Helmut, List: HR: ... implication itself has been derived from double negation in a quasi-evolution, so double negation is more primitive.
No, implication mirrors inference, which is more primitive than negation (single or double). Regards, Jon S. On Thu, Apr 8, 2021 at 9:27 AM Helmut Raulien <[email protected]> wrote: > Jon, List, > > I think, this is an example for reflection going the other way than > action, evolution: > > We can derive "vertebrate" from "kangaroo", but kangaroos are derived > (deriven?) from vertebrates, and vertebrates are (resp. were, when they > were not a class but merely a species) more primitive, than kangaroos are. > > In the same way, we, by reflection, can derive double negation from > implication, but implication itself has been derived from double negation > in a quasi-evolution, so double negation is more primitive. > > Best, Helmut > 08. April 2021 um 15:25 Uhr > "Jon Alan Schmidt" <[email protected]> > *wrote:* > Helmut, List: > > No, you had it right the first time. In intuitionistic/synechistic logic, > we can derive double negation (nested cuts/ovals) from implication > (scroll), but we cannot derive implication (scroll) from double negation > (nested cuts/ovals). Implication is primitive, single negation is derived > from it as the implication of falsity or absurdity, and double negation is > derived from it as a composite of two single negations. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Structural Engineer, Synechist Philosopher, Lutheran Christian > www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt > > On Thu, Apr 8, 2021 at 12:15 AM Helmut Raulien <[email protected]> wrote: > >> >> Supplement: Oh-oh, I have mixed it completely up. Every implication is a >> double negation, but not every double negation is an implication, so double >> negation is the superclass, and thus more primitive than implication. >> Just like every kangaroo is a vertebrate, but not every vertebrate is a >> kangaroo, so vertebrate is the superclass, and more primitive. The first >> vertebrate is said to have been a fish-like creature with a single >> spine-bone. >> Jon, List, >> >> if we distinguish at all between implication and double negation, we are >> in the field of nonclassical logic. In intuitionalistic logic, every >> implication is a double negation, but not every double negation is an >> implication. So implication is the superclass, and double negation the >> subclass. >> the folllowing I derive from Stanley N. Salthe´s paper >> "Salthe12Axiomathes": In a subsumption (classification), the subclass has >> inherited the classifying traits from the superclass, and then developed >> additional traits, that distinguish it from other subclasses of the same >> superclass. So the subclass is more complex, less primitive than the >> superclass. So implication is more primitive than double negation, and >> double negation is derived from implication. But is single negation derived >> from double negation, or is single negation even more primitive than >> implication, and is just the combination of two negations derived from >> implication? >> >> Best, Helmut >> >
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