  Continuum electrodynamics is an axiomatic formal theory based on the
macroscopic Maxwell equations and the constitutive relations. We apply the
formal theory to a thermodynamically closed system consisting of an
antireflection coated block of dielectric situated in free-space and
illuminated by a quasimonochromatic field. We show that valid theorems of the
formal theory are proven false by relativity and by conservation laws. Then the
axioms of the formal theory are proven false at a fundamental level of
mathematical logic. We derive a new formal theory of continuum electrodynamics
for macroscopic electric and magnetic fields in a four-dimensional flat
non-Minkowski material spacetime in which the speed of light is c/n.
