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 <[email protected]> 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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