Jon, List,
I guess, that the answer to the question, whether or not information is lost due to the projection (of a triadic relation towards three dyadic ones), depends on whether the triadic relation is intransparent, and thus casts three shadow-like pictures, or is sort of transparent, and thus casts three X-ray-like pictures.
Another problem is, that, as a relation may be upon one set, meaning between a set and a copy of the same set, then there are not only three, but six dimensions. But I guess, that only the representamen/sign can have a reasonable relation with itself, so perhaps there are only four dimensions: S,S,O,I. Or: S,s,O,I, or sign, representamen, object, interpretant, with sign and representamen being both identical and different in some mysterious (Re-entry?), yet to be elaborated, way... Or has Peirce already solved this mystery, but did not explain it, assuming that it is self-explaining? This hunch is based on the fact, that he used the term "sign" for both the whole and a part. With which matter we have problems, but maybe he did not, because for him, the solution to what for us feels like a paradoxon, felt somehow for granted?
Best,
Helmut
Peircers,
Here's the revised, extended edition of my last two posts on this thread:
https://inquiryintoinquiry.com/2017/05/06/icon-index-symbol-%e2%80%a2-16/
Icon Index Symbol • 16
======================
Questions Concerning Certain Faculties Claimed For Signs
Re: Peirce List Discussion
JAS:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00196.html
HR:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00200.html
Having lost my train of thought due to a week on the road, I would like to go back and pick up the thread at the
following exchange:
JAS:
“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.”
HR:
“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.”
The course of discussion after that point left a great many of the original questions about icons, indices, and symbols
unanswered, so I’d like to make another try at addressing them. The relevant facts about triadic relations and
relational reduction can be found at the following locations:
• Triadic Relations : Examples from Mathematics
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_mathematics
• Triadic Relations : Examples from Semiotics
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_semiotics
• Relation Reduction : Projective Reducibility of Triadic Relations
http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction#Projective_reducibility_of_triadic_relations
I introduced two examples of triadic relations from mathematics, two examples of sign relations from semiotics, and used
them to illustrate the question of projective reducibility, in another way of putting it, whether the structure of a
triadic relation can be reconstructed from the structures of three dyadic relations derived or “projected” from it.
• In the geometric picture of triadic relations, a dyadic projection is the shadow that a 3-dimensional body casts on
one of the three coordinate planes.
• In terms of relational data tables, a dyadic projection is the result of deleting one of the three columns of the
table and merging any duplicate rows.
• In Peircean terms, a projection is a type of “prescision” operation, abstracting a portion the structure from the
original relation and ignoring the rest.
The question then is whether we keep or lose information in passing from a triadic relation to the collection of its
dyadic projections. If there is no loss of information then the triadic relation is said to be reducible to and
reconstructible from its dyadic projections. Otherwise it is said to be irreducible and irreconstructible in the same vein.
Regards,
Jon
--
inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
facebook page: https://www.facebook.com/JonnyCache
-----------------------------
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 .
Here's the revised, extended edition of my last two posts on this thread:
https://inquiryintoinquiry.com/2017/05/06/icon-index-symbol-%e2%80%a2-16/
Icon Index Symbol • 16
======================
Questions Concerning Certain Faculties Claimed For Signs
Re: Peirce List Discussion
JAS:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00196.html
HR:https://list.iupui.edu/sympa/arc/peirce-l/2017-04/msg00200.html
Having lost my train of thought due to a week on the road, I would like to go back and pick up the thread at the
following exchange:
JAS:
“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.”
HR:
“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.”
The course of discussion after that point left a great many of the original questions about icons, indices, and symbols
unanswered, so I’d like to make another try at addressing them. The relevant facts about triadic relations and
relational reduction can be found at the following locations:
• Triadic Relations : Examples from Mathematics
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_mathematics
• Triadic Relations : Examples from Semiotics
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_semiotics
• Relation Reduction : Projective Reducibility of Triadic Relations
http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction#Projective_reducibility_of_triadic_relations
I introduced two examples of triadic relations from mathematics, two examples of sign relations from semiotics, and used
them to illustrate the question of projective reducibility, in another way of putting it, whether the structure of a
triadic relation can be reconstructed from the structures of three dyadic relations derived or “projected” from it.
• In the geometric picture of triadic relations, a dyadic projection is the shadow that a 3-dimensional body casts on
one of the three coordinate planes.
• In terms of relational data tables, a dyadic projection is the result of deleting one of the three columns of the
table and merging any duplicate rows.
• In Peircean terms, a projection is a type of “prescision” operation, abstracting a portion the structure from the
original relation and ignoring the rest.
The question then is whether we keep or lose information in passing from a triadic relation to the collection of its
dyadic projections. If there is no loss of information then the triadic relation is said to be reducible to and
reconstructible from its dyadic projections. Otherwise it is said to be irreducible and irreconstructible in the same vein.
Regards,
Jon
--
inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
facebook page: https://www.facebook.com/JonnyCache
-----------------------------
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 .
----------------------------- 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 .
