Abstract
The static properties of neutron stars are probed using phenomenological equations of state. These properties include the maximum mass, radii, central densities, and binding energies. It is found that quite different equations of state can produce similar neutron stars. Likewise, it is also found that equations of state which are quite similar near saturation density can produce very different neutron stars, since it is the high density behavior which is most important. Symmetric matter results cannot be used to uniquely constrain neutron matter because of model dependence on the symmetry energy.