Jon, List,
You wrote, that a dyadic relation of anything to itself is simply identity. Well, I dont know, how far you can apply the mathematical "relation" to the Peircean, but in mathematics it is not so: Eg. you have the set (mouse, dog, elephant), and the dyadic relation reason is "smaller than", then the relation is ((mouse,dog), (mouse, elephant), (dog, elephant)). The dyadic relation is a subset of all couples (tupels) that can be formed out of the elements of the set. If you have two sets, then the dyadic relation is a subset of tupels, each containing one element from one set, and one from the other.
In the case of representamen relation, mathematics transferred, the one set is the representamen (or sign), and there are three possible relation reasons/relations: Qualisign, sinsign, legisign.
I think, that the "proper" kind of projectional reduction is applied by Ogden/Richards, but Peirce did it differently, for some reason, and he also, for some reason, used the term "sign" for both representamen and triad. I guess, because projectionally (in his way) reduced, there is no difference: In eg. "Rhematic indexical legisign" the first two words are adjectives, traits, of the legisign, the representamen.
About the dynamical object, the dynamical and final interpretant: They are, spatially and/or temporally, outside of the sign as irreducible triad. But not outside of the projectionally-reduced-to-dyads-sign. Because indication towards something located outside, and anticipation into the future may both be called projections, I guess. But I am just guessing all the time..
Best,
Helmut
13. April 2017 um 22:26 Uhr
Von: "Jon Alan Schmidt" <jonalanschm...@gmail.com>
Von: "Jon Alan Schmidt" <jonalanschm...@gmail.com>
Helmut, List:
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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
On Thu, Apr 13, 2017 at 2:45 PM, Helmut Raulien <h.raul...@gmx.de> 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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