List: Taking up another question that I posted <https://list.iu.edu/sympa/arc/peirce-l/2025-10/msg00145.html> in this thread on 10/31 ...
JAS: What is the connection between a true continuum and a triadic relation? Peirce touches on this in his final 1898 Cambridge Conferences Lecture, "The Logic of Continuity"--the same one in which he later presents his blackboard diagram, although the relevant portion in this case (NEM 3:107-8, RLT 248-50) was largely omitted from the *Collected Papers*. He describes a continuum as a "potential collection" in which "the individuals are determinable as distinct," but not by virtue of having "distinctive qualities." Instead, it is "by means of relations that the individuals are distinguishable from one another." As Hilary Putnam observes in his "Comments on the Lectures" (RLT 95), this is evidently what Peirce means when he subsequently states, "Now continuity is shown by the logic of relations to be nothing but a higher type of that which we know as generality. It is relational generality" (CP 6.190, RLT 258). But what *kind* of relations distinguish the potential individuals within a continuum from each other? Peirce immediately rules out identity and then demonstrates that any "simple dyadic relation" would allow for "two possible exceptional individuals." This is problematic "because the whole idea of the system is the potential determination of individuals by means of entirely general characters." Here is the upshot. CSP: The generality of the case is destroyed by those two points of discontinuity,--the extremities. Thus, we see that no perfect continuum can be defined by a dyadic relation. But if we take instead a triadic relation, and say *A* is *r* to *B* for *C*, say to fix our ideas that proceeding from *A* in a particular way, say to the right, you reach *B* before *C*, it is quite evident, that a continuum will result like a self-returning line with no discontinuity whatever. A continuum (3ns) is *defined by* a triadic relation that holds among any three *potential* individuals that it involves (1ns), by means of which they are "determinable as distinct," i.e., capable of actualization (2ns). Accordingly, the *semiosic* continuum is defined by the triadic relation in which a sign "mediates between an object and an interpretant; since it is both determined by the object *relatively to the interpretant*, and determines the interpretant *in reference to the object* ... the one being antecedent, the other consequent of the sign" (EP 2:410, 1907). Moreover, because "a continuum is that of which every part has itself parts of the same kind" (CP 6.168, c. 1903-4), this triad involving three dyads and three monads is present not only *throughout* the continuum that it defines, but also at any scale *within* that continuum--zooming in or out, one *always* finds an object determining a sign to determine an interpretant. I suggest that *this* is why Peirce asserts, "There is a science of semeiotics whose results no more afford room for differences of opinion than do those of mathematics, and one of its theorems ... is that if any signs are connected, no matter how, the resulting system constitutes one sign" (R 1476, 1904); why he says that "the aggregate formed by a sign and all the signs which its occurrence carries with it ... will itself be a sign" (EP 2:545n25, LF 3/1:184, 1906); and why he declares "that there can be no isolated sign" (CP 4.551, 1906). It is also why I insist that the first step toward analyzing *any* individual sign is *prescinding* it from the real and continuous process of semiosis, followed by identifying *its* antecedent object and *its* consequent interpretant, both of which are likewise of the nature of a sign. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt >
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