Thread: JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/17890 GF:http://permalink.gmane.org/gmane.science.philosophy.peirce/17894 JBD:http://permalink.gmane.org/gmane.science.philosophy.peirce/17902 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/17907 HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/17911 GF:http://permalink.gmane.org/gmane.science.philosophy.peirce/17916
Helmut, I think a few people are making this harder than it needs to be. Let's put aside potential subtleties about elementary vs. individual vs. infinitesimal relatives and simply use “elementary relative” to cover them all at a first approximation. One of the advantages of this usage is that it allows us to exploit a very close analogy with the way “elementary transformations” function in linear algebra, affording a bridge to practical applications of semiotics. Let's make a concrete example. Say we have a universe of discourse X = biblical characters. Linguistic phrases like “brother of___” or “x is y's brother” and many others can be used to indicate a dyadic relation B forming a subset of X x X such that (x, y) is in B if a only if x is a brother of y. I will use Peirce's notation x:y for the ordered pair (x, y). Among other things it's easier to type on the phone. In the universe X of biblical characters, Abel : Cain is an elementary relation in the brotherhood relation B. But Abel : Cain also belongs to the relation E indicated by “elder brother of" and again to the relation V indicated by “victim of”. So the elementary relation by itself does not determine the general relation or general relative term that we may chose to consider it under. This means that classifying relations is a task at a categorically higher level than classifying elementary relations. In the special case of triadic sign relations, almost all the literature so far has tackled only the case of elementary sign relations. Regards, Jon http://inquiryintoinquiry.com > On Dec 3, 2015, at 5:52 PM, Helmut Raulien <[email protected]> wrote: > > Hi Jon, All, > I dont want to interrupt the discussion about terms, but I have a question > that is about the mathematical relation- but I think this consideration might > be expanded to semantics and semiotics. In mathematics, I have read > somewhere, a relation is a subset of a cartesian product. Now I think, that > there is a difference between the actual subset, and the reason for it, as > well as the result of it. So I think, there are three different things: > relation reason, actual relation (subset), and relation result. I wonder, > whether this is a matter in mathematics. It seems triadic somehow. Example: > Three equal sets A=B=C={1,2,3}. The relation reason is:"a unequal b unequal c > unequal a", in other words: "No equal elements in a tuple". The actual > relation is then: {(123)(132)(213)(231)(312)(321)}. Now this actual relation > could have had another relation reason too: "a+b+c=a*b*c", in words: "The > elements added is equal as the elements multiplied with each other". So, for > relation result you have the relation reason, plus this second thing, the > "might-have-been-too-reason". Of course this is a coincidence, but by > fetching a bit far, one might say, that it is a crude example for how > prejudices or myths come into being. Now, am I right with guessing, that the > actual relation (the subset) is the elementary relation, and eg. "no equal > elements" is a proper relation? > Helmut > > 03. Dezember 2015 um 21:00 Uhr > "Jon Awbrey" <[email protected]> > > Thread: > JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/17890 > GF:http://permalink.gmane.org/gmane.science.philosophy.peirce/17894 > > A budget of readings for present and future reference: > > Survey of Relation Theory > http://inquiryintoinquiry.com/2015/11/30/survey-of-relation-theory-%E2%80%A2-2/ > > First, we need to be clear about the difference between objects and signs: > > Relations are formal objects of discussion and thought while > Relative Terms are signs we use to denote/describe relations. > (The shorthand term "relative" is short for "relative term". > > The default meaning for "relative term" is "general relative term", > that is, a term whose denotation extends over many objects. > > The default meaning for "relation" is "general relation", > that is, a formal object that is a set of many elements. > > Next, we need to be clear about the distinction between > relatives (= general relatives) and elementary relatives. > > Note. There is a distinction in Peirce's usage between > elementary relatives and individual relatives, but if we > factor in what he says about the Doctrine of Individuals > and recognize that we are dealing with abstract forms > then it becomes a "distinction without a difference". > So I will tend to use the terms interchangeably. > > Here is one place where Peirce exhibits his appreciation > for the critical difference between relatives in general > and elementary or individual relatives. > > Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 7 > http://inquiryintoinquiry.com/2015/02/28/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-7/ > > <QUOTE> > > Chapter 3. The Logic of Relatives (cont.) > ========================================= > > §4. Classification of Relatives > > 225. Individual relatives are of one or other of the two forms > > A : A > A : B > > and simple relatives are negatives of one or other of these two forms. > > 226. The forms of general relatives are of infinite variety, > but the following may be particularly noticed. ... > > </QUOTE> > > It needs to be appreciated that classifying relations is vastly > more complex than classifying elementary or individual relations. > > In particular, classifying sign relations is vastly more complex > than classifying elementary or individual sign relations, which > is just about all that the massive literature on sign taxonomy > has been able to touch, albeit confusedly, from Peirce's time > to ours. > > Regards, > > Jon > > On 12/3/2015 11:31 AM, [email protected] wrote: > > Jon, > > > > This doesn't explain “the difference between relations proper and > > elementary relations” (which you said was > > "critically important to understand"), because the latter term is itself > > used in a specific "technical sense" by > > Peirce in the places you cite. It doesn't help to understand which > > “technical sense” of the word you have in mind. > > > > My guess is that what’s confusing some of us in understanding triadic > > relations is that some of them relate > > correlates which are themselves relations. (Perhaps correlates which are > > not relations are “individual relatives”?) > > > > Gary f. > > > > > > > > > > > > -----Original Message----- From: Jon Awbrey [mailto:[email protected]] Sent: > > 2-Dec-15 22:30 > > > > > > > > Peircers, > > > > > > > > As I wrote before, I used the phrase "relations proper" > > > > merely to emphasize that I was talking about relations in the technical > > sense. Another common idiom to the same > > purpose would be "relations, strictly speaking". > > > > > > > > As for "elementary relatives", Peirce uses this term in the 1870 Logic of > > Relatives. > > > > See, for example, CP 3.121ff and a later remark at 3.602ff. > > > > > > > > See Also: > > > > > > > > ☞ > > <https://www.google.com/search?hl=en&as_q=Peirce&as_epq=Elementary+Relative> > > https://www.google.com/search?hl=en&as_q=Peirce&as_epq=Elementary+Relative > > > > > > > > And toward the end of this section: > > > > > > > > ☞ > > <http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction#Operational_Representation> > > http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction#Operational_Representation > > > > > > > > Regards, > > > > > > > > Jon > > > > > > > >> Gary, all, > > > >> > > > >> I used the phrase “relations proper” to emphasize that I was speaking > > > >> of relations in the strict sense of the word, not in any looser sense. > > > >> I have been reading Peirce for almost 50 years now and I can't always > > > >> recall where I read a particular usage. In the 1970s I spent a couple > > > >> of years poring through the microfilm edition of his Nachlass and read > > > >> a lot of still unpublished material that is not available to me now. > > > >> But there is no doubt from the very concrete notations and examples > > > >> that he used in his early notes and papers that he was talking about > > > >> the formal objects that are variously called elementary relations, > > > >> elements of relations, individual relations, or ordered tuples. > > > >> > > > >> I did, however, more recently discuss a number of selections from > > > >> Peirce's > > > >> 1880 Algebra of Logic that dealt with the logic of relatives, so I can > > > >> say for a certainly that he was calling these objects or the terms > > > >> that denote them by the name of “individual relatives”. > > > >> > > > > … > > > >> > > > >> On 11/27/2015 12:42 PM, <mailto:[email protected]> [email protected] > >> wrote: > > > >>> Jon, > > > >>> > > > >>> If it’s critically important to understand the difference between > > > >>> “relations proper” and “elementary relations”, can you tell us what > > > >>> that difference is, or point us to an explanation? These are not > > > >>> terms that Peirce uses, so how can the rest of us tell whether we > >>> understand them or not? Being unfamiliar with > >>> those terms does not indicate lack of understanding of the important > >>> concepts they signify. > > > >>> > > > >>> Gary f. > > > >>> > > > >>> From: Jon Awbrey [ <mailto:[email protected]> mailto:[email protected]] Sent: > >>> 27-Nov-15 11:16 > > > >>> > > > >>> 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 > > > > > > > > > -- > > academia: http://independent.academia.edu/JonAwbrey > my word press blog: http://inquiryintoinquiry.com/ > inquiry list: http://stderr.org/pipermail/inquiry/ > isw: http://intersci.ss.uci.edu/wiki/index.php/JLA > oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey > facebook page: https://www.facebook.com/JonnyCache > > ----------------------------- > 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] > . 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