A Finite Projective Geometry Exercise 1.19.
The great tragedy of science—the slaying of a beautiful hypothesis by an ugly fact.
—Thomas Huxley (1825–1895)

Exercise 1.19.  Show the axiomatic system for a finite projective plane is incomplete.

An example that shows incompleteness of the axiomatic system. Consider the statement, "There exist at least 13 points." The statement cannot be proved directly from the axioms, since the statement is false with the model that has 7 points and the statement is true with the model that has 13 points.