  Phenomenological functions $\Sigma$ and $\mu$ (also known as $G_{\rm
light}/G$ and $G_{\rm matter}/G$) are commonly used to parameterize possible
modifications of the Poisson equation relating the matter density contrast to
the lensing and the Newtonian potentials, respectively. They will be well
constrained by future surveys of large scale structure. But what would the
implications of measuring particular values of these functions be for modified
gravity theories? We ask this question in the context of general Horndeski
class of single field scalar-tensor theories with second order equations of
motion. We find several consistency conditions that make it possible to rule
out broad classes of theories based on measurements of $\Sigma$ and $\mu$ that
are independent of their parametric forms. For instance, a measurement of
$\Sigma \ne 1$ would rule out all models with a canonical form of kinetic
energy, while finding $\Sigma-1$ and $\mu-1$ to be of opposite sign would
strongly disfavour the entire class of Horndeski models. We separately examine
the large and the small scale limits, the possibility of scale-dependence, and
the consistency with bounds on the speed of gravitational waves. We identify
sub-classes of Horndeski theories that can be ruled out based on the measured
difference between $\Sigma$ and $\mu$.
