Measurement may be defined abstractly as: the process of relating an observed value to a known (and commensurable!) value (the unit of value employed as the basis of measurement).
Note that by nature a value MUST be unitized, i.e., it must be a definite definite quantity along a specific spectrum of possible outcomes (thus QM insistence on observables expressed as linear operators, with the eigenvalues determining the spectrum of possible outcomes of measurement).
Note also that the observer’s focus determines the unit of comparison, and one only needs to consider those facts about an entity that are relevant to the given context considered. So, if one is only interested in color of things, then the rest of their properties can be excluded from consideration as irrelevant.
An actual entity has multiple observable properties, each with a specific unit; the nature of the entity can be described as the integrated set of observations of its properties and functions. So, e.g., shape is no problem, it just requires observation of multiple properties to pin down … and one of those properties is the topology of the shape itself (topological forms are the available observables).
So, measurement omission is the basis of conceptualization because it is not the actual value of measurement(s) that determines the entity’s type/class; and emergent or unknown properties are no problem either … at a higher order, the determination of a given entity’s type, in terms of its known properties, does not preclude the discovery of other properties with experience. The type itself is an observable and evolves over time (concepts are contextual). In a sense, relative to the set of all observable properties of an entity, one’s focus on a specific subset of properties involves measurement omission, yes; but it also involves property omission, because one must winnow out irrelevancies even in cases where one knows in principle all the properties of an entity. For example, the fact of a person’s gender is not relevant when considering their character – in the context of assessing character, we not only omit measurements (e.g., of one’s actions), we also ignore properties that are irrelevant.
So, concepts in all their glory come from measurement omission applied to similar entities; but the measurements one focuses on and omits are also a matter of choice, i.e., the observer’s context masks out only the known properties relevant to current consideration.
Finally, notice that the notion of class type in object oriented software languages provides a convenient and accurate means to represent a concept. Conceptual hierarchies can be directly and reliably modeled as object oriented class hierarchies. And, when one decides to add another property to one’s concept of a given class of entities, then one need only add another member variable to the corresponding OOP class type.
Now this is interesting. I’ll be starting a thread on that soon.
Cheers.