Concept-Formation as an Algebraic Process

The basic principle of concept-formation (which states that the omitted measurements must exist in some quantity, but may exist in any quantity [see: The Metaphysical Status of Concepts]) is the equivalent of the basic principle of algebra, which states that algebraic symbols must be given some numerical value, but may be given any value. In this sense and respect, perceptual awareness is the arithmetic, but conceptual awareness is the algebra of cognition.

The relationship of concepts to their constituent particulars is the same as the relationship of algebraic symbols to numbers. In the equation $2a = a + a$, any number may be substituted for the symbol “$a$” without affecting the truth of the equation. For instance: $2 \times 5 = 5 + 5$, or: $2 \times 5{,}000{,}000 = 5{,}000{,}000 + 5{,}000{,}000$. In the same manner, by the same psycho-epistemological method, a concept is used as an algebraic symbol that stands for any of the arithmetical sequence of units it subsumes.

Let those who attempt to invalidate concepts by declaring that they cannot find “manness” in men, try to invalidate algebra by declaring that they cannot find “$a$-ness” in $5$ or in $5{,}000{,}000$.¹