List: I heartily disagree with Jon's interpretation of the CSP's writings with respect to the concept of a relation.
Jon's basic hypothesis of the concept of expressing mathematics as "tuples" (a set of symbols? a set of numbers? a permutation group? a vector? discrete semantic objects?) obfuscates the question of what is meant by the term "relation" (relative, relate, correlate) and other entailments of the Latin root from which these terms originate, e.g., illate. Jon's interpretation may also be contradicted by CSP's view of continuity and his extra-ordinary definition of it. My reading of CSP writings indicate that his philosophy of mathematics and logic started with syllogisms and counting and developed over a half century of diligently seeking a coherent world view that included the concept of a relation in its most general semantic forms. Graphs, medads and triadicity are only components of the wider developments of his thinking about the notion of a "relation". Before one can conceptualize a relation, one must first have the notion of an identity in mind. Thus, the metaphysical assertion: "The union of units unites the unity." expresses a sentence that infers relations (among units) without making any assertion about linear ordering of symbols or the meaning of symbols. I concur with your remark: > But nothing but confusion will reign from propagating the categorical error. Cheers Jerry On Nov 27, 2015, at 10:15 AM, Jon Awbrey wrote: > Gary, all, > > It is critically important to understand the difference between relations > proper and elementary relations, also known as tuples. > > It is clear from his first work on the logic of relative terms that Peirce > understood this difference and its significance. > > Often in his later work he will speak of classifying relations when he is > really classifying types of elementary relations or single tuples. > > The reason for this is fairly easy to understand. Relations proper are a > vastly more complex domain to classify than types of tuples so one naturally > reverts to the simpler setting as a way of getting a foothold on the > complexity of the general case. > > But nothing but confusion will reign from propagating the categorical error. > > Regards, > > Jon > > http://inquiryintoinquiry.com > > On Nov 27, 2015, at 10:21 AM, <[email protected]> <[email protected]> wrote: > >> 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 . > > > >
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