ONT Re: Rightful Reigning Regent
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RRR. Dialogical Note 3
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MB = Michel Balat
MB: Il semble bien que nous soyons d'accord,
mais si on se refere aux remarques de Peirce
sur l'algebre, les formes logiques sont a dominante
iconique, certes, mais ne sont "exploitables" qu'a l'aide
d'indices (les "indices" mathematiques ou les quantificateurs
existentiels). Ce n'est qu'alors que ces formes logiques sont
symboliques, permettant d'aller jusqu'au quantificateur universel
(qui est vide s'il n'y a pas d'indice pris dans un ensemble non vide).
Il me semble que la problematique est differente si l'on part de la
question du rheme, la "fonction insaturee" de Frege. Il me semble
que la, nous rencontrons autrement la question des formes logiques
comme symboles "appelant à" un indice, ou une ligne d'identite
comme dans les graphes existentiels. D'ailleurs il me semble
qu'il y a des questions qui peuvent ne pas se poser dans le
cadre des GE, particulierement bien des questions liees a
la theorie des classes. Meme si cette derniere a fournit
les magnifiques "insights" de Boole et de Morgan, il me
semble que Peirce a fourni un autre cadre de pensee,
bien plus riche: je pense evidemment a sa theorie
si interessante de l'univers du discours. Je ne
peux m'empecher de penser etre un peu "parallele"
aux questions que tu poses! Desole d'avance,
amicalement Michel.
Michel,
There are many questions about this "realm of inquiry" (ROI)
for which I have neither "automatic" nor very "fast" answers.
I started working on "combinatory logic" (CL) in the mid 80's,
in a context of models for the "lambda calculus" (LC), and all
of this work is still ongoing. In that context of mathematical
work, I started to recall some things that I had read in Peirce
a long time before, and when I showed these things to my prof in
this area, he was utterly amazed at how up-to-date it all sounded,
often in points of concrete detail about "recent" discoveries that
were almost uncanny, if not downright scary! Peirce as Nostradamus,
born again?
So where I am at the present time is a bit like this:
Once we clear the slate of the more simplistic ideas
as to how signs mean anything at all -- for instance,
the fixed idea and fond notion that all mathematics
and even all natural languages themselves reduce to
a minor extension of "first order logic" (FOL), then
we pretty much have to start afresh, from scratch,
all over again, with "logic as formal semiotic",
just for LAFS. How the many faces of signhood
relate to each other can then be examined anew.
Maybe it is just my early years as a physics student, but I tend
to see this as "one of those wave/particle things" all over again,
where we now have the triality of icon/index/symbol instead of the
duality of wave/particle. There is a minimum degree to which we can
reduce any real sign to any one of its conjugate dimensions of being.
The proof of the analogy or the paradigm is in its utility in practice.
There are more details in your message than I can address right now,
so I will have to hope that I can return to them on a later occasion.
Cheers,
Jon
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