Sung, The relationship between the sign vehicle/representamen and the object may be motivated or unmotivated. If the relationship is one of similarity or spatio-temporal contiguity, the sign is said to be motivated. If the relationship between the sign vehicle and the object only exists though convention the sign is said to be arbitrary. If the graphical representation of the formula share similarities with the representations of the data distributions, the sign is motivated, which is to say *NOT ARBITRARY*
Another way to think about is that a graph is a one-to-many function where one graph type represents many (but not any) graph objects. An arbitrary sign function is an any-to-one function where any sign vehicle could be selected to represent one object. Out of phonetic space many arrangements of sounds could be selected at random to refer to the same object. Just in the english language alone, "dog", "hound", "puppy", "canine" etc. have all been selected to refer to the same object despite being unrelated sounds, because the object does not constrain the form of phonetic space we use to represent it. In science however, the object does constrain the form of possible representations (which is to say in science we aim to make sure our representations are motivated). I hope this clarifies the "arbitrariness of the sign". --- Ulysses On Sun, Aug 10, 2014 at 1:09 PM, Benjamin Udell <[email protected]> wrote: > Frank, list, > > Thanks for your response. I've been quite busy myself. I've tried to make > some Arisbe pages friendlier to people who have trouble using a mouse - > using tab to move from link to link, shift tab to move likewise but > backward, etc. > http://www.cspeirce.com/menu/library/aboutcsp/aboutcsp.htm , > http://www.cspeirce.com/menu/library/bycsp/bycsp.htm , > http://www.cspeirce.com/newbooks.htm , and > http://www.cspeirce.com/pastbooks.htm . > Those should work for such people better now than before in recent > versions of Internet Explorer and Firefox. I doubt that I can make > everything work with all browsers, since they're up to differing speeds on > 'accessibility' issues. Of course I should do it with the home page too! > But I wanted to get the most complex pages done before I did the home > page. Once I get this modicum of accessibility accomplished, I'll get back > to adding books to the book pages. > > You wrote, > > [Quote] > When I was coming up with a response, I realized I had been thinking of > the nature of the dynamical object, in which the Third in that trichotomy > is a collective, and that's what made me think the charcar example > appropriate. But after considering it further, I recall that the symbol > would not only be a sign that is a collective but also a type, so I suppose > you must be right. I had been thinking that a common purpose was enough, > but now I see a common type is required too for a symbol. > [End quote] > > That's an adjunct to the ten trichotomies of signs in the letter to Lady > Welby, the trichotomy of objects. I thought that it was kind of odd that he > dubbed it 'collective', maybe he thought that the object as such needs to > be 'secundan' in some way. But it's been a while since I read it. Then I > remembered a passage from a letter to William James (in EP 2:492, and in CP > 8.177 including editorial end note 4) > http://www.commens.org/dictionary/entry/quote-letters-william-james-6 > > > A Sign is a Cognizable that, on the one hand, is so determined (i.e., > specialized, '_*bestimmt*_') by something _*other than itself_*, called > its Object (or, in some cases, as if the Sign be the sentence "Cain killled > Abel," in which Cain and Abel are equally Partial Objects, it may be more > convenient to say that that which determines the Sign is the Complexus, or > Totality, of Partial Objects. And in every case the Object is accurately > the Universe of which the Special Object is member, or part), while, on the > other hand, it so determines some actual or potential Mind, the > determination whereof I term the Interpretant created by the Sign, that > that Interpreting Mind is therein determined mediately by the Object. > > It is hard to avoid thinking of a Universe of Discourse as a collective. > It consists of the things that can bear relative or polyadic predicates. > Even a propositional or a monadic logic involves 2nd-order objects with > 2nd-order relative predicates such as conjunction and disjunction. Some > polyadic conditionals express the kinds of things that Peirce regarded as > would-be's, such as rules or laws. Well, I could ramble, I'm not sure quite > what to make of all this. > > Regarding 'term' and 'word', the distinction is one to which Peirce > appeals but which, as far as I know, did not originate with him. I was > taught it in high school, if I remember correctly. _*Term*_ is to _*word*_ > as _*proposition*_ is to _*sentence*_. Now, Quine and others rejected the > idea of the _*proposition*_ as a thought or idea or meaning, > linguistically to be expressed, yet apart from expression in a particular > language, and preferred to talk only of _*statements*_ and, later, _ > *sentences*_, by which they meant actual utterances of a certain kind, > discussed generically or as to individual occurrences. Yet, oddly enough, > they retained the word or term 'term' instead of replacing it with 'word.' > However, insofar as the word/term and sentence/proposition distinctions > remain useful and meaningful, why not retain them and our words and terms > that express those distinctions? Briefly digressing: The word 'phrase' > raises an issue. A term may be expressed by a single word in one language > but only by a phrase in another language. More than once I've been brought > up short in wondering whether to describe a given phrase as a term. > (Michael Shapiro says no http://languagelore.net/?p=2962). > > You wrote, > > [Quote] > Ben, you said "it's true that animals share some sort of quality of > appearance, so that one can't say that animal is to fish _entirely_ as > abstract symbol is to linguistic symbol. But Peirce's classifications are > global divisions according to such basics as phenomenological category and > logical quantity, so one will find these deeper differences between kinds." > I'm not sure what you mean by "so one will find these deeper differences > between kinds." Would you please clarify what you meant by that? What > differences and what kinds in this context? I get a little dizzy trying to > figure out which ones you mean to compare and contrast, what relevant > differences and what relevant kinds. > [End quote] > > I generally use the word 'kind', unqualified, when I'm trying to avoid > using a term of art such as 'class' or 'species' or 'genus'. A difference > between two kinds (involving a taxon difference) such as a fish and an > animal 'in general' involves a difference between more specificity, and > less specificity, of appearance. A difference between the following two > 'kinds': an word-symbol and an abstract symbol, - involves a difference > between specificity of appearance and flat-out non-specificity of > appearance - in both cases, external, physical appearance, at least. (Even > an abstract meaning can have a kind of thought-quality or thought-tone.) > The difference between more and less specificity of appearance seems less > deep than the difference between specificity and flat-out non-specificity > of appearance. This deeper difference is such as one associates with > category differences, and Peirce defines his sign classes on the basis of > his categories, so one would expect such deeper differences between some > examples of signs from different classes. > > Best, Ben > > On 8/10/2014 1:03 AM, Frank Ransom wrote: > > Ben, list, > > I am sorry for the much delayed response! I have had a lot going on > recently, and have been able to catch up only just now. > > Ben, you said "The charcar example involves a gathering of individual > objects, and such cannot constitute a symbol in Peirce's classification, > but only an individual index that instantiates a symbol, and furthermore an > instance of a symbol that prescribes the qualities of appearance of its > instances, that is, the look &/or sound etc. of those objects, whereby one > will recognize it as an instance of said symbol." When I was coming up with > a response, I realized I had been thinking of the nature of the dynamical > object, in which the Third in that trichotomy is a collective, and that's > what made me think the charcar example appropriate. But after considering > it further, I recall that the symbol would not only be a sign that is a > collective but also a type, so I suppose you must be right. I had been > thinking that a common purpose was enough, but now I see a common type is > required too for a symbol. > > On a different point: Ben, you said  "I don't understand why you think > you can arbitrarily make a symbol (or an instance of a symbol) out of a > collection of objects, but can't arbitrarily make up a purposeful word." I > did not mean that a symbol can be made up arbitrarily, but exactly that it > must always have some purpose; which, I believe, I have already said. So > you're not-understanding is backwards: I believe a symbol can be produced > that has purpose, but that a symbol without purpose, one that is purely > arbitrary, is impossible to make up. There is always a purpose at work. > > I think you are right to point out that tradition can involve purpose. > Even more, it might be said that since a symbol is a symbol in virtue of > being interpreted as a sign, then tradition could be considered nothing > other than established symbols, fixed as such by being traditionally > interpreted to be signs of what they are interpreted to signify in the > tradition. Perhaps there is more similarity between Peirce's views and > those of Saussure than I have hitherto been prepared to countenance. > > Also I suppose I was too quick to think that you were conflating Peirce > with Saussure when you said Saussure's symbols are Peirce's linguistic > symbols. But I wanted to clarify just how far that connection goes, and I > suppose you have clarified somewhat what you meant by that, although I > think it is still in part not yet clear. > > Ben, you said "Peirce's solution to the question of whether "dog" and > "perro" are one symbol or two is not to see it as an exclusive alternative. > For some purposes they are the same, i.e., the same _term_, expressible > variously in various languages, and for some purposes they are different, > i.e., different _words_, insofar as a word belongs to a language. Term, > proposition, argument, as opposed to word, (declarative-mood) sentence, > linguistically expressed argument." Previously, I had said " To my mind, > the purposes at work are one and the same for the abstract symbol and the > words, so there is only one symbol. Though I suppose that different > languages might be considered their own purposes, so an instance of "dog" > is really a meeting between two purposes, the dog species and the English > language, and could serve as an index for either symbol." Now setting aside > the fact that we agree there can be multiple purposes at work, and hence > multiple symbols involved, the point for me is about what here a word is, > whether it is in fact the abstract symbol itself, or something else than > that abstract symbol. I say that the word and the abstract symbol are one > and the same. Hence the quote from Peirce does not conflict with my > position. Both "dog" and "perro" are instances of the same word-symbol, a > symbol which expresses itself differently depending upon the context in > which it appears; one important element of that context being the community > of human symbols, or language, at use in the present environment. Consider > Peirce's statement from one of your quotes: "The word and its meaning are > both general rules; but the word alone of the two prescribes the qualities > of its replicas in themselves. Otherwise the "word" and its "meaning" do > not differ, unless some special sense be attached to "meaning."" I > emphasize the last sentence of his statement. > > Ben, you said "it's true that animals share some sort of quality of > appearance, so that one can't say that animal is to fish _entirely_ as > abstract symbol is to linguistic symbol. But Peirce's classifications are > global divisions according to such basics as phenomenological category and > logical quantity, so one will find these deeper differences between kinds." > I'm not sure what you mean by "so one will find these deeper differences > between kinds." Would you please clarify what you meant by that? What > differences and what kinds in this context? I get a little dizzy trying to > figure out which ones you mean to compare and contrast, what relevant > differences and what relevant kinds. > > --Franklin > > > On Sat, Jul 12, 2014 at 1:41 PM, Benjamin Udell <[email protected] > > wrote: > >> Frank, list, >> >> I've been discussing Peirce's views on sign classification and my ideas >> on what those views require, not my own views per se on sign >> classifications. The charcar example involves a gathering of individual >> objects, and such cannot constitute a symbol in Peirce's classification, >> but only an individual index that instantiates a symbol, and furthermore an >> instance of a symbol that prescribes the qualities of appearance of its >> instances, that is, the look &/or sound etc. of those objects, whereby one >> will recognize it as an instance of said symbol. Peirce distinguishes >> between (A) a word as a symbol and legisign, and (B) an individual instance >> of a word (such as an individual utterance of the word "dog"). >> >> I don't understand why you think you can arbitrarily make a symbol (or an >> instance of a symbol) out of a collection of objects, but can't arbitrarily >> make up a purposeful word. Your charcar example is purposeful AS an >> example, but the same is true of such invented words as "grue" and "bleen" >> which have been discussed a good deal in philosophy. Whether such symbols, >> words, etc., are purposeful beyond the purpose OF being an example for >> theoretical discussion, whether such symbols are cogent, fertile, >> growth-capable, useful etc., in thought more generally, is another >> question; it is much harder to make up such thriving symbols, and such are >> the symbols in which Peirce is principally interested. >> >> As regards tradition versus purpose, Peircean symbols may be natural, >> social, etc.; they all depend on purpose or function in a broad sense. >> They depend on their sheer functionality, depend on that they will be >> interpreted in certain ways, irrespectively of their resembling or being >> factually connected to their represented objects. Often the purpose or >> function is traditional, a community's habitual purpose from back in time. >> A English word such as "dog" has a traditional purpose of evoking the idea >> of a dog, and it also has a traditional purpose to look and sound distinct >> from other words such as "dock" and "hog." For whatever reasons - its >> polyglot vocabulary resources, its sound-shift history, etc., - English has >> many homonyms, but often they're still spelt differently, although for >> example there seem to be six or so separate words that look and sound like >> "mole," and often enough we're reduced to depending on context to >> distinguish words. The Spanish word "perro" has a traditional purpose of >> evoking the idea of a dog, and a traditional purpose to look and sound >> distinct from such words as "pero" and "pajaro." >> >> Generally I've meant that Saussure is a linguist concerned with words, >> sentences, etc., while for Peirce words etc. are just one kind of symbol. I >> haven't meant that their theoretical frameworks regarding words are alike >> enough that one can plug conceptions from one framework freely into the >> other. >> >> Now, if "dog" and "perro" are two in some sense, and if one is speaking >> of the words in their habitual or general being and not speaking of two >> individual instances or utterances of words, and if, as you say, they're >> the same symbol, then of what are they two? What are they two OF? Well, >> they're two signs, but two of what kind of sign? This question is in terms >> of generic semiotics and categorics, pertaining to signs, qualities, norms, >> etc. There's no good excuse in a Peircean system for ignoring the question, >> and the question is pressed upon one when one seeks examples of Peircean >> semiotic phenomena in actual language. >> >> Peirce's solution to the question of whether "dog" and "perro" are one >> symbol or two is not to see it as an exclusive alternative. For some >> purposes they are the same, i.e., the same _*term* _, expressible >> variously in various languages, and for some purposes they are different, >> i.e., different _*words* _, insofar as a word belongs to a language. >> Term, proposition, argument, as opposed to word, (declarative-mood) >> sentence, linguistically expressed argument. He regards all signs as >> icons, indices, or symbols. It's a three-way global division. He regards >> the individual instances of symbols such as utterances of "dog" as indices >> to one's experience of the symbolized objects. He does not regard words >> such as "dog" and "perro" as icons, since they do not resemble their >> represented objects. He regards the words (not their individual instances) >> as symbols because, like terms, they fit his definition of symbol. They are >> habits or dispositions of representation of objects, such that said >> representation does not depend on resemblance or factual connection to >> those represented objects. >> >> it's true that animals share some sort of quality of appearance, so that >> one can't say that animal is to fish _*entirely* _ as abstract symbol is >> to linguistic symbol. But Peirce's classifications are global divisions >> according to such basics as phenomenological category and logical quantity, >> so one will find these deeper differences between kinds. >> >> Here are the quotes, I previously linked to one and the other was sent to >> peirce-l by Gary Richmond. >> >> [From MS 517, EP 2:317, "Kaina Stoicheia [New Elements]"] >> A symbol is defined as a sign which becomes such by virtue of the fact >> that it is interpreted as such. The signification of a complex symbol is >> determined by certain rules of syntax which are part of its meaning. A >> simple symbol is interpreted to signify what it does from some accidental >> circumstance or series of circumstances, which the history of any word >> illustrates. For example, in the latter half of the fifteenth century, a >> certain model of vehicle came into use in the town of Kots (pronounced, >> *kotch* ) in Hungary. It was copied in other towns, doubtless with some >> modifications, and was called a *kotsi szeker* , or Kots cart. Copied in >> still other towns, and always more or less modified, it came to be called, >> for short, a *cotch* . It thus came about that the *[word]* *coach* was >> used, first, for a magnificent vehicle to be drawn by horses for carrying >> persons in state and in such comfort as that state required; then, for a >> large and pretentious vehicle to be drawn by four or more horses for >> conveying passengers from one town to another; and finally, to any large >> vehicle for conveying passengers at a fare by the seat from one town to >> another. In all ordinary cases, it is, and must be, an accidental >> circumstance which causes a symbol to signify just the characters it does; >> for were there any necessary, or nearly necessary, reason for it, it would >> be this which would render the sign a sign, and not the mere fact that so >> it would be interpreted, as the definition of a symbol requires. It will be >> well here to interpose a remark as to the identity of a symbol. A sign has >> its being in its adaptation to fulfill a function. A symbol is adapted to >> fulfill the function of a sign simply by the fact that it does fulfill it; >> that is, that it is so understood. It is, therefore, what it is understood >> to be. Hence, if two symbols are used, without regard to any differences >> between them, they are replicas of the same symbol. [.... More at >> http://www.cspeirce.com/menu/library/bycsp/stoicheia/stoicheia.htm ] >> >> >> [From CP 2.292, EP 2:274 (Syllabus, 1903).] >> A Symbol is a Representamen whose Representative character consists >> precisely in its being a rule that will determine its Interpretant. All >> words, sentences, books, and other conventional signs are Symbols. We speak >> of writing or pronouncing the word "man"; but it is only a replica, or >> embodiment of the word, that is pronounced or written. The word itself has >> no existence although it has a real being, consisting in the fact that >> existents will conform to it. It is a general mode of succession of three >> sounds or representamens of sounds, which becomes a sign only in the fact >> that a habit, or acquired law, will cause replicas of it to be interpreted >> as meaning a man or men. The word and its meaning are both general rules; >> but the word alone of the two prescribes the qualities of its replicas in >> themselves. Otherwise the "word" and its "meaning" do not differ, unless >> some special sense be attached to "meaning." >> >> [From CP 2.249, EP 2:292 (Syllabus, 1903).] >> >> A Symbol is a sign which refers to the Object that it denotes by virtue >> of a law, usually an association of general ideas, which operates to cause >> the Symbol to be interpreted as referring to that Object. It is thus itself >> a general type or law, that is, is a Legisign. As such it acts through a >> Replica. Not only is it general itself, but the Object to which it refers >> is of a general nature. Now that which is general has its being in the >> instances which it will determine. There must, therefore, be existent >> instances of what the Symbol denotes, although we must here understand by >> "existent," existent in the possibly imaginary universe to which the Symbol >> refers. >> >> More at this link: http://www.commens.org/dictionary/term/symbol >> >> Best, Ben >> >> On 7/8/2014 11:49 PM, Frank Ransom wrote: >> >> Ben, list, >> >> Ben, thank you kindly for this response. I would like to follow-up. So >> here goes: >> >> With respect to the linguistic symbol: The letters "d", "o", and "g", >> ordered in a particular way on a surface or in sound, are not the object of >> the symbol, as you said. But I was discussing the word "dog", not as an >> object, but as a linguistic symbol. So I don't understand what you mean by >> the charcar example being irrelevant. I don't think that a symbol can form >> without some purpose at work, and I worked to demonstrate that, with the >> charcar example, there is a purpose in coming up with the example in the >> first place; and secondly suggested that a purpose would make itself known >> otherwise. A 'linguistic' symbol, on the other hand, struck me as something >> which a person can come up with, and do away with, irrespective of any real >> purpose, and I don't think there can be any such symbol that is prescribed >> or prescribable in this way. I also don't think that you mean that "dog" or >> "perro" are linguistic symbols in this sense that I am discussing, but I do >> think that admitting that some symbols prescribe qualities while denying >> that other symbols do is confusing, especially when you apply it to a >> distinction between linguistic vs. non-linguistic symbols, and here's why: >> As I understand it, Saussure believed signs are fixed by tradition, not >> purpose. Since you admitted that Saussure's signs are Peirce's linguistic >> symbols, I think you made it seem that Peirce's linguistic symbols, which >> prescribe qualities of appearance, are fixed by tradition, not by purpose. >> Maybe I jumped the gun on that and assumed too much from what you said, but >> I do think some could interpret it so. I add that, because you say that an >> abstract symbol does not prescribe its qualities of appearance, but that I >> would expect qualities of appearance to be determined according to the >> final cause at work, I am somewhat confused by how you view the >> relationship between the final causes of the abstract symbol and the words >> "dog" and "perro", unless you agree with Saussure that linguistic symbols >> prescribe qualities of appearance according to tradition, not purpose. To >> my mind, the purposes at work are one and the same for the abstract symbol >> and the words, so there is only one symbol. Though I suppose that different >> languages might be considered their own purposes, so an instance of "dog" >> is really a meeting between two purposes, the dog species and the English >> language, and could serve as an index for either symbol. >> >> With respect to the relationship of the abstract symbol to the words >> "dog" and "perro" as the relationship of genus to species, I am uncertain >> on this point. I accept the distinction between genus-species, as the >> distinction between animal and fish is one of genus to species. But whether >> this is the case with how the abstract symbol relates to "dog" and "perro" >> is what I hold in question, since after all I have been denying that "dog" >> and "perro" are properly symbols at all, and that there is but one symbol, >> manifested in two instances with different qualities of appearance (the one >> with the characters "d", "o", "g", and the other appearing with the >> characters "p", "e", etc.). Clearly, then, whether or not you thought I >> meant the abstract symbol and the word "dog" are like Peter and Paul, I >> should say that I never thought them related in such a way, because I deny >> their distinctness from each other as being more than one symbol. Since you >> brought up the debate between Joe and Tom, I suppose you probably >> recognized this to be my position. Then again, there is some plausibility >> to your suggestion, if after all I am willing to accept the genus-species >> distinction as applicable in some cases. But there is an important >> difference in this case, because you are saying that the abstract symbol >> does not prescribe qualities of appearance, while animal certainly >> prescribes qualities for individuals of fish; there are certain >> characteristics which must appear in the phenomena of fish that animal says >> must appear; e.g., the power of locomotion. >> >> You said: "Some time later I argued with Joe, saying that there should be >> a way at the general sign-classificational level to account for divergent >> forms of the same symbol, and that all of the elements of the question were >> generically categorial - signs, symbols, qualities of signs, etc." I think >> this is a very interesting question, which leads into questions of >> metaphysics, or so it seems to me. As a way towards working to an answer: >> since semiotics and logic are really the same science, and the >> genus-species distinction is a logical one, I think there must be some >> semiotically describable way of articulating the diverging of forms from >> the same symbol, if they do indeed diverge; at least, if the genus-species >> distinction has application, it would seem that there should be a way to >> articulate it. However, I am not aware of how that should work. Would you >> like to take a stab at that one? By semiotically describable, I don't mean >> just saying one or more than one symbol diverges from another symbol and >> appears; that would of course be unhelpful. I mean looking at the structure >> of semiosis and showing how symbols can develop from other symbols in the >> way you are suggesting. If it's possible to just reference me to your >> previous discussions on articulating your idea, that should certainly be >> sufficient. There is no need to say it all over again, unless it's too much >> trouble to find that previous discussion, or if you never detailed it from >> a semiotic standpoint before. >> >> You said: "Then at some point I or somebody dug up what Peirce said about >> how some symbols (symbolic legisigns), replicas of still more-general >> symbolic legisigns, prescribe qualities of appearance for their individual >> instances (corresponding sinsigns a.k.a. tokens)." I would very much like >> to see the quote(s), in order to put his statement(s) into context. Well, >> if you can supply them off-hand. No worries if you can't. I note that you >> didn't say that Peirce claimed the more-general symbolic legisigns don't >> prescribe qualities of appearance as well for the individual instances. In >> connection with this, consider what I just said above about animal and >> instances of fish. >> >> -- Franklin >> >> > > > > ----------------------------- > 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 > . > > > > > > -- Ulysses
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