We treat continuum electrodynamics as an axiomatic formal theory based on the macroscopic Maxwell-Minkowski equations applied to a thermodynamically closed system consisting of an antireflection-coated block of a simple linear dielectric material situated in free-space that is illuminated by a quasimonochromatic field. We prove that valid theorems of the formal theory of Maxwellian continuum electrodynamics are inconsistent with conservation laws for the energy and the momentum of an inviscid incoherent flow of non-interacting particles (photons) in the continuum limit (light field) in the absence of external forces, pressures, or constraints (unimpeded flow) through a continuous simple linear dielectric medium. That remains true even if we view Maxwellian continuum electrodynamics as a subsystem: If we add a material energy-momentum tensor to the electromagnetic energy-momentum tensor as a phenomenological resolution of the Abraham-Minkowski controversy (as required by the past and current scientific literature) then the total energy, the total linear momentum, and the total angular momentum are constant in time but the four-divergence of the total (electromagnetic plus material) energy-momentum tensor is self-inconsistent, violates Poynting's theorem, and violates spacetime conservation laws. We also show that demonstrably correct theorems of Maxwellian continuum electrodynamics are inconsistent with the extant (Laue) application of Einstein's special relativity to a dielectric medium. Obviously, the fundamental physical principles of Maxwell's electrodynamics, spacetime conservation laws, and Einstein's special relativity, which are intrinsic to the vacuum, are not affected. However, the extant theoretical treatments of macroscopic continuum electrodynamics, dielectric special relativity, and energy-momentum conservation in a simple linear dielectric, theories that are extrapolated (derived, but with various assumptions, limits, and approximations) from the fundamental vacuum theories, must be regarded as being mutually inconsistent for macroscopic fields in ponderable media. Having proven that the extant applications of fundamental physical principles to dielectric materials result in mutually inconsistent theories, we derive mutually consistent alternative theoretical treatments of electrodynamics, special relativity, and energy-momentum conservation in an isotropic, homogeneous, linear dielectric-filled, flat, non-Minkowski, continuous material spacetime. There is sufficient commonality with the classic macroscopic theories that the extensive theoretical and experimental work that is correctly described by Maxwellian continuum electrodynamics, spacetime conservation laws, and dielectric special relativity has a nearly equivalent formulation in the new theory. The more complex issues of the Abraham-Minkowski momentum controversy and the Rosen-Laue dielectric special relativity dilemma have robust resolutions in the new theory.