A fellow named G. Spencer-Brown wrote a book called "The Laws of Form". In it he begins with the most fundamental, indeed metaphysical, logical "step" or "unit": the act of distinguishing ...
(Quite literally the first page of "Laws of Form" and the first verse of the "Tao Te Ching" are expressing the same thing.)
From there he goes on to derive all of logic and mathematics. He uses a simple formalism of "marks" that captures the behaviour of logic and equations.
Then, in "The Markable Mark", a fellow named G. Burnett-Stuart has created an interactive circle-based rendering of the "Logic of the "Mark" and illustrated the build up of higher-order systems of reasoning rigorously from that basis.
Check them out, they're very cool. (I'm working on a system that uses them as a basis for reasoning programs.)