List, Ulysses, Thanks Ulysses,
First of all, I must point out that this is not my opinion, but what Peirce may have said in 1903 when he delivered his fifth lecture at the Lowell Institute, if he provided proof of the results he asserted, based on his logical and mathematical knowledge at the time. Personally, I settled this question, in my view, more than fifty years ago with functors for sign classes and natural transformations of functors for lattices. I discuss this in my article. You can find it in the publications I have posted on Academia.edu, the main one being The trichotomic machine (*Semiotica*, vol. 2019, no. 228, May 2019). As for the simple Python code you propose, it hides an assumption, which is that of the two concatenated determinations of the sign by the object and of the interpretant by the sign. This is exactly what the editors of the CP are doing, in a somewhat amateurish way (no offense intended), in the note I quote: using the future to explain the present. It corresponds to a radical change in Peirce's definition of the sign, which abandons the focus on triadic relations (these will be the consequences of the new axioms) by placing an Object in the world, the sign in the world too, but determined by the Object, in such a way that it determines a mind in the time of the perception of the sign, thanks to its own capacities to support mediation, as the Object could have done if it had been perceived. This is a change of focus: we look differently at the constituent elements we had and proceed to a new hypostatic abstraction that reconfigures their relations in pairs, with determinations, that is oriented relations. You have seen it clearly: from the most complex to the least complex, passing through a middle level of complexity of the sign, with complexity being associated with possible natures. All that remains is to algebraize (in the category of relational structures or apply to computer science with Python, the new model lends itself better to this). You have modeled this yourself by choosing the numbers 3, 2, and 1 in the premises of your code, which you wrote in one of the six possible orders, the reverse of the natural order, and this is unspoken. I have not mentioned all the related issues, as there are many and they are the subject of recurring debates and sometimes heated discussions... Attached you will find the Python code that Le Chat, the chatbot from French Ai Mistral that I also use, sent me at my request. Sincerely yours, Robert Marty Honorary Professor ; PhD Mathematics ; PhD Philosophy fr.wikipedia.org/wiki/Robert_Marty *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* Honorary Professor ; PhD Mathematics ; PhD Philosophy fr.wikipedia.org/wiki/Robert_Marty *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* Le mar. 24 juin 2025 à 13:51, Ulysses <[email protected]> a écrit : > Interesting work Marty. > > Can you explain what your method tells us that a simple combinatorial > script does not? > > For example if you create a simple python script like this, you can easily > derive the 10 classes from three trichotomies. > > # Script: > trichotomy = 1,2,3 > i = 0 > for a in trichotomy: > > for b in trichotomy: > > for c in trichotomy: > > if a >= b >= c: > > i+=1 > > print(i, ": ", a, b, c) > > > # Output: > 1 : 1 1 1 > 2 : 2 1 1 > 3 : 2 2 1 > 4 : 2 2 2 > 5 : 3 1 1 > 6 : 3 2 1 > 7 : 3 2 2 > 8 : 3 3 1 > 9 : 3 3 2 > 10 : 3 3 3 > > Is your work aimed at giving motivation to how the three correlates can be > related to natural numbers, and therefore would obey this sort of > combinatorial ordering? Or are you saying that this combinatorial ordering > itself is not even necessary and the structure of the 10 classes emerges > from even simpler assumptions about Min(), Max() and Mid() / Any(), All(), > Some() ? > > Thank you, > Ulysses > > > > On Tue, 24 Jun 2025 at 12:51 pm, robert marty <[email protected]> > wrote: > >> List, >> >> In this part1 of my project, I propose an original contribution: a >> logical path *a priori* within triadic relations alone that leads to ten >> classes without any recourse to external or posterior notions, precisely as >> the Peirce's text asserts. A second innovation concerns the method used to >> spare the reader from tedious manual combinations, that is, using >> Artificial Intelligence. >> >> I will accept any comments or critical remarks, even the harshest ones, >> as a gift. >> >> >> https://www.academia.edu/130131910/Modeling_and_finalizing_Peirces_semiotics_with_AI >> >> Sincerely yours, >> >> Robert Marty >> Honorary Professor ; PhD Mathematics ; PhD Philosophy >> fr.wikipedia.org/wiki/Robert_Marty >> *https://martyrobert.academia.edu/ <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 >> [email protected] . >> ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] >> with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in >> the body. More at https://list.iu.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. > >
TEN CLASSES - PYTHON CODE.docx
Description: MS-Word 2007 document
_ _ _ _ _ _ _ _ _ _ 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 [email protected] . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iu.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.
