  This letter describes a novel derivation of general relativity by considering
the (non)self-consistency of theories whose Hamiltonians are constraints. The
constraints, from Hamilton's equations, generate the evolution, while the
evolution, in turn, must preserve the constraints. This closure requirement can
be used as a selection mechanism for general relativity starting from a very
simple set of assumptions. The configuration space is chosen to be a family of
$3 \times 3$ positive definite symmetric matrices on some bare 3-manifold. A
general Hamiltonian is constructed on this space of matrices which consists of
a single constraint per space point. It is assumed that this constraint looks
like an energy balance relationship. It will be the sum of a `kinetic' term
which is quadratic and undifferentiated in the momenta, and a `potential' term,
which is any function of the configuration variables. Further, the constraint
must be a scalar under the linear group, the natural symmetry group of the
configuration space. This inexorably leads to the ADM Hamiltonian for general
relativity. Both the space of Riemannian geometries (Wheeler's superspace), and
spacetime are emergent quantities in this analysis.
