Peircers, I think Helmut is probably recalling any number of messages or links I posted on triadic relations and relational reduction, versions of which can be found at these locations:
http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_mathematics http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation#Examples_from_semiotics 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 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 3 coordinate planes. In terms of relational data tables, a dyadic projection is the result of deleting one of the 3 columns of the table and merging any duplicate rows. In Peircean terms, a projection is a type of prescision operation, in the sense that it ignores a portion of the structure in the original relation. Still a bit fatigued from travel, so will break here ... Jon On 5/5/2017 3:12 PM, Jon Awbrey wrote:
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 composition- >>> ally 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 >>> >> > -- 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
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