Helmut, Jon, List ...
Having lost my train of thought due to a week on the road,
I would like to go back and pick up the thread again here:
HR:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00200.html
JAS:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00203.html
The direction and pace of discussion after that point left a great many
of the original questions unanswered, so I'd like to make another try
at addressing them.
For now, though, just a note to anchor the thread.
Regards,
Jon
On 4/13/2017 4:26 PM, Jon Alan Schmidt wrote:
Helmut, List:
That is a very interesting suggestion, and some quick Googling confirms
that Jon Awbrey has written about compositive vs. projective reduction in
the past. He even cited the Sign relation as a specific example of a
triadic relation that is "projectively reducible." I still wonder,
though--did Peirce ever write anything along these lines, or otherwise
explaining this aspect of his Sign classifications?
By the way, I suspect that the proper "projective reduction" is your first
guess--(S,O), (O,I), (I,S). The reason why Peirce never discusses the
(O,I) relation is that it is always the same as the (S,O) relation. The
first of the three 1903 trichotomies (Qualisign/Sinsign/Legisign) divides
the Sign itself as a correlate, not a relation; the dyadic relation of
anything to itself is simply *identity*.
Thanks,
Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
On Thu, Apr 13, 2017 at 2:45 PM, Helmut Raulien <[email protected]> wrote:
Jon, List,
You wrote:
"To be honest, given that the Sign relation is genuinely *triadic*, I
have never fully understood why Peirce initially classified Signs on the
basis of one correlate and two *dyadic *relations. Perhaps others on the
List can shed some light on that."
I have a guess about that: I remember from a thread with Jon Awbrey about
relation reduction something like the following:
A triadic relation is called irreducible, because it cannot
compositionally be reduced to three dyadic relations. Compositional
reduction is the real kind of reduction. But there is another kind of
reduction, called projective (or projectional?) reduction, which is a kind
of consolation prize for people, who want to reduce. It is possible for
some triadic relations.
Now a triadic relation, say, (S,O,I) might be reduced projectionally to
(S,O), (O,I), (I,S).
My guess is now, that Peirce uses another kind of projectional reduction:
(S,S), (S,O), (S,I).
It is only a guess, because I am not a mathematician. But at least I would
say, that mathematically a relation wit itself is possible, so the
representamen relation can be called relation too, instead of correlate.
Best,
Helmut
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