“All relations are either qualitative or quantitative.”

— Benjamin Peirce, Linear Associative Algebra

§ 3.
Linear Associative Algebra (1882)
Context: All relations are either qualitative or quantitative. Qualitative relations can be considered by themselves without regard to quantity. The algebra of such enquiries may be called logical algebra, of which a fine example is given by Boole.
Quantitative relations may also be considered by themselves without regard to quality. They belong to arithmetic, and the corresponding algebra is the common or arithmetical algebra.
In all other algebras both relations must be combined, and the algebra must conform to the character of the relations.

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Benjamin Peirce24

American mathematician 1809–1880

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