Ben, list I remember discussions on this list about that paragraph with follows the p. 271 warning in this text
“A Sign, or Representamen, is a First which stands in such a genuine triadic relation to a Second, called its Object, as to be capable of determining a Third, called its Interpretant, to assume the same triadic relation to its Object in which it stands itself to the same aObject” EP: 272-3 - and being chastised and even sneered at, when I suggested that the terms of First, Second and Third, referred to ordinal numbers and not to the modal categories. The list members, several who still post here, insisted in very authoritative terms, that those words referred to the categories! But a small bit of thought would have shown that it makes no logical sense for a Representamen to be in a mode of Firstness - for it would then have been unable to interact with an Object or Interpretant unless they also were in a mode of Firstness!. However, the list wasn’t willing to take this ’small bit of thought’. I think the whole point of the semiosic process is its generative capacity; ie, that a semiotic triad is capable of developing and creating new knowledge and therefore, new forms. The reason it can do this is because the object and interpretant are separated from each other by the mediative function of the representamen. So- rather than mitosis, or mimetic clones where x produces another x, [ which has its functionality] you get the more complex meiosis where x produces y - ie, a unique cell. With the triad, its this ‘insertion’ of a mediating force, the representamen, that gathers information from other interactions over time, develops habits or knowledge of ‘how to deal with the external world’ and thus enables both anticipation and yes, adaptation, for Thirdness isn’t only ‘pure’ or genuine, but can connect indexically with the outside world [Thirdness-as-Secondness] , and thus, inform itself of those external properties and come up with adaptive Interpretants. Edwina > On Jan 7, 2024, at 12:53 PM, Ben Udell <baud...@gmail.com> wrote: > > Hi, Robert, all, > > I wish a whole lot of us 15 or 20 years ago had noticed a paragraph that you > quote in your message, > > The conceptions of a First, improperly called an "object," and of a Second > should be carefully distinguished from those of Firstness or Secondness, both > of which are involved in the conceptions of First and Second. A First is > something to which (or, more accurately, to some substitute for which, thus > introducing Thirdness) attention may be directed. It thus involves Secondness > as well as Firstness; while a Second is a First considered as (here comes > Thirdness) a subject of a Secondness. An object in the proper sense is a > Second. (EP 2: 271) > > We had some long arguments many years ago at peirce-l about what Peirce meant > by "First" etc., when he wasn't explicitly tying those adjectives to the > categories. Joe Ransdell, Gary Richmond, I, and probably others, argued > that, yes, Peirce was alluding to his categories. > > I also remember a whole lot of discussion about Peirce's shift to viewing the > sign as not only determining the interpretant but also being determined by > the object. At the time, a 1906 quote was the earliest that I could find (I > happened to find it at Commens.org I think), and Joe came up with a quote > that prefigured Peirce's shift, from 1905 or 1904, I wish I could remember > (and I tried years ago without success to find Joe's message about it), but I > don't want send anybody on a wild goose chase. > > Folks, here, by the way, is a link to Robert's "76 DEFINITIONS OF THE SIGN BY > C.S. PEIRCE" > http://perso.numericable.fr/robert.marty/semiotique/76defeng.htm > > It includes added quotes absent from the Arisbe version. > > Robert, you wrote below that "O → S → I" reads: > > "O determines S, which determines I." > > I haven't tried to learn any category theory, since I got intimidated by its > being reputedly based in very high or abstract algebra. > > Generally I recall people saying that — > > an object determines a sign to determine an interpretant > > — rather than that — > > an object determines a sign, which determines an interpretant > > — a phrasing which makes the sign's determination of an interpretant seem > possibly coincidental to the sign's being determined by an object, like > dominoes toppling, each one the next, though the earlier dominoes are not > finally-caused to topple the later ones (except if they are literal dominoes > that some person set up to fall that way). I remember (though not in detail) > a whole lot of discussion of this at peirce-l. Does the category-theoretical > understanding of "O determines S, which determines I" avoid that seeming > problem? To put it another way, how does "O → S → I" keep from breaking down > into dyads "O → S" and "S → I"? I'm not trying to be argumentative, I'm > actually wondering. > > Best, Ben > > On 1/7/2024 10:10 AM, robert marty wrote: > > Cécile, List > > I present here, in the most condensed form possible, the merits of a purely > algebraic formalization of Peirce's semiotics, entirely indexed to the > history of its development. > > How do we distinguish the correlates of a triadic sign? > How do we formalize the triadic sign? > > This question arises because the definition of a triad, strictly speaking, > implies no a priori distinction between the elements it links together. If > you represent them by letters, you're surreptitiously introducing > lexicographical order and by numbers, the order of natural integers. This is > why I draw attention to an important warning Peirce gives about "First" and > "Second" in a footnote to the Syllabus in Part III (EP 2, selection 20): > > *The conceptions of a First, improperly called an "object," and of a Second > should be carefully distinguished from those of Firstness or Secondness, both > of which are involved in the conceptions of First and Second. A First is > something to which (or, more accurately, to some substitute for which, thus > introducing Thirdness) attention may be directed. It thus involves Secondness > as well as Firstness; while a Second is a First considered as (here comes > Thirdness) a subject of a Secondness. An object in the proper sense is a > Second. (EP 2: 271) > > This warning should shed light on the following definition of the Sign > (which, in my opinion, is far from the best) on page 272: > > A Sign, or Representamen, is a First which stands in such a genuine triadic > relation to a Second, called its Object, as to be capable of determining a > Third, called its Interpretant, to assume the same triadic relation to its > Object in which it stands itself to the same Object. (EP 2: 272) > > On the other hand, the definition given in the fifth version of the Syllabus > (EP 2, selection 21), which is much more precise, will avoid confusion: > > 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. (EP 2: 290 or CP 2.242 ) > > This is the version Jon Alan Schmidt has chosen to formalize the sign and > semiosis as a spiral. This definition is not that of an ordinary triad since > one correlate, the First, has the power to determine another, the Third, to > make it the new First of a new triad, conferring on it the same power, and so > on. Hence, the image of the spiral, of which Jon Alan Schmidt provides a > projection on a plane, requires raising this projection in the reader's mind. > The repeated addition of the notation S ïI is intended to capture this > "power" and, in fine, "to capture the idea that the sign mediates between the > object and interpretant." > > But Peirce himself did much better to achieve this. Once again, I must point > out that Peirce modified his definitions of the Sign by introducing, around > 1904-1905, the determination of the sign S by the object O. Anybody can > consult the list of 76 definitions I published in 1990: it's available on > Peirce.org. There's no need to mention Existential Graphs, which require a > considerable intellectual investment, especially for non-expert readers. > > Perhaps the most straightforward is this one (emphasis added): > > A sign may be defined as something (not necessarily existent) which is so > determined by a second something called its Object that it will tend in its > turn to determine a third something called its Interpretant in such a way > that in respect to the accomplishment of some end consisting in an effect > made upon the interpretant the action of Sign is (more or less) equivalent to > what that of the object might have been had the circumstances been different. > (n° 36 - v. 1906 - MS 292. Prolegomena to an Apology for Pragmaticism) > > The most explicit about the creation of the triadic relation due to the > concatenation of the two determinations is the following: > > I define a Sign as anything which on the one hand is so determined by an > Object and on the other hand so determines an idea in a person's mind, that > this latter determination, which I term the Interpretant of the Sign, is > thereby mediately determined by that Object. A sign, therefore, has a triadic > relation to its Object and to its Interpretant. (n° 47 bis – 1908 - Letter to > Lady Welby in CP 8.343 ). > > It's clear, then, that the composition of the two determinations gives rise > to the triadic relation for Peirce. That's why I've underlined "therefore." > Consequently, the formalization is simplified considerably, without any loss > of information, by : > > O → S → I > > The arrows represent determinations, and this diagram reads: > > O determines S, which determines I > > Referring to the Peircean conception of a determination: > > We thus learn that the Object determines (i.e. renders definitely to be such > as it will be) the Sign in a particular manner. (CP 8.361, 1908) > > We can see that O determines I by transitivity. Peirce verified this in MS > 611 (Nov. 1908). > > This diagram has the considerable advantage of being equivalent to the > mathematical object below: > > Schematic representation of a category with objects X, Y, Z and morphisms f, > g, g ∘ f. > <https://upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Commutative_diagram_for_morphism.svg/200px-Commutative_diagram_for_morphism.svg.png> > (click) > > It's an algebraic category, the simplest there is (non-trivial). This one is > the archetypal example of a category on the Wikipedia site devoted to this > part of mathematics, which emerged in the second half of the 20th century > (Category theory - Wikipedia > <https://en.wikipedia.org/wiki/Category_theory>). In 1977 (in French) and > 1982 (in English), I was able to use it to generate, in just a few pages, not > only classes of triadic signs but also, above all, to show that these classes > are naturally organized in a lattice structure (which Peirce had intuited in > the form of affinities). I've verified that Peirce knew about this type of > structure, but limited by set theory, he couldn't obtain it formally. In his > classification of the Sciences, this lattice occupies the place of the > Grammatica Speculativa. It's his ultimate form. > > Robert Marty > Honorary Professor ; PhD Mathematics ; PhD Philosophy > fr.wikipedia.org/wiki/Robert_Marty > <https://fr.wikipedia.org/wiki/Robert_Marty> > https://martyrobert.academia.edu/ > > _ _ _ _ _ _ _ _ _ _ > ARISBE: THE PEIRCE GATEWAY is now at > https://cspeirce.com and, just as well, at > https://www.cspeirce.com . It'll take a while to repair / update all the > links! > ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in > the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . > ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and > co-managed by him and Ben Udell.
_ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
