Jon, List :
Peirce asks himself questions and only questions to know which trichotomies of which virtual or abstract thought objects (ie the Ai of my protosigns) he could choose to place them in the 10 places. At this moment they are trichotomies *independentes* of any determination between these objects. There are actually 59049. It's enough to impress Lady Welby and William James! But once this choice is made we would obviously fall back on the usual 66 classes. This is not the first time he has evaluated his task: Peirce: CP 5.488 Cross-Ref:†† 488. I here owe my patient reader a confession. It is that when I said that those signs that have a logical interpretant are either general or closely connected with generals, this was not a scientific result, but only a strong impression due to a life-long study of the nature of signs. My excuse for not answering the question scientifically is that I am, as far as I know, a pioneer, or rather a *backwoodsman*, in the work of clearing and opening up what I call semiotic, that is, the doctrine of the essential nature and fundamental varieties of possible semiosis; and I find the field too vast, the labor too great, for a first-comer. I am, accordingly, obliged to confine myself to the most important questions. The questions of the same particular type as the one I answer on the basis of an impression, which are of about the same importance*, exceed four hundred in number*; and they are all delicate and difficult, each requiring much search and much caution. At the same time, they are very far from being among the most important of the questions of semiotic. Even if my answer is not exactly correct, it can lead to no great misconception as to the nature of the logical interpretant. There is my apology, such as it may be deemed." (dated v.1936) 400 is much less than 59049! However, anyone can declare themselves an explorer today, this is the condition of any free search. As far as I am concerned, I constantly control that my explorations stick to Peirce's fundamental writings, paragraph by paragraph, word by word. You end with a moral injunction based on the authority of John Sowa: *"That is why I insist on faithfulness to Peirce's own writings when employing his terminology and seeking to apply his ideas today. Otherwise, we do not actually "build on and extend his work," but rather create something new of our own invention and wrongly attribute it to him."* I wonder who it can apply to and I don't feel concerned. On the other hand, I fear that there is still much to clear in the forest and that there is not yet time to plant trees on the freed parts won. Le ven. 24 avr. 2020 à 04:15, Jon Alan Schmidt <jonalanschm...@gmail.com> a écrit : > Robert, List: > > I agree that pursuing a tree structure effectively abandons the quest for > exactly 66 classes of signs, since that number depends directly on a > linear arrangement of the ten trichotomies. Perhaps that is why Peirce > made the following remarks in draft letters to Lady Welby and William > James, respectively. > > CSP: On these considerations I base a recognition of ten respects in > which Signs may be divided. I do not say that these divisions are enough. > But since every one of them turns out to be a trichotomy, it follows that > in order to decide what classes of Signs result from them, I have 3^10, or > 59,049, difficult questions to carefully consider; and therefore I will not > undertake to carry my systematical division of Signs any farther, but will > leave that for future explorers. (EP 2:482, 1908 Dec 24-28) > > CSP: I might have drawn more than ten distinctions; but these ten exhibit > all the distinctions that are generally required in logic; and since > investigation of these involved my consideration,--virtually at least,--of > 59,049 questions, still leaving me on the portico of logic, I thought it > wise to stop with these. (EP 2:501, 1909 Dec 25) > > > Note that he wrote both of these passages *after *his famous statement > that "instead of making 59,049 classes, these will only come to 66" (EP > 2:481, 1908 Dec 23). Perhaps he was already reconsidering that assessment > a couple of days later, resulting in the first quote, while the second one > comes a few weeks after the Logic Notebook entry in which he sketched out > the hierarchical approach. > > In any case, we are now among the "future explorers" for whom Peirce left > various follow-up tasks to undertake, including further investigation of > alternatives for a "systematical division of Signs." As John Sowa quoted > him earlier today, "One generation collects premises in order that a > distant generation may discover what they mean" (CP 7.87, 1902); but if we > get the premisses wrong, then the conclusions that we derive from them > will also be wrong. That is why I insist on faithfulness to Peirce's own > writings when employing his terminology and seeking to apply his ideas > today. Otherwise, we do not actually "build on and extend his work," but > rather create something new of our own invention and wrongly attribute it > to him. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Professional Engineer, Amateur Philosopher, Lutheran Layman > www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt > > On Thu, Apr 23, 2020 at 12:02 PM robert marty <robert.mart...@gmail.com> > wrote: > >> "The designations here are the same as above, although the reference is >> to a longer entry in the Logic Notebook written a few days later. As >> Bellucci summarizes, "the ten trichotomies are arranged in a >> *tree-structure*, not as a *linear succession,*" but "Peirce never >> managed to apply to his tenfold taxonomy of signs the new step-by-step >> method." Bellucci does not attempt to do so himself; and as far as I know, >> no one else has tried yet either." >> >> If you put a tree structure on the ten trichotomies you can say probably >> goodbye to the 66 classes of signs which are coextensive with a linear >> series of successive determinations. >> >> what will you do if you finish by a fork ? >> >> Exemple with a final fork : >> >> A1--> A2--> A3--> A4--> A5-->A6-->A7 -->A8 >> | >> V >> A9 >> | >> V >> A10 >> you have in fact 2different suites of 8 objects : >> >> A1--> A2--> A3--> A4--> A5-->A6-->A7 -->A8 >> >> A1--> A2--> A3--> A4--> A5-->A6-->A9-->A10 >> >> the number of classes of signs obtained is [(9*10)/2]*2=90 >> >> it is easy to see that the cases with equal branches give the following >> numbers of classes according to the length n of the common core: >> >> n=2, 56 ; n=4 , 72 ; n=6 , 90; n=8, 110 >> >> but maybe you see things differently ? >> >
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