Simplest Primary Algebra
George Spencer-Brown is a master of axiomatic logical algebra. He managed to reduce the five Principia axioms for propositional algebra to just two axioms:
However, in my last blog, I have shown you that position can be taken as the single axiom for the primary algebra. In this blog I will show you how easy is to derive position as the consequence of the simplest axiom: cancelation. So cancelation 
which can be seen as definition of FALSE if we define
as TRUE.
Cancelation NOT TRUE = FALSE can be seen as the single base axiom for the primary algebra.
Consequently, the whole Boolean algebra can be derived from the binary principle of logic: TRUE and FALSE.
Even the classical valid categorical syllogisms can be easily proven using the single cancelation axiom. For example the Barbara syloogism
IF ( all a is b) AND (all b is c) THEN (all a is c) = TRUE
is written in the laws of form as
Proof of Barbara
