Hello Gary F. In the remarks on the opening pages of NDTR (CP 2.238-9): "This would give us a second set of trichotomies that would generate ten classes of triadic relation, but again, Peirce uses only the first of those trichotomies in his analysis of sign types. This trichotomy is according as the dyadic relations between Sign and Object (constituted by the S-O-I relation) are of the nature of possibilities (icon), facts (index), or laws (symbol)." Why think that, in this essay, he is only focusing on the division of the ten classes based on the triadic relations between the three correlates. On my view, he has worked out a rather elaborate account of the triads that hold between the dyadic relations in "On the Logic of Mathematics, an attempt to develop my categories from within" and in "Nomenclature and Division of Dyadic Relations (NDDR). My hunch is that the triads of the dyadic relations between sign and object, sign and interpretant, and interpretant and object are the building blocks out of which larger triads of triadic relations are formed. At this point, we are then dealing with thoroughly genuine triadic relations--as he calls them in "The Logic of Mathematics."
--Jeff Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354 ________________________________________ From: g...@gnusystems.ca [g...@gnusystems.ca] Sent: Saturday, November 28, 2015 10:10 AM To: 'PEIRCE-L' Subject: [PEIRCE-L] RE: signs, correlates, and triadic relations Continuing the study (begun yesterday) of Nomenclature and Divisions of Triadic Relations: CP 2.238. 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. [If we substitute the names of the three Correlates of S-O-I as given in 242 (yesterday), the first sentence tells us that this type of triadic relation is divisible into three trichotomies. The first is according to whether the Sign is a mere possibility (i.e. qualisign), an actual existent (sinsign), or a law (legisign). The second is according to whether the Object is a mere possibility, an actual existent, or a law. The third is according to whether the Interpretant is a mere possibility, an actual existent, or a law. Due to the principle cited just previously (235-7), this would give us ten classes of S-O-I. But only the first trichotomy gives us classes of Signs, and only that one is used by Peirce to define the ten types of signs. In this essay he does not elaborate further on the other two trichotomies, or the ten classes of triadic relations they would generate, or their subdivisions.] 239. 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. [This would give us a second set of trichotomies that would generate ten classes of triadic relation, but again, Peirce uses only the first of those trichotomies in his analysis of sign types. This trichotomy is according as the dyadic relations between Sign and Object (constituted by the S-O-I relation) are of the nature of possibilities (icon), facts (index), or laws (symbol). Or as Peirce puts it in 243, “according as the relation of the sign to its object consists in the sign's having some character in itself, or in some existential relation to that object, or in its relation to an interpretant”; for that last relation can only be a law, or habit, in Peircean terms.] 240. It may be convenient to collect the ten classes of either set of ten into three groups according as all three of the correlates or dyadic relations, as the case may be, are of different natures, or all are of the same nature, or two are of one nature while the third is of a different nature. [As far as I can see, Peirce does not attempt such a collection in NDTR. That leaves Peirce’s third trichotomy of Signs unaccounted for, so far; and my guess is that this trichotomy can only apply to genuine triadic relations, such as are embodied in the processes of representing and determining — which in my opinion are both genuine, partly because they are mirror images of each other. But the next paragraph contains the only replica of the word “genuine” in NDTR, and Peirce does not use its antonym term “degenerate” here at all, so I’ll say no more about it here.) 241. In every genuine Triadic Relation, the First Correlate may be regarded as determining the Third Correlate in some respect; and triadic relations may be divided according as that determination of the Third Correlate is to having some quality, or to being in some existential relation to the Second Correlate, or to being in some relation of thought to the Second for something. [Again substituting the semiotic terms for the more general names of the Correlates, this tells us that the Sign determines the Interpretant in some respect; and this gives us Peirce’s third trichotomy of Signs: according as that determination of the Interpretant is to having some quality (rheme), or to being in some existential relation to the Object (dicisign), or to being in some relation of thought to the Object for something (argument). That brings us to the point where we left off yesterday, CP 2.242, which is followed by Peirce’s definition of the three trichotomies which will give us his ten classes of signs. And that’s where I’ll leave it for today. — gary f.] 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. 243. Signs are divisible by three trichotomies: first, according as the sign in itself is a mere quality, is an actual existent, or is a general law; secondly, according as the relation of the sign to its object consists in the sign's having some character in itself, or in some existential relation to that object, or in its relation to an interpretant; thirdly, according as its Interpretant represents it as a sign of possibility or as a sign of fact or a sign of reason.
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
