Hello, I'd like to follow up on the post that Gary F. made some weeks back about the first two pages in NDTR. Let me focus on two paragraph that are found on the second page of the essay in the EP:
Triadic relations are in three ways divisible by trichotomy, according as the First, the Second, or the Third Correlate, respectively, is a mere possibility, an actual existent, or a law. These three trichotomies, taken together, divide all triadic relations into ten classes. These ten classes will have certain subdivisions according as the existent correlates are individual subjects or individual facts, and according as the correlates that are laws are general subjects, general modes of fact, or general modes of law. (CP 2.238) There will be besides a second similar division of triadic relations into ten classes, according as the dyadic relations which they constitute between either the First and Second Correlates, or the First and Third, or the Second and Third are of the nature of possibilities, facts, or laws; and these ten classes will be subdivided in different ways. (CP 2.239) How do these claims fit together? For the time being, let's set aside the two systems of classification, and let's focus on the relations themselves. In CP 2.238, Peirce describes triadic relations between the first, second and third correlates. In 2.239, he describes three dyadic relations between the correlates. How are the three dyadic relations connected to the triadic relation or relations? In the opening remarks in the discussion of triadic relations in "The Logic of Mathematics; an attempt to develop my categories from within," he says the following about the connections between the dyadic and the triadic relations: Each of the three subjects introduces a dyad into the triad, and so does each pair of subjects. (CP 1.472) How should we understand his claims about the manner in which the dyads are being introduced into the triad? --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________________ From: [email protected] [[email protected]] Sent: Friday, November 27, 2015 8:21 AM To: 'PEIRCE-L' Subject: RE: [PEIRCE-L] Re: signs, correlates, and triadic relations List, Recent discussions have made it clear to me that some readers of Peirce who focus on the famous diagram of ten sign types (EP2:296) tend to overlook its context, the “Nomenclature and Divisions of Triadic Relations” (NDTR), and especially the first page or so, where Peirce is discussing triadic relations generally before narrowing his focus to semiotic relations. So I thought it might be worthwhile to present some of it here, in Peirce’s own words, along with some comments of a corollarial and non-controversial nature. The text begins on EP2:289, but I’ve used the paragraph numbering in the CP text here to facilitate reference. From this point on, all words in this font are directly quoted from Peirce, and my comments are inserted in [brackets]. I have made bold those parts of Peirce’s text that I wish to highlight. Nomenclature and Divisions of Triadic Relations CP 2.233. The principles and analogies of Phenomenology enable us to describe, in a distant way, what the divisions of triadic relations must be. But until we have met with the different kinds a posteriori, and have in that way been led to recognize their importance, the a priori descriptions mean little; not nothing at all, but little. Even after we seem to identify the varieties called for a priori with varieties which the experience of reflexion leads us to think important, no slight labour is required to make sure that the divisions we have found a posteriori are precisely those that have been predicted a priori. In most cases, we find that they are not precisely identical, owing to the narrowness of our reflexional experience. It is only after much further arduous analysis that we are able finally to place in the system the conceptions to which experience has led us. In the case of triadic relations, no part of this work has, as yet, been satisfactorily performed, except in some measure for the most important class of triadic relations, those of signs, or representamens, to their objects and interpretants. [Most of NDTR will be about this “most important class of triadic relations,” which Peirce defines here but does not name. I will refer to it simply as S-O-I, or R-O-I. But before he begins to divide this class into subclasses, Peirce presents some ‘leading principles’, drawn from Phenomenology, which will be applied a posteriori to the classification of signs as familiar phenomena. In my comments, I will add some corollaries which follow from these general principles and frame the classification which follows.] 234. Provisionally, we may make a rude division of triadic relations, which, we need not doubt, contains important truth, however imperfectly apprehended, into— Triadic relations of comparison, Triadic relations of performance, and Triadic relations of thought. 1. Triadic relations of Comparison are those which are of the nature of logical possibilities. 2. Triadic relations of Performance are those which are of the nature of actual facts. 3. Triadic relations of Thought are those which are of the nature of laws. [The numbering I have supplied here suggests how the phenomenological categories (Firstness, Secondness and Thirdness) apply to this “rude division of triadic relations.” Thus we may reword the first to say that logical possibilities are triadic relations in which 1ns predominates; actual facts are triadic relations of Performance, in which 2ns predominates; and laws are triadic relations of Thought, in which 3ns predominates. The ordering of these relations proceeds from simple to complex, as Peirce explains next:] 235. We must distinguish between the First, Second, and Third Correlate of any triadic relation. The First Correlate is that one of the three which is regarded as of the simplest nature, being a mere possibility if any one of the three is of that nature, and not being a law unless all three are of that nature. 236. The Third Correlate is that one of the three which is regarded as of the most complex nature, being a law if any one of the three is a law, and not being a mere possibility unless all three are of that nature. 237. The Second Correlate is that one of the three which is regarded as of middling complexity, so that if any two are of the same nature, as to being either mere possibilities, actual existences, or laws, then the Second Correlate is of that same nature, while if the three are all of different natures, the Second Correlate is an actual existence. [The importance of this general principle can hardly be overestimated. Taken together with the text that follows, it explains why the application of three trichotomies to S-O-I gives us only ten classes and not 27 (3³), why a Qualisign cannot be a Symbol or a Symbol a Qualisign, etc. But this is difficult to see until we see how Peirce analyzes the R-O-I relation by its correlates, which he does in CP 2.242:] 242. 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. A Sign is a representamen of which some interpretant is a cognition of a mind. Signs are the only representamens that have been much studied. [That last sentence explains why the rest of this paper on triadic relations is all about those relations in which a Sign is the First Correlate, i.e. S-O-I). The preceding sentence defines the Sign as one kind of representamen, which has been defined as the First Correlate of a triadic relation (i.e. of R-O-I). But since no other kind of representamen has been “much studied,” Peirce confines his discussion of them to signs. Tomorrow I will return to CP 2.238-41, where Peirce mentions several ways of classifying triadic relations, the different trichotomies they produce, and the classification systems generated by combining these trichotomies in various ways. Some of these are developed in detail in NDTR and some are not, presumably because the correlates of the latter have not been studied as much as signs have. But the classifications given a priori by Peirce furnish the framework for the detailed study of semiotic relations which follows after CP 2.242.] Gary f.
----------------------------- 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 .
