Helmut, List: I am not familiar with "projective reduction," so I do not know whether it means the same thing as what Peirce called "involution" and what Robert is calling "presupposition."
I am not aware of any text where Peirce says or implies that a dynamical object "involves two aspects or parts," but I can tell you that he associated intension and extension with (respectively) logical depth and breadth, signification and denotation, interpretant and object. In my current view, "dog" or "unicorn" is a type whose definition corresponds to its immediate interpretant or essential depth/intension, which is whatever it *possibly could* signify to someone sufficiently acquainted with English as a system of signs. Its immediate object or essential breadth/extension is whatever it *possibly could* denote accordingly, regardless of whether any such thing actually exists. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Mon, Apr 13, 2020 at 3:14 PM Helmut Raulien <[email protected]> wrote: > > Supplement: My English is not too good: I have not read about projective > reduction "at" Jon Awbrey´s (restaurant?), but in a post of his. Also my > use of terms is neither perfect: Is involution / involvement the same as > projective reduction outcome? To call the involved things "parts" is > problematic too: The "parts" do not "make" the involver, but the function > of the involver functionally consists of the involved´s functions, but > additionaly of itself, in the sense like a system is more than its parts. > This way it is not (really, compositionally...) reducible, but merely > projectively reducible. I think, that the nature of the sign is the same > like the relation of the sign with itself, but I am not sure if it is > justified to say so, maybe in pure Peircean terms it is not, but in modern > mathematical relation concept it is (?). > Jon, List, > > Maybe what I have called projective reduction (a term I have read at Jon > Awbrey´s sometime) is the same as involution. I think, that e.g. the > dynamic object involves two aspects or parts of its: The immaterial and the > material, or in case of concept, the concept´s intension and extension. In > case of "dog" it is easy: The immaterial or intensional DO-part is all > doggishness conceptually existing externally to the sign, and the material > or extensional DO-part is all dogs now and in the past. When the sign is > over, its IO will have become part of the DO-intension. In the case of > unicorn, I guess the extensional DO-part is e.g. horses, teeth of narwhales > etc. This is my understanding, I have no quotes to corrobate. > > Best, > Helmut >
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