Virtual logic is not logic, nor is it the actual subject matter of the
mathematics, physics or cybernetics in which it may appear to be embe
dded. Virtual logic Lives in the boundary between syntax and semantics
. It is the pivot that allows us to move from one world of ideas to an
other. This paper studies the virtuality of ordinary and mathematical
logic. Through examples it is shown how what we call 'ordinary reason'
is itself a paradox. Reason itself is not at all reasonable! Each new
mathematical construction, each new distinction, each theorem is an a
ct of creation. Ordinary reason itself is virtual. The credo of clarit
y is not ordinary. It goes beyond reason into a world of beauty, commu
nication and possibility.