We consider mercury porosimetry from the perspective of the statistical thermodynamics of penetration of a nonwetting liquid into a porous material under an external pressure. We apply density functional theory to a lattice gas model of the system. and use this to compute intrusion/extrusion curves. We focus on the specific example of a Vycor glass and show that essential features of mercury porosimetry experiments can be modeled in this way. The lattice model exhibits a symmetry that provides a direct relationship between intrusion/extrusion curves for a nonwetting fluid and adsorption/desorption isotherms for a wetting fluid. This relationship clarifies the status of methods that are used for transforming mercury intrusion/ extrusion curves into gas adsorption/desorption isotherms. We also use Monte Carlo simulations to investigate the nature of the intrusion and extrusion processes.