  A quantitative knowledge of the nuclear Equation of State (EoS) requires an
accurate estimation of the uncertainties on the EoS parameters and their mutual
correlations. Such correlations are empirically observed in a large set of EoS
models by different authors, but they are not always fully understood. We show
that some of these correlations can be interpreted from basic physical
constraints imposed on a simple Taylor expansion of the binding energy around
saturation density. In particular, we investigate the correlations among the
following empirical parameters: the symmetry energy $E_{sym}$, the slope and
curvature of the symmetry energy $L_{sym}$ and $K_{sym}$, and the curvature and
skewness of the binding energy in symmetric matter $K_{sat}$ and $Q_{sat}$. The
uncertainties on these correlations is estimated through analytical modelling
as well as a meta-modelling analysis of the EoS subject to physical
constraints. We show that a huge dispersion of the correlations among low order
empirical parameters is induced by the unknown higher order empirical
parameters, such as $K_{sym}$ (second order) and $Q_{sat}$ and $Q_{sym}$ (third
order). We also propose an explanation of the reason why $Q_{sat}$ is weakly
constrained by present experimental data. We conclude that selective
observables on high order parameters, such as $K_{sym}$ and $Q_{sat}$, should
be better determined before the present uncertainties on the EoS can be further
reduced.
