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Concept - thing - expression*
Mar. 17th, 2016 11:21 amGoing over Treatise of Intuitionist Logic, by JG Granstorm for the second time (see fig and text below):
This points to an possible interesting connection between imagination that creates concepts and the process of "learning by doing" that converts the concepts into things. The more complex the thing that embodies the concept, the more communications we need to have with other people who participate in doing the thing. As a result, the expression side of the triangle begins to grow. (upd. In a dynamic model we need expressions to communicate between the same person at diffent time periods.)
Based on this model, to represent a system in terms of the Category Theory, we would have to have at least three types of Objects that play Sources and Targets, and at least three (or likely six?) types of Arrows that go between them. For example, an individual's artistic sci-fi imagination can be formalized as: ImaginationA: Concept -> Expression,
while Edison-style craftsman imagination as: ImaginationE: Concept -> Thing
Furthermore, if we want to model an evolution of the system, we would have to introduce all these objects at at least two times periods, e.g. today and tomorrow. This will cause us add three more arrows, e.g.
EvolveConcept: ConceptAtTime1 -> ConcepAtTime2
* I'm using "thing" instead of "object" to avoid confusion with objects in the Category Theory.
This points to an possible interesting connection between imagination that creates concepts and the process of "learning by doing" that converts the concepts into things. The more complex the thing that embodies the concept, the more communications we need to have with other people who participate in doing the thing. As a result, the expression side of the triangle begins to grow. (upd. In a dynamic model we need expressions to communicate between the same person at diffent time periods.)
Based on this model, to represent a system in terms of the Category Theory, we would have to have at least three types of Objects that play Sources and Targets, and at least three (or likely six?) types of Arrows that go between them. For example, an individual's artistic sci-fi imagination can be formalized as: ImaginationA: Concept -> Expression,
while Edison-style craftsman imagination as: ImaginationE: Concept -> Thing
Furthermore, if we want to model an evolution of the system, we would have to introduce all these objects at at least two times periods, e.g. today and tomorrow. This will cause us add three more arrows, e.g.
EvolveConcept: ConceptAtTime1 -> ConcepAtTime2
* I'm using "thing" instead of "object" to avoid confusion with objects in the Category Theory.
