We obtain the probability distribution for the volume of excursion sets in a three-dimensional Gaussian field, in order to develop the approximation to the cosmic mass function that follows directly from the assumption that the spherical collapse criteria may be applied to field points. We also use this distribution to develop an analytical treatment for the best approach to deriving the cosmic mass function. By comparing both approaches, we conclude that the spherical collapse criteria cannot be applied to field points. We discuss the general conditions for the validity of the analytical derivations of the cosmic mass function and suggest how to remove their main source of uncertainty.