Boolean algebras aren't algebras (to the best of my understanding).
So why are they called algebras?
Wouldn't it make more sense to call them a "Boolean system" or a "Boology" or something else like that?
boolean-algebrasoft-questionterminology
Boolean algebras aren't algebras (to the best of my understanding).
So why are they called algebras?
Wouldn't it make more sense to call them a "Boolean system" or a "Boology" or something else like that?
Best Answer
Because Boole himself introduced the word "algebra" into the subject.
The term "algebra of logic" appears in Boole's 1854 book on Laws of Thought:
Boole strongly emphasized the relation between logic and algebra. References to algebra and its correspondence with logic permeate the book.
Other writers continued to use "algebra of logic" for Boole's system and its later simplification to what is now called Boolean algebra. For example, MacFarlane Principles of the Algebra of Logic (1874), C.S. Pierce "On the Algebra of Logic" (1880), and E. Schroeder Algebra der Logik (1890).
In addition to the analogy that Boole had observed with ordinary algebra, there is an equivalence of Boolean algebras with rings satisfying $x^2=x$ for all $x$, which are equivalent to some algebras (in the modern sense) over the 2-element field.