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The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions. The analysis extends directly to other concrete categories (groups, rings, vector spaces, etc.) where the objects are sets with a certain type of structure and the morphisms are functions that preserve that structure. Then the elements & distinctionsbased definitions can be (...) 

For millennia, knowledge has eluded a precise definition. The industrialization of knowledge (IoK) and the associated proliferation of the socalled knowledge communities in the last few decades caused this state of affairs to deteriorate, namely by creating a trio composed of data, knowledge, and information (DIK) that is not unlike the aporia of the trinity in philosophy. This calls for a general theory of knowledge (ToK) that can work as a foundation for a science of knowledge (SoK) and additionally distinguishes (...) 

In finite probability theory, events are subsets S⊆U of the outcome set. Subsets can be represented by 1dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events." Probabilities are introduced for classical events, superposition events, and their mixtures by using density matrices. Then probabilities for experiments or `measurements' of all these events can be determined in a manner exactly like in quantum mechanics (QM) using density matrices. Moreover the transformation of the density (...) 