In Proper and Improper concepts (1927) Carnap argued for the distinction between proper concepts (the ones that are explicitly defined)
”It is essential to a proper concept that for any object it is in principle decidable whether the object falls under that concept or not; and the decision can be made in practice given sufficient knowledge of the object.” (Carnap, 1927, p. 13)
and improper concepts (which are implicitly defined by axiomatic systems),
“for an improper concept, the question whether a particular object falls under it is not decidable, and thus has no sense, regardless of how much is known about the object." (Carnap, 1927, p. 13).
I wonder whether this might provide some light on the concepts of information, matter and energy which are quite commonly referred to as fundamental. Each of them seems to be implicitly defined by their corresponding theories (or structurally dependend on the implicit concepts of those theories). For instance, quantum information (von Neumann entropy) is structurally dependent on the axioms of abstract quantum theory (and on the implicit definition of what is a physical system - that which can be assigned state vector in Hilbert space, is measured according to the measurement postulate, can be composed according to the fourth postulate and evolves in time according to the second one). Is my understadning correct - are information, matter and energy improper concepts?