Robert and list
I break the silence of retirement to thank you for your excellent proof
about the sign classes.
I like proofs by induction because their simplicity throw out
definitively any doubt off the subject matter.
Being given a chain of successive determinations of sign features, being
given the ordering of the three peircean phaneroscopic categories, the
number of the resulting classes of signs (as well as their affinities in
a lattice) is ipso facto known. Then the length of the sign features at
hand, be it 3 (triad) or 6 (hexad) or 10 enters as a parameter into the
calculation.
But I think that basing your proof on the properties of mathematical
category theory makes room to go a little bit further, namely passing
from what you call "protosigns" to the signs themselves. First we have
to fix the length and the succession of the Ai objects chain. As to the
length your paper makes me shift in opinion : 3, 6 or 10 is probably a
question of the required accuracy for the expected usage of the
generated sign classes (I was more inclined to think that it was a
doctrinal question before having seen it as a "parameter"). The method
of separating two categories in order to apply functors from the one to
the other makes also things clearer I think.
Then, there remain the question that has bothered me for many years now
: what was the motive of Peirce for inventing what he called "My second
way of dividing signs" into 66 classes ? I remain convinced that he was
creating his own machine, a workbench, in order to test the sign theory
by means of the phanerons observed in the so called real world. And more
broadly the relevance of the three categories themselves.
This program has not yet been undertaken as far as I know. But your
work, Robert, makes it conceivable.
Thanks
Bernard
Le 09/05/2020 à 16:12, Jon Awbrey a écrit :
This is sequence No. A000217 ( https://oeis.org/A000217 )
in The On-Line Encyclopedia of Integer Sequences,
N.J.A. Sloane (ed.), https://oeis.org/
See: https://oeis.org/wiki/Welcome
Regards,
Jon
-----------------------------
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 the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
