Jon, List,
ok, another argument, then I probably will have run out of them: In a no-identity- one-way- implication/inferation the implied/inferred-to is more primitive than the implier/inferred-from, as it must have fewer traits than the implier/inferred-from. The implier has more traits, some of which distinguish in the way, that the implied is not a kind of every kind of the implier.
Example: "Tennis ball" implies "ball". "Ball" merely has the trait of being roughly spherical. This is more primitive than "tennis ball", which has additional traits, that lead to the fact, that not every ball is a tennis ball.
Best, Helmut
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, HelmutHelmut, 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, USAStructural Engineer, Synechist Philosopher, Lutheran ChristianOn 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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