Jerry, I still don't understand what you mean by your mantra
""The union of units unites the unity." Sung On Fri, Nov 27, 2015 at 12:58 PM, Jerry LR Chandler < jerry_lr_chand...@me.com> wrote: > 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, <g...@gnusystems.ca> <g...@gnusystems.ca> > 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 > 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 > . > > > > > > > > ----------------------------- > 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 > . > > > > > > -- Sungchul Ji, Ph.D. Associate Professor of Pharmacology and Toxicology Department of Pharmacology and Toxicology Ernest Mario School of Pharmacy Rutgers University Piscataway, N.J. 08855 732-445-4701 www.conformon.net
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