite propositions define, or rather partially define, each other on the *recto *and by which two general propositions mutually limit each other upon the *verso*; or, in a unitary formula, by which two indeterminate propositions mutually determine each other in a measure. (CP 4.583, 1906) Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Sat, Jul 19, 2025 at 5:19 PM Helmut Raulien <[email protected]> wrote: > Gary, Jon, List, > > You have agreed about a lot of things, and I too think, that your > positions are not contradicting each other: The prescinded sign is only a > correlate is true, even tautological, as prescission is treating it by > thought as a correlate, for analytical purpose. That the real sign (not the > prescinded one) is inseparable from object and interpretant, is of course > also true. > > In the triad, the sign plays, other than e.g. the object, the central > role, on one hand, because the (prescinded) dyads are S, S-O, S-I, and not > e.g. S-O, O-I, I-S (I think like in the Ogden-Richards-model), and on the > other hand, because the sign has real (not only prescinded) properties, > that make it discernable from its environment. It is noticeable, even for > people who don´t understand it as a sign, while an object might be e.g. a > place in empty space, as I wrote sometime before. So, if something (the > triad or the interpretant) reenters somewhere, the target of this reentry > would be the sign, and not e.g. the object, I believe. > > What bothers me about Spencer-Brown`s "distinction" is, that I doubt, that > "distinction" is a common type. You can distinguish kinds or parts. Both is > very different (see Stanley N. Salthe´s paper "Salthe 12 Axiomathes"). So > you can distinguish (at least) two kinds of distinction. Wikipedia says, > that Laws of Form is isomorphic with Entitative graphs. I guess then it > would be isomorphic with Existential graphs too, because the rules for > calculation are the same. In Existential graphs the blank page denotes > "truth" (I propose "all" would do , for not merely talking about > propositions, but elements in general), so a distinction there is that of a > kind of truth, or something taken out from "all", a classification. In > Entitative graphs the blank page denotes "false" (I propose "nothing"). So > something- with or without a cut around- is an artifact, an added element, > not a kind of "false", but a put-in part. And a variable without a cut > around it is already a distinction, while with Spencer-Brown a distinction > comes only with a "cross". So I suspect, Entitative graphs and Laws of Form > are not isomorphic. Entitative and Existential graphs are, but the former > are about composition, "Or", synthesis, and the latter about > classification, "And", specification, analysis. > > Best regards, Helmut >
_ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iu.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
