My sojourns into the philosophy of set theory back in 2021 reintroduced me – this time more deeply – to the concept of “rational” numbers, which are numbers that can be expressed as a “ratio” of whole numbers. Ratio apparently, is a backformation from rational; which itself is sort of an inverse case from what the Greeks called “illogical” numbers, if there wasn’t a way to express a numeric quantity as a proportional relation of two other natural numbers.
Natural numbers are those used for counting, often called cardinal numbers, which can be used to express the sizes of sets. Without delving too deeply, sets are abstract constructs which we axiomatically define to be composed of 0 or more elements. Whether or not the elements of a set can be subdivided in some other axiomatic context is irrelevant. In the context of this discussion, the elements are held to be axiomatically atomic.
I’ve taken to using “rational” distinctly from “reason” as it lets me separate cardinal conformulation from ordinal approach. This approach has helped me to see that some things can be rational in a scope-constrained sense. Rational things vary in a uniformly measurable way in the context in which they are defined. Rational things are necessarily commensurable. Calculating one value that is shown to be rationally related to another it to be able to deal with that other also, and vice versa.
Pursuit of Value 