  I point out a radical indeterminism in potential-based formulations of
Newtonian gravity once we drop the condition that the potential vanishes at
infinity (as is necessary, and indeed celebrated, in cosmological
applications). This indeterminism, which is well known in theoretical cosmology
but has received little attention in foundational discussions, can be removed
only by specifying boundary conditions at all instants of time, which
undermines the theory's claim to be fully cosmological, i.e., to apply to the
Universe as a whole. A recent alternative formulation of Newtonian gravity due
to Saunders (Philosophy of Science 80 (2013) pp.22-48) provides a conceptually
satisfactory cosmology but fails to reproduce the Newtonian limit of general
relativity in homogenous but anisotropic universes. I conclude that Newtonian
gravity lacks a fully satisfactory cosmological formulation.
