This paper addresses the formulation of a foveal scale-space and its relation to the scaling property of receptive field sizes with eccentricity. It is shown how the notion of a fovea can be incorporated into conventional scale-space theory leading to a foveal log-polar scale-space. Natural assumptions about uniform treatment of structures over scales and finite processing capacity imply a linear increase of minimum receptive field size as a function of eccentricity. These assumptions are similar to the ones used for deriving linear scale-space theory and the Gaussian receptive field model for an idealized visual front-end.