A.17:5 - Archetypal Grounding (System & Episteme Examples)

In a physical system (U.System): Consider a Distance Characteristic defined for a pair of physical objects. For example, two machines in a factory have a Distance of 3.5 meters between them. Here Distance is a Relation-Characteristic (applies to the pair), with an associated Scale (e.g. a ratio scale in meters), and the measured 3.5 m is a Coordinate on that scale. If we instead look at an Engine Temperature Characteristic (unary), a particular engine might have a Temperature of 350 K at some moment – Temperature (the Characteristic) is clearly separated from how it’s measured (Scale in Kelvin) and the reading (350, a Coordinate on that scale). A value of 360 K is hotter than 350 K. Whether it is preferable depends on the intended operation: heating and cooling can prefer opposite changes while using the same temperature Scale.

In an epistemic context (U.Episteme): Consider a Formality Characteristic to rate a documentation episteme’s rigor. We might define an ordinal Scale with named Levels such as Informal, Semi-formal, Formal. A given specification document can then be said to have High Formality – meaning it occupies the “Formal” Level on the Formality Scale. Here Formality (Characteristic) captures what we measure about the document, while the tiered Scale (with qualitative levels) expresses how we categorize it. Because we use an ordinal scale, we can rank documents by Formality, but we would not average “Semi-formal” and “Formal” (avoiding meaningless arithmetic on an ordinal metric). In another knowledge context example, one could define a Characteristic Reliability for a knowledge source with a percentage Scale from 0 to 100%. An article’s reliability might be 85% – which is only interpretable by knowing it refers to “Reliability” on a 0–100% Scale (i.e. a specific Coordinate on that Characteristic’s scale).