  Klein-Gordon gravity, 1920s-30s particle physics, and 1890s Neumann-Seeliger
modified gravity suggest a "graviton mass term" *algebraic* in the potential.
Unlike Nordstr\"om's "massless" theory, massive scalar gravity is invariant
under the Poincar\'e group but not the 15-parameter conformal group. It thus
exhibits the whole Minkowski space-time structure, indirectly for volumes.
Massive scalar gravity is plausible as a field theory, but violates Einstein's
principles of general covariance, general relativity, equivalence, and Mach.
Geometry is a poor guide: matter sees a conformally flat metric due to
universal coupling, but gravity sees the rest of the flat metric (on long
distances) in the mass term. What is the `true' geometry, in line with
Poincar\'e's modal conventionality argument? Infinitely many theories exhibit
this bimetric `geometry,' all with the total stress-energy's trace as source;
geometry does not explain the field equations. The irrelevance of the
Ehlers-Pirani-Schild construction to conventionalism is evident given
multi-geometry theories. As Seeliger envisaged, the smooth massless limit
yields underdetermination between massless and massive scalar gravities---an
unconceived alternative. One version easily could have been developed before
GR; it would have motivated thinking of Einstein's equations along the lines of
his newly reappreciated "physical strategy" and suggested a rivalry from
massive spin 2 for GR (massless spin 2, Pauli-Fierz 1939). The
Putnam-Gr\"unbaum debate on conventionality is revisited given a broad modal
scope. Massive scalar gravity licenses a historically plausible rational
reconstruction of much of space-time philosophy in light of particle physics.
An appendix reconsiders the Malament-Weatherall-Manchak conformal restriction
of conventionality and constructs the `universal force' in the null cones.
