No, if you substitute k = n + 1.
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Oops, I have done much hullaballoo about few: The formula is just the Gaussian sum-formula for triangle arrangement for k, with
Tr. = k * (k + 1)/2
if you substitute n = k + 1.
Robert, Jon, Alan, List,
Here I have made a visually enhanced derivation of the formula. The LibreCAD-program with Linux works very well and is for free. I have not yet learned how to put the pdf-pages together, so it is 5 attachments.
Best,
Helmut
08. Mai 2020 um 18:53 Uhr
"robert marty" <robert.mart...@gmail.com>
wrote:
"robert marty" <robert.mart...@gmail.com>
wrote:
Jon Alan , List
Here is a proof by induction of the formula (N+1)(N+2)/2 ....
Best regards,
Robert
Le jeu. 7 mai 2020 à 03:43, Jon Alan Schmidt <jonalanschm...@gmail.com> a écrit :
Helmut, List:What helped me first come to understand how a linear series of N trichotomies results in a total of (N+1)(N+2)/2 classes of signs was the attached diagram that appears on p. 46 of John K. Sheriff's 1994 book, Charles Peirce's Guess at the Riddle: Grounds for Human Significance. The vertical and angled lines indicate that as you go down the list from one trichotomy to the next, a possible (1ns) can only determine a possible (1ns), an existent (2ns) can determine a possible (1ns) or an existent (2ns), and a necessitant (3ns) can determine a possible (1ns), an existent (2ns), or a necessitant (3ns).Applying this to only the first two trichotomies yields six classes accordingly--iconic qualisign, iconic sinsign, iconic legisign, indexical sinsign, indexical legisign, and symbolic legisign. Adding the third trichotomy results in ten classes as numbered at the bottom of the diagram--an iconic qualisign, sinsign, or legisign must be rhematic; an indexical sinsign or legisign can be rhematic or dicent; and a symbolic legisign can be rhematic, dicent, or an argument. Applying the same rule to six trichotomies gives 28 classes, while ten trichotomies produce 66 classes. Is that any clearer?Regards,Jon Alan Schmidt - Olathe, Kansas, USAProfessional Engineer, Amateur Philosopher, Lutheran LaymanOn Wed, May 6, 2020 at 11:51 AM Helmut Raulien <h.raul...@gmx.de> wrote:Jon, List,Thank you, Jon! I do have to say, that have had a concept of composition, of which Robert and Jon A.S. said it is not good, and it rather is all about determination and correlates. The concept of composition was, that a secondness would consist of two, and a thirdness of three parts, and this would go on eternally. Like, for example, a dynamic object (2.2.) consists of (2.2.1.) and (2.2.2.). I thought, this would make sense, as there might be identified two parts of the dynamic object: Its conceptuality outside the sign, and its ontologic part (outside too).This way, there were 3, 6, 10, 15, 21, and so on parts. But the sign classes are not created this way, but by regarding determination of correlates, and this way there are 10, 28, 66 sign classes. How this is done, I have not yet understood. Does there exist a text for dummies?By comparing AB-AC-BC with SS-SO-SI, I thougt to have had identified the nonexistent OI- relation for a "missing link". In spite of the catchiness of this term, I have the hunch, that this my stream of consideration might be based on not having understood the signtree and the determination issue, and I should work on this understanding before. But nevertheless I am very much looking forward to your answer and the subject of projective reduction in case of the sign!Best,HelmutHelmut,
I've been trying to get back to your message of 4/12/2020
under the subject line "Categories and Speculative Grammar",
but I'll reply under Robert's original subject line as the
profusion of titles has been derailing my train of thought.
Some of the material you allude to below has gone missing
off the live web, and the fragments I can still find need
a bit of reformatting, so I'll go address those issues and
return to these questions as soon as I can.
Regards,
Jon
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