Is Listing Axiomatic?

Choices in behavior are more pronounced when they result in pain from consequence (mental anguish) or corporal discipline (physical pain response.)

I asserted that this results in a binary tree of possible characters in any individual.

However, some choices are not strictly binary, resulting from a list instead. 

Machiavelli's book, "The Prince," is authoritative for it's use of binary logic. However, the necessity of "Discourses On Livy," points out that The (unabridged) Prince is not exhaustive of all government. 

I theorize the omissions are the result of dichotomies based on lists, which are divided into a single major choice contrasted against all others in the list. Information not in The Prince would be found in subsections treating on list headings abbreviated under an umbrella choice that is contrasted to a single opposing option.

I hasten to admit that speaking authoritatively on these would be challenging, but also erudite and worthwhile.

However, these two observations led me to contemplate the list of axioms in Mathematics.

AND, OR, XOR, NOT, Null and Unity/Identity are axiomatic, as are Counting and Addition Multiplication is NOT axiomatic, as it is repeated addition. However, I am inspired to ask:

IS LISTING AXIOMATIC? It appears to differ from counting by contributing or defining order.

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